”On Modulation and Detection Schemes for Low-Complexity Impulse Radio UWB Communications

”On Modulation and Detection Schemes for Low-Complexity Impulse Radio UWB Communications
On Modulation and Detection Schemes
for Low-Complexity Impulse Radio
UWB Communications
Muhammad Gufran Khan
Blekinge Institute of Technology doctoral dissertation series
No 2011:15
On Modulation and Detection Schemes
for Low-Complexity Impulse Radio
UWB Communications
Muhammad Gufran Khan
Doctoral Dissertation in
Telecommunications
School of Engineering
Blekinge Institute of Technology
SWEDEN
2011 Muhammad Gufran Khan
School of Engineering
Publisher: Blekinge Institute of Technology,
SE-371 79 Karlskrona, Sweden
Printed by Printfabriken, Karlskrona, Sweden 2011
ISBN: 978-91-7295-222-5
ISSN 1653-2090
urn:nbn:se:bth-00516
Abstract
Due to wealth of advantages offered by short range ultra wideband (UWB) technology,
such as capacity improvement, fading reduction and localization, it has gathered a
considerable attention. Distinct UWB qualities also pose many system design challenges
like difficulties in using digital processing, complex channel estimation and different
propagation characteristics. The main objective of the thesis is to develop and evaluate
efficient modulation and detection schemes for impulse radio (IR) UWB with a focus
on wireless sensor networks characterized by low cost and low power consumption. The
content of the thesis comprises of five parts.
In Part I, a coherent RAKE and non-coherent energy detector (ED) and transmitted
reference (TR) receivers are examined and their bit-error-rate (BER) performance is
evaluated using channels measured in an industrial environment. In specific, selective
RAKE (SRake) and partial RAKE (PRake) for both maximal ratio combining (MRC)
and equal gain combining (EGC) are compared. Based on the analysis and simulation
results, it is concluded that the SRake with the EGC is to be preferred, whereas the
best complexity/performance trade-off is provided by the ED based receivers. Part II
presents several signaling and detection schemes; the proposed schemes are recursive TR
(R-TR), dual-doublet TR (DDTR), doublet-shift TR (DSTR) and binary pulse position
modulation (BPPM)/DSTR. Analysis and simulations verify that the proposed schemes
may be preferred over the conventional TR in terms of BER, energy efficiency and/or
implementation complexity.
Part III presents a non-coherent kurtosis detector (KD) and a fourth-order detector
(FD), which can discriminate between Gaussian noise and non-Gaussian IR-UWB signals by directly estimating the fourth-order moment of the received signal. Empirical
evaluations and simulations using channel measurements conducted in a corridor, an office and a laboratory environment verify that performance of the proposed FD receiver
is slightly better than the ED in the low SNR region and its performance improves
as the SNR increases. Part IV presents a robust weighted ED (WED) in which the
weighting coefficients are estimated adaptively based on the received stochastic data.
Simulation results confirm that performance of the proposed weight estimation method
is close to that of a data-aided (DA) scheme.
Finally, Part V focuses on a multi-user scenario and develops a weighted codemultiplexed TR (WCM-TR) receiver employing the robust adaptive weight estimation
scheme. Secondly, a BPPM/CM-TR UWB system is presented to mitigate inter-frame
interference (IFI) and multi-user interference (MUI) from other asynchronous users.
The BPPM/CM-TR system is 3 dB energy-efficient and improves the BER performance
by mitigating MUI/IFI in the high SNR region, while for the low SNR region and a
single-user scenario, a dual-mode BPPM/CM-TR system is suggested.
v
Preface
This doctoral thesis summarizes my work within the field of signal processing and wireless communications. The focus of the work is on design and performance evaluation of
modulation and detection schemes for low-complexity, low data rate IR-UWB systems.
The research work has been carried out at the Department of Electrical Engineering,
School of Engineering, at Blekinge Institute of Technology, Sweden. The thesis is comprised of an introduction followed by five independent parts:
Part I
Performance Evaluation of Coherent and Non-coherent Receivers for IRUWB Systems using Multipath Channels for Industrial Environments.
Part II
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra
Wideband Communications.
Part III
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio
UWB Signals: Empirical evaluation using Channel Measurements.
Part IV
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB PPM Signals.
Part V
BPPM/Code-Multiplexed Transmitted-Reference and Weighted Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems.
vii
Acknowledgements
My journey towards the Ph.D degree would not have been possible without the
support of many people and I would like to take this opportunity to acknowledge
them for the support and guidance that I have received.
First of all, I would like to express my sincere gratitude to my main supervisor
Professor Ingvar Claesson for his guidance and encouragement during my Ph.D.
studies. His knowledge and expertise have always been a source of inspiration
for me. I am also indebted to my co-supervisor Dr. Jörgen Nordebrg for guiding
me in my research and for always giving me very constructive feedback. I am
particularly thankful to both Ingvar and Jörgen for guiding me in my everyday
life in Sweden.
I am very grateful to my secondary co-supervisor Dr. Benny Sällberg for
his support and valuable feedback particularly in the later stage of my Ph.D.
studies. His expertise, positive attitude and vibrant personality have always
motivated and encouraged me. I would also like to thank Assoc. Professor
Fredrik Tufvesson from Lund University for introducing me to the area of UWB
wireless communications during my M.Sc. thesis and, secondly, for collaborating
and guiding me during my Ph.D. studies.
My great appreciation goes to all my colleagues for making a supportive
and nice atmosphere at the department; special thanks to Professor Abbas Mohammed, Professor Han-Jürgen Zepernick, Dr. Benny Lövström and Mr. Imran
Iqbal. Further, I would like to thank administrative staff at the department for
making administrative issues easy for me.
I have no words to thank my parents for providing me the education that
enabled me to achieve this goal, and for teaching me good values of life; you are
always in my dreams. I am also thankful to my brothers and sisters for their
love, care and affection. Finally, I would like thank my dear wife Kanwal and my
cute daughter Manahal for making my life so beautiful.
Muhammad Gufran Khan
Karlskrona, November 2011
ix
Acronyms and Abbreviations
ADC
ATR
AWGN
BER
BPPM
BPSK
bps
CD
CM-TR
CSI
DA
DD
DDTR
DS
DSTR
ED
EGC
FD
FSR
Hz
IFI
IR
IPI
ISI
KD
LOS
MC-UWB
MIMO
MPC
Analog-to-Digital Converter
Averaged Transmitted Reference
Additive White Gaussian Noise
Bit-Error-Rate
Binary Pulse Position Modulation
Binary Phase Shift Keying
Bits Per Second
Correlation Detector
Code-Multiplexed Transmitted Reference
Channel State Information
Data-Aided
Decision-Directed
Dual-Doublet Transmitted Reference
Direct-Sequence
Doublet-Shift Transmitted Refrence
Energy Detector
Equal Gain Combining
Fourth-order Detector
Frequency-Shifted Reference
Hertz
Inter-Frame Interference
Impulse Radio
Inter-Pulse Interference
Inter-Symbol Interference
Kurtosis Detector
Line-Of-Sight
MultiCarrier UWB
Multiple-Input Multiple-Output
MultiPath Components
xi
xii
Acronyms and Abbreviations
MRC
MUI
NCR
NDA
NOR
ns
OCS
OFDM
OOK
PDF
PDP
Pe
PRake
PSD
R-TR
RX
SNR
SR
SRake
SVD
TH
TR
TX
UWB
WED
WCM-TR
WLAN
WPAN
Maximal Ratio Combining
Multi-User Interference
Non-Coherent Receiver
Non-Data-Aided
Noise-Only Region
Nanosecond
Orthogonal Code Sequence
Orthogonal Frequency Division Multiplexing
On-Off Keying
Probability Distribution Function
Power Delay Profile
Probability of Error
Partial RAKE
Power Spectral Density
Recursive Transmitted Reference
Receiver
Signal-to-Noise Ratio
Signal Region
Selective RAKE
Singular Value Decomposition
Time-Hopping
Transmitted Reference
Transmitter
Ultra Wideband
Weighted Energy Detector
Weighted Code-Multiplexed Transmitted Reference
Wireless Local Area Network
Wireless Personal Area Network
Publications List
Part I: This Part is based on the following publications:
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Performance
Evaluation of RAKE Receiver for Low Data Rate UWB Systems using Multipath
Channels for Industrial Environments”, Research report, Blekinge Institute of
Technology, 2008, Issue: 4, ISSN: 1103-1581.
Muhammad Gufran Khan, Jörgen Nordberg, Abbas Mohammed, and Ingvar
Claesson, “Performance evaluation of RAKE receiver for UWB systems using
measured channels in industrial environments,” in Proceedings of AusWireless’06,
March 2006, Sydney, Australia.
Part II: This Part is based on the following publications:
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Recursive
Transmitted Reference Receivers for Impulse Radio UWB Systems”, Research
report, Blekinge Institute of Technology, 2008 Issue: 5, ISSN: 1103-1581.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Signaling
and Detection of UWB Signals based on a Dual-Doublet Transmitted Reference
Scheme”, in Proceedings of RVK’08, The twentieth Nordic Conference on Radio
Science and Communications, June 9-11, 2008, Växjö, Sweden.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Detection
of Impulse Radio ultra wideband Signals using Recursive Transmitted Reference
Receivers”, in Proceedings of IEEE International Conference on Ultra Wideband,
September 24-26, 2007, Singapore.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “A DoubletShift Transmitted Reference Scheme for ultra wideband Communication Systems”, in Proceedings of IEEE International Conference on Ultra Wideband,
September 24-26, 2007, Singapore.
xiii
xiv
Publications List
Part III: This Part is based on the following publications:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Non-coherent detection of impulse radio UWB signals based on fourth order
statistics”, in Proceedings of IEEE International Conference on UWB, 2009, pp.
824–828, Canada.
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, Fredrik Tufvesson
and Ingvar Claesson, “Non-Coherent Fourth-Order Detector for Impulse Radio
Ultra Wideband Systems: Empirical evaluation using Channel Measurements”,
published in Springer Journal of Wireless Personal Communications, Online First
on November 01, 2011.
Part IV: This Part is based on the following publication:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Robust Weighted Non-Coherent Receiver for Impulse Radio UWB PPM
Signals” IEEE Journal of Communications Letters, vol. 15, no. 6, pp. 614-616,
June 2011
Part V: This Part is based on the following publication:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Energy Efficient Binary PPM/Code-Multiplexed Transmitted-Reference
Multi-user UWB System, in Proceeding of IEEE International Conference on
UWB, 2011, pp. 615–619, Bologona, Italy.
Other publications in conjunction with the thesis:
Muhammad Gufran Khan, Asim A. Ashraf, Johan Karedal, Fredrik Tufvesson,
and Andreas F. Molisch, “Measurements and Analysis of UWB Channels in Industrial Environments,” in Proceedings of Wireless Personal Multimedia Communications (WPMC), Sept. 2005, Aalborg, Denmark.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “An Energyefficient Signaling and Detection Scheme for Transmitted Reference UWB Systems”, in Proceedings of INCC’08 International Networking and Communications
Conference, May 1-4, 2008, LUMS, Lahore, Pakistan.
Contents
Abstract
v
Preface
vii
Acknowledgements
ix
Acronyms and Abbreviations
xi
Publications List
xiii
Contents
xv
Introduction
1
Wireless Communication System Overview
2
Ultra Wideband (UWB) Overview . . . . .
3
Types of UWB System . . . . . . . . . . . .
4
Characteristics of UWB Channels . . . . . .
5
IR-UWB Receivers . . . . . . . . . . . . . .
6
Motivation and Scope . . . . . . . . . . . .
7
Author’s Contributions . . . . . . . . . . . .
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I Performance Evaluation of Coherent and Non-coherent
Receivers for IR-UWB Systems using Multipath Channels for Industrial Environments
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Introduction . . . . . . . . . .
System Model . . . . . . . . .
UWB Channel . . . . . . . .
RAKE Receiver . . . . . . . .
Conventional TR Receiver . .
Conventional Energy Detector
Performance Evaluation . . .
Conclusions . . . . . . . . . .
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5
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xvi
CONTENTS
Bibliography
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II Recursive and Doublet-Based Transmitted Reference Schemes
for Ultra Wideband Communications
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1
2
3
4
5
6
7
Introduction . . . . . . . . . . . . . . . .
Recursive Transmitted Reference System
Dual-Doublet TR System . . . . . . . .
Doublet-Shift TR System . . . . . . . .
BPPM/DSTR System . . . . . . . . . .
Performance Evaluation . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . .
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Bibliography
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III Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB Signals: Empirical evaluation
using Channel Measurements
121
1
2
3
4
5
6
Introduction . . . . . . .
System Model . . . . . .
Non-Coherent Detectors
Channel Measurements .
Performance Evaluation
Conclusions . . . . . . .
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Bibliography
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IV Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB PPM Signals
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1
2
3
4
5
6
Introduction . . . . . . . . . .
System Model . . . . . . . .
Weighted ED (WED) . . . .
Weight Estimation for WED
Performance Evaluation . . .
Conclusions . . . . . . . . . .
Bibliography
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CONTENTS
xvii
V Weighted Code-Multiplexed Transmitted-Reference and
BPPM/Code-Multiplexed Transmitted-Reference Multiuser UWB Systems
169
1
2
3
4
5
6
7
Introduction . . . . . . . . . . . . . . . . .
CM-TR UWB System . . . . . . . . . . .
Weighted CM-TR UWB System . . . . .
BPPM/CM-TR UWB System . . . . . . .
Dual-Mode BPPM/CM-TR UWB System
Performance Evaluation . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . .
Bibliography
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Introduction
Since the advent of wireless communication era, the demand and deployment
of wireless communication networks has increased manyfold, especially in the
last decade. Beginning with Guglielmo Marconi’s pioneering work in 1890s, the
methods and technologies to communicate wirelessly have also evolved to meet
demands and requirements of the users. The emerging technologies played a
major role in the exponential growth of mobile cellular communications by providing higher data rates and improved quality of service (QoS). Due to these
enabling technologies coupled with advances in electronic circuit fabrication, a
wide range of application areas employing wireless communications have observed
similar trends in growth, such as satellite communications, radioastronomy, wireless local area networks (WLANs), wireless personal area networks (WPANs) and
wireless sensor networks.
Currently, fourth generation (4G) mobile communication networks providing
broadband solution are being deployed throughout the world. To ensure long
term competitiveness of mobile communication networks, a 4G access technology,
termed as Long Term Evolution (LTE), targets reduced latency, higher user data
rates, improved system capacity and coverage, and reduced cost for the operator
[1]. The next major evolution of the LTE, called LTE-Advanced, defines a set
of performance targets, which include extended bandwidth support of up to 100
MHz and peak data rates in excess of 1 Gbps in the downlink for low mobility [2].
In addition, WLANs, also referred to as Wi-Fi, based on IEEE 802.11b standard
with a data rate about 11 Mbps have also been deployed widely in recent years for
in-home networking. IEEE 802.11a/g WLANs have increased the data rate up
to 54 Mbps and IEEE 802.11n next-generation WLANs are intended to achieve
data rates over 100 Mbps over a range of 70 m [5].
The short range wireless communication technologies for connectivity in office, home and other indoor environments have also seen tremendous interest and
growth. It is envisioned that WPANs, also known as piconets, based on IEEE
802.15.3 standard will provide high data rate communications over a distance of
10 m to support multimedia applications. On the other hand, IEEE 802.15.4
group deals with low data rate WPANs and sensor networks having low complexity and long battery life; it has developed standards for both physical and
data-link layers.
Bluetooth is a widely proliferated short range WPAN technology (IEEE 802.15.1
standard), which provides low power, short range communications between both
1
2
Introduction
consumer electronics and portable devices. It operates in the unlicensed industrial, scientific and medical (ISM) band at 2.4 to 2.485 GHz. The flexible connectivity via adhoc networks and an environment “without wires” is achieved;
however, it can support only medium data rate applications (about 1 Mbps).
According to the specifications, the range of Bluetooth devices is a minimum
distance of 10 m, but it can be increased by the manufacturer depending upon
the application. Zigbee technology (IEEE 802.15.4 standard) also operates in
the ISM band and targets to provide very low data rate (20 − 250 Kbps), over
longer distances of between 10 − 75 m [6]. Zigbee is intended to achieve simpler,
low power and low cost wireless networking in comparison to the other WPAN
technologies, such as Bluetooth.
The physical layer of evolving future generation mobile cellular networks is
based on orthogonal frequency division multiplexing (OFDM) and multiple-input
multiple-output (MIMO) techniques [3, 4]. OFDM is a modulation scheme that
exploits frequency diversity inherent in a wideband channel to achieve robust performance even in severe multipath fading channel [4]. MIMO techniques permit
severalfold increase in achieved data rates and spectral efficiency through spatial
processing and the use of multiple transmit and receive antennas [5]. The design of physical layer of future high-performance WLANs is also based on MIMO
and OFDM [5], while Bluetooth and Zigbee technology are implemented using
frequency-hopping (FH) and direct-sequence (DS) spread spectrum techniques,
respectively.
Ultra wideband (UWB) radio is another promising technology, which has
emerged as a transmission technique for applications requiring either high bit
rates over short ranges or low bit rates over medium-to-long ranges [7]. The
approach employed by UWB radio devices is based on sharing already occupied
unlicensed spectrum resources by means of the overlay principle or coexistence [6].
The main idea of UWB radio is to transmit very low power signal spread across
a wide bandwidth, which results in a noise-like signal of very low power spectral
density. Additionally, UWB signal qualities, such as high time-domain resolution,
improved channel capacity and multiple access capability, have made UWB an
attractive physical layer technology for WPANs and wireless sensor networks.
In conventional time-domain UWB system, called impulse radio (IR), the
information is transmitted using a train of short, often subnanosecond, pulses
using, e.g., pulse position modulation (PPM) or pulse amplitude modulation
(PAM), whereas signal detection is accomplished using either a coherent or a
non-coherent receiver. As IR-UWB systems are intended for multi-user scenarios, it is important to avoid collisions between the signals of different users using
appropriate multiple access techniques. By far the most commonly used multiple
access methods to provide robustness against multi-user interference (MUI) at
the physical layer of IR-UWB system are time-hopping (TH) and direct-sequence
3
(DS). Though frequency-domain implementations of UWB system are also popular in the context of high data rate systems, time-domain implementation of
UWB system is considered herein. The objective of the research that this thesis accounts for is to investigate and develop efficient modulation and detection
schemes for low data rate IR-UWB systems.
The introduction part is intended to briefly describe an overview of the UWB
systems and to facilitate the understanding of the scope of this thesis. In Section
1, a general overview of a wireless communication system is given. Section 2
provides background and characteristics of UWB systems. In Section 3, types and
overview of UWB systems is given briefly. The characteristics of UWB channels
and IR-UWB receivers are discussed briefly in Section 4 and 5, respectively.
Finally, the thesis motivation and scope is presented in Section 6 and the main
contributions are summarized in Section 7.
1
Wireless Communication System Overview
A simplified overview and block diagram of a typical wireless communication
system is given in Fig. 1, where TX and RX stand for the transmitter and receiver, respectively. On the transmitter side, the source originates a message,
e.g., a speech or video signal, which is converted to digital data or binary information bits. Typically, the binary information bits are encoded to remove the
redundancy in the transmitted signal for efficient transmission, this is also called
source coding. Additionally, the reliable transmission over a noisy wireless channel is achieved by introducing controlled redundancy in the signal, called channel
coding. In the subsequent step, the bit to symbol mapping is performed, where
each symbol can be regarded as a member of a finite alphabet set containing M
members. For M > 2, each symbol is made up of a sequence of two or more bits,
referred to as M −ary symbol. The bit stream is converted to baseband waveforms
using a pulse shaping filter, which assigns a particular bandwidth to the signal.
Finally, if the medium supports only passband signals, the bandpass modulation
is employed to transmit the baseband pulse-shaped signals on a particular carrier
frequency.
The relationship between the received signal and the transmitted signal of a
communication system is typically referred to as the channel [8]. The transmitted
signal is impacted and corrupted by the the channel characteristics, random noise
and antenna effects. On the receiver side, the signal received by the antenna is
demodulated by frequency down-conversion to extract the baseband signal. After
demodulation, an equalizer is generally used to mitigate the distortion effects
introduced by the channel. Equalization can be described as a filtering operation
to recover the transmitted signal degraded by the channel. The detection of the
4
Introduction
TX
Source
Coding
Bit to Symbol
Mapping
Pulse
Shaping
Modulation
RX
Destination
Decoding
Symbol to Bit
Mapping
Detection
Equalization
Demodulation
Figure 1: Block diagram representation of a typical wireless communication system.
recovered signal is performed subsequently and the detected symbols are mapped
back to bits and decoded to achieve the binary source signal.
In wireless systems, since the channel has a major impact on the system performance, thorough understanding of the wireless channel characteristics is vital.
The transmission of a signal over a wireless channel results in multipath components (MPCs) that arrive at the receiver with different attenuations and delays
after reflections from different objects, as illustrated in Fig. 2. As a result, the
amplitude fluctuations in the received signal occur due to the time-varying nature
of the channel impulse response, this phenomena is called multipath propagation
and leads to signal distortion and fading . Due to the random nature of wireless channels, as accurate as possible channel modeling and analysis is crucial for
system design and evaluation. The channel modeling is typically performed in
a stochastic fashion, based on the channel measurement data obtained from a
specific environment.
Generally, employing stochastic channel modeling, the envelope of the timevarying channel impulse response is modeled as Rayleigh distributed if the channel impulse response can be modeled as a zero-mean complex-valued Gaussian
process [13]. This happens when a line-of-sight (LOS) component is not present
in the received signal, it is referred to as non-LOS (NLOS) condition; this kind
of channel is called a Rayleigh fading channel. However, if a LOS component
exists in the received signal, the channel is called a Rician fading channel and its
impulse response can be modeled as a non-zero mean complex valued Gaussian
process [13]. The Rician fading is often described in terms of a Rician factor
which is defined as the ratio between the deterministic signal power and the variance of the multipath [14]. As the dominant path decreases in amplitude, the
Rician distribution degenerates to a Rayleigh distribution [14]. Nakagami fading,
which is related to the Nakagami distribution, is also commonly used to model
5
TX
Multipath
Propagation
RX
Figure 2: An illustration of multipath propagation over a wireless channel.
the amplitude variations in the received signal [8]. The Nakagami distribution is
a generalized distribution and for specific values of its shape parameter, it boils
down to a Rician or a Rayleigh distribution.
Though signal distortion due to multipath fading is a major problem, there
are also other limiting factors in wireless communications such as intersymbol
interference (ISI), co-channel interference (CCI), multi-user interference (MUI)
and noise. ISI is caused by long channel delay spread, while CCI usually occurs
due to overcrowding of spectrum or poor planning in terms of frequency reuse.
MUI is always present if multiple users access the medium, however effective
multiple access techniques have been developed to combat it. To alleviate these
performance limiting factors, the receiver structures need to incorporate channel
equalization, interference mitigation and noise reduction techniques to recover
the original signal.
2
2.1
Ultra Wideband (UWB) Overview
Brief History
Despite the fairly recent research interest and enthusiasm about UWB technology,
its history dates back to Marconi’s first experiments using spark-gap transmitter,
which may be considered based on pulse-based signaling. Later, in 1963, Ross
introduced the concept of an impulse signal in order to describe the response of
a linear time invariant system. However, the interest in continuous-wave systems
dominated the field due to limitations in technology concerning the implementation aspects of pulse-based systems. Due to this reason, the early applications
of UWB technology were primarily related to radar, driven by the promise of
6
Introduction
UWB EIRP Emission Level [dBm/MHz]
−30
6
−40
8.5
1.99
−50
3.1
10.6
−60
−70
0.96
1.61
−80
FCC Indoor
−90
−100
0
ECC
2
4
6
8
10
12
Frequency [GHz]
Figure 3: FCC and ECC allocated emission limits.
fine-range resolution that comes with large bandwidth [15]. Beginning in the
late 1980’s, small companies specializing in UWB engaged in basic research and
development on communications and positioning systems [15]. In 1993, Scholtz
demonstrated the potential of IR-UWB to the academic community [16] and later,
Win et. al. published their pioneering work on time-hopping (TH) IR-UWB for
multi-user communications [17–19]. In April 2002, after extensive commentary
from industry, the US frequency regulator, the Federal Communications Commission (FCC), issued its first report and order on UWB technology, thereby
providing regulations to support deployment of UWB radio systems [15,20]. The
FCC regulations classify UWB applications into several categories with different emission regulations in each case [15]. The PSD limit of UWB systems is
−41.3 dBm/MHz within 3.1 GHz to 10.6 GHz range. In the subsequent years,
the regulation activities started in Asia and Europe to determine suitable frequency bands and PSD limits for UWB applications. The European regulatory organization, the Electronic Communication Commission (ECC), proposed
a spectral mask in 2006, allowing UWB transmissions between 6 − 8.5 GHz with
a PSD limit of −41.3 dBm/MHz. The spectral masks assigned by the FCC and
the ECC are shown in Fig. 3.
2.2
Definition of UWB
According to the FCC definition, UWB characterizes transmission systems with
an instantaneous spectral occupancy of 500 MHz or a fractional bandwidth of
7
PSD [dB]
Narrowband
UWB
−10 [dB]
fL
fC
Frequency [Hz]
fH
Figure 4: Comparison of the fractional bandwidth of a narrowband and ultra
wideband communication system [8].
more than 20% [21]. The fractional bandwidth is defined as
fBW =
fH − fL
,
fC
(1)
where fC = (fH + fL )/2 with fH being the upper frequency of the −10 dB
emission point, and fL the lower frequency of the −10 dB emission point [21],
as shown in Fig. 4. At the physical layer level, UWB communication systems
operate by spreading rather small amounts of average effective isotropic radiated
power, always less than 0.56 mW, across a very wide band of frequencies relative
to its center frequency [6].
2.3
Distinguishing Characteristics
The main reason behind the attention given to UWB system is some of its distinguishing characteristics in comparison to existing narrowband systems. These
characteristics are summarized below.
Improved Capacity
Due to the very wide frequency spectrum of UWB systems, the channel capacity
is improved, i.e., according to Shannon’s capacity theorem [15],
C = W log2 (1 + SN R),
(2)
8
Introduction
which illustrates that the channel capacity C of the band-limited additive white
Gaussian noise (AWGN) channel increases linearly with bandwidth W and logarithmically with the signal-to-noise ratio (SNR).
Reduced Fading
The use of signals with GHz bandwidths also means that multipath is resolvable
down to path differential delays on the order of a nanosecond or less, i.e., down
to path length differentials on the order of a foot or less [19]. This significantly
reduces fading effects even in indoor environments [18, 19].
Rich Multipath Diversity
A pulse of width Tp , at the subnanosecond scale, occupies UWB with bandwidth
B ≈ 1/Tp [21]. Such an ultra-short pulse gives rise to multiple resolvable received
pulse copies, and thus, a significant amount of multipath diversity is available at
the receiver [21].
High Resolution
The large signal bandwidth yields a distance resolution between communicating
devices within a few centimeters, which enables an unprecedented localization
capability [22].
Low Power Spectral Density
Extremely low average power levels and excessive signal bandwidth yield PSDs
in the order of some tens of nW/MHz [22].
2.4
Applications and Standardization
In the context of imaging and radar, the traditional applications of UWB include
through-wall imaging, medical imaging, vehicular radar and ground-penetrating
radar etc. [20]. In addition, the capability to highly resolve multipath combined
with the ability to penetrate through materials makes UWB technology viable
for high-quality, fully mobile short range indoor radio systems [19]. For communication purposes, applications of UWB can be broadly categorized into high and
low data rates types depending on the standardization efforts.
The high data rate applications of UWB, according to IEEE 802.15.3a group,
are short range (about 10 m) wireless personal area networks (WPANs). Two
competing proposals to become the physical layer standard for these WPANs were
multiband-OFDM and direct-sequence UWB. Though a single standard was not
endorsed by IEEE 802.15.3a group, multiband proposal is widely adopted by the
9
industry. WPANs based on this standard are envisioned for wireless connectivity
across a wide range of consumer electronics, communications and computing
devices.
UWB radios can also trade a reduced information rate for increased link
range, potentially combined with accurate location tracking capabilities, offering an operational mode defined here as low data rate and location tracking [6].
A multitude of applications for medium to long distances (about 100 m) with
relatively low data rates and location tracking capability are identified by IEEE
802.15.4a standardization group. These applications include e.g., sensor, positioning and identification network (SPIN), wireless body area network (WBAN)
etc. A SPIN is a system characterized by a high density (e.g., hundreds per
floor) of devices (intelligent sensors or tags) in industrial factories or warehouses
transmitting low-rate data combined with position information (e.g., data rate
greater than several tens of kilobits per second and position accuracy well within
1 m) [6]. In addition, sensor networks may be used for control of home appliances
and in search-and-rescue applications for avalanche or earthquake victims.
3
Types of UWB System
In general, UWB systems are classified as multicarrier UWB (MC-UWB) and
impulse radio UWB (IR-UWB), an introduction of both systems is given briefly
in the following subsections.
3.1
MC-UWB System
MC systems use properly spaced simultaneous carriers for transmission by splitting a single high data rate stream into multiple parallel low data rate streams;
this approach minimizes ISI and achieves spectral efficiency [8]. The transmitted
MC-UWB signal of the k th user is written as [8]
(k)
sMC-UWB (t) =
∞ Q−1
X
X (k)
p
Ep
bi,q p(t − iTs )exp j2πqf0 (t − iTp ) ,
(3)
i=−∞ q=0
where Tp is the pulse duration, Q is the number of subcarriers, f0 is the funda(k)
mental frequency (f0 = 1/Tp ) and bi,q is the k th user symbol that is transmitted
in the ith transmission interval over the q th subcarrier.
OFDM is a special case of MC transmission that permits subcarriers to overlap in frequency without mutual interference and hence spectral efficiency is increased [8]. The core idea of multiband-OFDM for high data rate UWB systems is to divide the available spectrum into subbands with a minimum subband
bandwidth of 500 MHz, where the subbands are not necessarily adjacent, and
10
Introduction
Frequency
Guard interval
Cyclic prefix
Channel 3
Symbol
Channel 2
Channel 1
One period
Time
Figure 5: An example of transmitted OFDM symbols using time-frequency code
of length 3, on three subbands, in a multiband-OFDM system.
each OFDM symbol is transmitted using orthogonal sub-carriers which are timeinterleaved across subbands using time-frequency codes [8,23]. This approach not
only provides high throughput, frequency diversity and multiple access but also
flexibility in shaping the spectrum [23]. Fig. 5 shows an example of a transmitted
sequence of OFDM symbols in a multiband-OFDM system. A cyclic prefix and
a guard interval are inserted to the beginning and end of each OFDM symbol,
respectively. The guard interval ensures sufficient time for TX and RX to to
switch between different frequencies, whereas cyclic prefix provides robustness
against multipath dispersion [23].
3.2
IR-UWB System
IR communicates with baseband pulses of very short duration, typically on the
order of a nanosecond, thereby spreading the energy of the radio signal very thinly
from near dc to a few GHz [24]. Typically, each symbol consists of multiple frames
which are subdivided into multiple chips, and one pulse per frame is transmitted
within the duration of a chip. Multiple pulses are associated with a single symbol to obtain a sufficient energy per symbol while maintaining sufficiently low
PSD [8].
Due to baseband (carrier-less) nature of IR signals, frequency up-conversion
and down-conversion is not usually required in the transceiver. This reduction in
the complexity, coupled with saving in the power consumption of the transceiver,
makes IR-UWB suitable for wireless sensor networks. The main aspects of IRUWB system such as pulse shapes, modulation and multiple access schemes are
discussed in the following subsections.
11
1
0.8
0.6
Gaussian pulse
Gaussian monocycle
Gaussian doublet
Amplitude
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time [ns]
Figure 6: Waveforms of the Gaussian pulse, Gaussian monocycle and Gaussian
doublet.
UWB Pulse Shape
Generally adopted and by far the most discussed pulse shapes for UWB communications are the Gaussian pulse, the first derivative of the Gaussian pulse (referred
to as Gaussian monocycle) and the second derivative of the Gaussian pulse (referred to as Gaussian doublet) [21], depicted in Fig. 6. The Gaussian monocycle
pulses are typically obtained by directly driving an antenna with short-duration
electrical signals (assumed to be Gaussian) [1,8]. The importance of these pulses
lays in the fact that, beside being easier to generate, the derivatives of the Gaussian pulse may be used in shaping the spectrum of signal and, in addition, have
zero PSD at dc. The second derivative of a Gaussian function is described by [19],
t 2 −2π( τt )2
m
p(t) = 1 − 4π( ) e
,
τm
(4)
where τm is the shape factor; reducing the value of τm shortens the pulse, which
in turn enlarges the bandwidth of the transmitted signal [8]. Several other pulse
shapes with different spectral characteristics have been proposed in the literature
such as the Laplacian pulse [26] and Hermite pulses [27].
12
Introduction
Modulation Schemes
The commonly used modulations for IR-UWB are antipodal pulse amplitude
modulation (A-PAM), also called binary phase shift keying (BPSK), binary pulse
position modulation (BPPM), on-off keying (OOK) and frequency shift keying
(FSK). Transmitted reference (TR) is another modulation which has been suggested for IR-UWB [28, 29]. Since higher order modulations e.g., M −ary PPM
and M −ary PAM are generally used if higher data rates are desired, these modulations are not preferred in low power and low-complexity UWB systems.
For BPSK, the two possible signals generated by the transmitter corresponding to binary information symbol b ∈ {−1, 1} are
sBPSK (t) =
p
− pEp p(t)
Ep p(t)
if
if
b = −1
b= 1
(5)
where p(t) is the energy-normalized pulse and Ep is the energy per pulse.
The two possible signals generated by the transmitter for BPPM are
sBPPM (t) =
p
pEp p(t)
Ep p(t − TBP P M )
if
if
b = −1
b= 1
(6)
where TBP P M is the time shift.
The transmitted signal for OOK modulation can be written in a similar manner as
if
b = −1
p0
sOOK (t) =
(7)
Ep p(t)
if
b= 1
In TR modulation, a reference and a data-modulated signal separated by
a fixed delay Td are transmitted together. TR modulation is mostly used in
conjunction with BPSK, and the two possible signals generated by the transmitter
of TR BPSK are written as
p if
b = −1
pEp p(t) − p(t − Td )
sTR (t) =
(8)
Ep p(t) + p(t − Td )
if
b= 1
For FSK, the two possible signals generated by the transmitter are
sFSK (t) =
p
pEp p(t)cos(2πfc1 t)
Ep p(t)cos(2πfc2 t)
if
if
b = −1
b= 1
(9)
where p(t) is modulated with two sinusoidal carriers, which shift the spectrum of
the baseband pulse to center frequency fc1 or fc2 depending on the bit value.
13
Modulated Pulse
Position
Symbol i = 0 ;
Unmodulated Pulse
Position
Symbol i = 1 ;
Bit b0 = 1
Pulse
Bit b1 = −1
(a)
Tf
Tc
Ts
2Ts
(b)
Td
Ts
2Ts
(c)
Ts
Tc
2Ts
Figure 7: An example of transmitted sequences for two symbols, if b0 = 1 and
b1 = −1, (a) TH BPSK system, where Nh = 8 and Nf = 4 and hopping pattern
of the pulses is shown according to TH code of the user cT H = [0, 2, 6, 3]. (b)
TH TR system, where Nh = 8 and Nf = 4 and hopping pattern of the pulses is
shown according to TH code of the user cT H = [0, 3, 1, 2]. (c) DS UWB system,
where Nc = 7, Ts = 7Tc and DS code of the user is cDS = [1, −1, −1, 1, 1, −1, 1]
.
14
Introduction
Multiple Access Schemes
In multiuser IR-UWB systems, multiple access capability is usually enabled with
time-hopping (TH) and direct-sequence (DS) UWB. The TH and DS spreading
not only provide multiple access but also smooth the transmit PSD [21]. The
signal models for TH and DS IR-UWB systems are given as follows.
Time-hopping (TH) IR-UWB:
In TH IR-UWB, each pulse is positioned within each frame duration according
to a user-specific TH sequence [21]. The transmitted TH BPSK signal of the k th
user is written as [30]
(k)
sTH BPSK (t)
f −1
∞ NX
X
p
(k)
(k)
= Ep
bi p(t − iTs − jTf − cT H,j Tc ).
(10)
i=−∞ j=0
In a similar manner, the transmitted TH BPPM and TH TR signal are written,
respectively, as [30]
(k)
sTH
BPPM (t) =
∞ NX
f −1
X
p
(k)
Ep
p(t − iTs − jTf − cT H,j Tc − di TBP P M ), (11)
i=−∞ j=0
(k)
sTH
TR (t)
=
f −1 h
∞ NX
X
p
(k)
Ep
p(t − iTs − jTf − cT H,j Tc )
i=−∞ j=0
+
(k)
bi p(t
i
(k)
− iTs − jTf − cT H,j Tc − Td ) ,
(12)
where, in Eqs. (10), (11) and (12), Tf is the frame duration, Tc is the chip
(k)
duration (≥ pulse width) and Nf is the number of frames. In addition, cT H,j
(k)
is the pseudo-random TH sequence in the range 0 ≤ cT H,j ≤ Nh − 1, where
Nh is the number of hops. For BPPM, each frame is divided in two halves and
the position of the pulse in one of these two halves is determined depending on
di ∈ {0, 1}, which is evaluated from the bit bi as di = (bi + 1)/2. Fig. 7 (a)
and (b) show examples of transmitted sequences for the TH BPSK and TH TR
systems, respectively.
Direct-Sequence (DS) IR-UWB:
In DS UWB impulse radio, each information symbol is direct-sequence modulated using a spread spectrum pseudo-noise (PN) code specific to each user. As
15
these PN codes are orthogonal and known at the transmitter and the receiver, the
multiple-access interference is negligible. The transmitted DS UWB modulated
signal is written as [31]
(k)
sDS UWB (t) =
NX
∞
c −1
X
p
(k)
(k)
Ep
bi
cDS,j p(t − iTf − jTc ),
i=−∞
(13)
j=0
where Tc is the chip duration, Nc is the number of chips per information bit
(k)
(k)
bi ∈ {−1, 1}, Ts = Tf = Nc Tc , cDS,j ∈ {−1, 1} is the spread spectrum code
of user k. Fig. 7 (c) shows an example of transmitted sequences for DS UWB
system.
4
Characteristics of UWB Channels
Previously, most of the work has been performed in the area of narrowband channel modeling and characterization, whereas channel modeling for UWB systems
is relatively a new area [10]. In [32–34], UWB channel measurement results are
presented and channel models are proposed based on the results. The narrowband channel models can not be generalized to UWB channels due to following
important differences, as described in [10, 35]:
• Each multipath component of UWB signal can lead to delay dispersion
by itself, due to the frequency-selective nature of reflection and diffraction
coefficients. This effect is especially important for systems with a large
relative bandwidth.
• The UWB signals are received with excellent delay resolution. Therefore, it
often happens that only a few multipath components make up one resolvable
MPC. That implies that the central limit theorem is not fulfilled anymore,
and the amplitude statistics of such a resolvable MPC are not complex
Gaussian anymore. Similarly, there is an appreciable probability that areas
of “no energy” can exist during which no significant amount of energy is
arriving at the receiver.
• The statistics of arrival times of multipath components strongly vary with
the bandwidth, as well as with the center frequency of the UWB signal.
• Due to wide frequency band, the propagation signals experience frequency
dependent effects. Specifically, the path loss is described as a function of
frequency as well as of distance when the relative bandwidth is large.
16
4.1
Introduction
IEEE 802.15.4a UWB Channel Model
The IEEE 802.15.4a group has proposed a channel model (CM) for sensor networks and similar devices with data rates between 1 Kbps and several Mbps; it
covers indoor residential LOS (CM1) and NLOS (CM2), indoor office LOS (CM3)
and NLOS (CM4), outdoor LOS (CM5) and NLOS (CM6), and industrial LOS
(CM7) and NLOS (CM8) scenarios [36]. Since IEEE802.15.4a channel model is
mainly used for performance evaluation of IR-UWB systems in the subsequent
parts, key features of the channel model are discussed in the following subsections.
Path loss and shadowing
The large-scale channel modeling involves modeling the signal attenuation with
distance and is generally referred to as path loss [8]. The path loss in a narrowband system is conventionally defined as [36]
P L(d) =
E{PRX (d, fc )}
,
PT X
(14)
where PT X and PRX are the transmit and receive power, respectively, d is the
distance between transmitter and receiver, fc is the center frequency and the
expectation E{·} is taken over an area that is large enough to allow averaging out
of shadowing as well as the small-scale fading. Due to the frequency dependence
of propagation effects in an UWB channel, the wideband path loss is a function
of frequency as well as of distance [36]. Thus, a frequency-dependent path loss is
defined as [36]
n Z f +∆f /2
o
2
P L(d, f ) = E
|H(f˜, d)| df˜ ,
(15)
f −∆f /2
where H(f˜, d) is the transfer function from transmitting antenna connector to
the receiving antenna connector, and ∆f is chosen small enough so that diffraction coefficients, dielectric constants etc., can be considered constant within that
bandwidth. The total path loss is obtained by integrating over the whole bandwidth of interest [36].
It is assumed that the path loss, as a function of frequency and distance, can
be written as a product of the terms [36]
P L(d, f ) = P L(f )P L(d).
The frequency dependence of the path loss is given as [37, 38]
p
P L(f ) ∝ f −κ ,
where κ is the frequency dependence factor.
(16)
(17)
17
The variation in the received signal power about its mean value is typically
termed “shadowing” [8]. The distance dependence of the path loss (averaged over
small-scale fading) in dB is written as [36]
P L(d) = P Lo + 10n log10
d
+ S,
do
(18)
where S accounts for shadowing and is a Gaussian distributed random variable
with zero mean and the standard deviation σs , and the reference distance do is
set to 1 m, P Lo is the path loss at the reference distance, and n is the path loss
exponent. The path loss exponent depends on the environment and on whether
a LOS connection exists between the transmitter and receiver or not [36].
Power delay profile
A power delay profile (PDP) relates the power of received signal with the delay
experienced by the multipath component and is defined as the square magnitudes
of impulse response of the signal averaged over a local area as [14]
P DP (τ ) = |h(t; τ )|2 ,
(19)
where |h(t; τ )| is the absolute value of impulse response of the signal. In this
model, the impulse response (in complex baseband) is based on the well-known
Saleh-Valenzuela (SV) model and is given, in general, as [39]
hdiscr (t) =
L−1
X K−1
X
l=0 k=0
αk,l exp(jφk,l )δ(t − Tl − τk,l ),
(20)
where αk,l is the tap weight of the k th component (path) in the lth cluster, Tl is the
arrival time of the lth cluster and τk,l is the delay of the k th MPC relative to the
lth cluster arrival time Tl , see Fig. 8. The phases φk,l are uniformly distributed,
i.e., for a bandpass system, the phase is taken as a uniformly random variable in
the range from 0 to 2π [36].
The number of clusters is an important parameter of the model and is assumed
to be Poisson-distributed; the distribution of cluster arrival times are given by
a Poisson process and the ray arrival times are modeled with mixtures of two
Poisson processes [36]. In addition,the power delay profile (the mean power of
different paths) is modeled as exponential within each cluster and the mean
(over cluster-shadowing) mean (over small-scale fading) energy of the each cluster
follows in general an exponential decay [36]. Finally, the cluster decay rates are
defined to depend linearly on the arrival time of the cluster [36].
18
Introduction
Amplitude
Clusters of MPCs
Cluster Decay
Ray Decay
Delay
Figure 8: Principle of Saleh-Valenzuela (SV) model.
Delay dispersion
Delay dispersion is defined to occur when the channel impulse response lasts for a
finite amount of time or if the channel is frequency selective [10]. Delay dispersion
in multipath channels is characterized by two important parameters, mean excess
delay and root mean square (rms) delay spread [10].
Excess delay is the relative delay of the k th received multipath component as
compared to the first arriving path, and is denoted as τk [14]. Mean excess delay,
also referred to as mean delay spread, is defined as the first moment of the PDP
given by [14]
R∞
P DP (τ )τ dτ
.
(21)
τm = R−∞
∞
P DP (τ )dτ
−∞
The rms delay spread is defined as the second central moment of the PDP given
by [36]
v
!2
uR ∞
R∞
u
P DP (τ )τ 2 dτ
P DP (τ )τ dτ
−∞
−∞
t
R∞
τrms =
− R∞
.
(22)
P DP (τ )dτ
P DP (τ )dτ
−∞
−∞
The delay spread depends on the distance, however, this effect is usually neglected
in the channel model for simplicity [36].
Small scale fading
The rapid fluctuations of the received signal strength over very short travel distances (on the order of few wavelengths) or short time durations (on the order
of seconds) is called small-scale fading [14]. Based on the observations that
19
Matched Filter
Energy
Received Signal
Integrator
ADC
Baseband
Processing
& Decision
Template
Generator
Timing/
Synchronization
Figure 9: Block diagram of a coherent correlation detector (CD) receiver.
Nakagami distribution offers a good fit to the fading of received amplitude components, the distribution of small scale amplitudes is modeled as Nakagami distributed [36], i.e.,
pdf (x) =
m
m
2
( )m x2m−1 exp(− x2 ),
Γ(m) Ω
Ω
(23)
where m ≥ 1/2 is the Nakagami m−factor, Γ(m) is the gamma function, and Ω
is the mean-square value of the amplitude i.e., mean power. The m−parameter
is modeled as a lognormally distributed random variable, logarithm of which has
a mean µm and a standard deviation σm [36]. Both of these values can have a
delay dependence [36]
µm (τ )
σm (τ )
= mo − km τ,
= m
bo − b
km τ.
(24)
(25)
For the first component of each cluster, the Nakagami factor is assumed to be
deterministic and independent of delay, i.e., m = m̃o [36].
5
IR-UWB Receivers
The coherent and non-coherent IR-UWB receivers commonly used for the detection of a distorted and noisy received signal are discussed briefly in the following
subsections.
20
5.1
Introduction
Coherent Receivers
Coherent receivers may be classified into simple correlation detector (CD) and
RAKE receiver for coherent demodulation.
Correlation Detector (CD)
The coherent CD receiver is also known as a matched filter receiver and has been
used in narrowband communication systems for several decades [8]. The CD
receiver makes use of a locally generated reference template and an integrator
in order to perform correlation with the received signal [11], as also depicted in
Fig. 9. The output of the multiplier of the correlator is a function of how well the
template waveform matches the received signal waveform in time and shape [8].
However, in order to perfectly match the received signal with a locally generated
reference template, knowledge of the channel parameters is required. In the absence of channel estimate, a sub-optimal pulse-matched CD can be implemented
under the assumption that the transmitted pulse shape is not modified by the
channel.
RAKE Receiver
RAKE receiver, a name stemming from the function of a garden rake, may be
used in any kind of spread spectrum communication system to accumulate the
energy in the significant multipath components [8]. The use of a RAKE receiver is
also common in UWB systems to collect the rich multipath diversity available at
the receiver. The coherent RAKE receivers take advantage of the time-diversity
provided by an UWB multipath channel. This scheme was invented by Price and
Green [40] in 1958. It consists of a bank of matched filters (also called fingers)
with each finger matched to a different replica of the same transmitted signal,
see Fig. 10. The outputs of the fingers are appropriately weighted and combined
to reap the benefits of multipath diversity [11].
5.2
Non-Coherent Receivers
The non-coherent receivers have gathered a lot of interest since they do not
generally require channel estimation. Non-coherent receivers for UWB may be
categorized into popular energy detection and transmitted reference based receivers.
Energy Detector (ED)
An energy detector collects the energy of the received signal within a specified
frequency band using a bandpass filter, a square-law device and an integrator, see
21
Matched Filter 1
ADC
Matched Filter 2
ADC
Received Signal
Combiner
Matched Filter K
Decision
ADC
Path Searcher
Timing/
Synchronization
Figure 10: Block diagram of a RAKE receiver with K fingers.
Fig. 11. The optimum non-coherent receiver requires a front-end filter matched
to the UWB channel but this implementation would destroy the complexity advantage of non-coherent receiver [43]. Typically, a front-end filter matched to the
transmitted UWB pulse provides a tradeoff between complexity and performance.
Due to the absence of phase information at the detector, PSK modulation can not
be used. Therefore, the most popular non-coherent modulation options for the
ED are OOK and BPPM [46]. FSK can also be used; it requires a non-coherent
receiver with parallel branches for energy detection with each branch having a
bandpass filter centered at one of the modulation frequencies [43].
In OOK based energy detectors, the decisions are made by comparing the
estimated noise energy or signal-plus-noise energy at the output of the integrator with a threshold [46]. In order to avoid the complexity of decision threshold
estimation, BPPM is preferred for energy detection. In case of BPPM, the integration is performed at two different pulse positions and the decision is made by
comparing the received pulse energies at the two positions.
Transmitted Reference (TR) Receiver
A non-coherent receiver in which phase comparison of the two received pulses
is performed prior to the energy integration is called a transmitted reference receiver. A reference and a data-modulated signal separated by a fixed delay is
22
Introduction
Received Signal
Bandpass
Filter
Square-law
Device
Energy
Integrator
ADC
Decision
Timing
Figure 11: Block diagram of a non-coherent energy detector (ED) receiver.
Received Signal
Energy
Bandpass
Filter
Integrator
Delay
ADC
Decision
Timing
Figure 12: Block diagram of a non-coherent transmitted reference (TR) receiver.
transmitted and BPSK is usually used due to phase comparison at the receiver.
As opposed to the ED, the square-law device is replaced by an analog delay line
and a mixer (or multiplier) to compare the signal phase at two time instants corresponding to the delay lag [43], see Fig. 12. The integrator combines the energy
of the signal at the output of the multiplier. This receiver is also called autocorrelation receiver as its signal processing is equivalent to an analog implementation
of an autocorrelation device for a fixed delay lag [12, 43].
Frequency-shifted Reference (FSR) Receiver
The limiting factors in the realization of time-domain TR receivers have motivated the development of a frequency-shifted reference system, which may be
seen as a frequency domain implementation of the TR system. The FSR receiver
obviates the need for an analog delay element in the TR UWB system by utilizing a carrier generator at the receiver [49], see Fig. 13. In an FSR system, the
reference and the data-modulated pulses become orthogonal to each other over a
symbol period Ts by introducing a slight frequency shift of 1/Ts between the two
overlapping pulses [50]. The data-modulated pulse is orthogonal to the reference
pulse but still goes through a nearly equal channel as the frequency shift is well
below the coherence frequency of the channel [49].
23
Received Signal
Bandpass
Filter
Energy
Square-law
Device
Integrator
Carrier
Generator
ADC
Decision
Timing
Figure 13: Block diagram of a non-coherent frequency-shifted reference (FSR)
receiver.
Received Signal
Bandpass
Filter
Energy
Square-law
Device
Integrator
Code
Sequence
ADC
Decision
Timing
Figure 14: Block diagram of a non-coherent code multiplexed TR (CM-TR)
receiver.
Code multiplexed Transmitted Reference (CM-TR) Receiver
In addition to time and frequency domain implementation of a TR system, a
newer concept is introduced, referred to as code multiplexed TR, in which the reference and the data-modulated pulses are separated in the code-domain [50, 53].
The performance of a CM-TR UWB system relies on orthogonality between the
reference and data-modulated pulses, in order to accomplish this, orthogonal code
sequences (OCSs) taken from the rows of an Hadamard matrix [50]. In a multiuser scenario, selection of an optimum code sequence set provides a significant
improvement in performance [54].
6
Motivation and Scope
Generally, the received signal in any wireless communications system is an attenuated, delayed, and possibly distorted version of the signal that was transmitted,
plus noise and (possibly) interference [8]. In order to determine the performance
and robustness of a wireless system, the amount of received signal energy that can
be collected at the receiver and the receiver complexity play a crucial role [23].
If UWB systems are considered, the characteristics of wide bandwidth signals
24
Introduction
pose difficulties to design low-complexity and low cost solutions. The propagation characteristics of UWB signals are also different from traditional narrowband
systems [10], especially a rich multipath diversity is found in the received signal.
Moreover, the receiver structures require high sampling frequency and wide input
bandwidth analog to digital converters (ADCs) to process the signal digitally [8];
these ADCs increase the power consumption and the cost. There are also other
issues such as frequency dependent signal distortion, accurate synchronization
and complex channel estimation [8, 9]. The synchronization at subnanosecond
scale and channel estimation task demand the development of sophisticated signal processing algorithms.
Well-known RAKE combining may be used for multipath energy capture but
the drawback of the RAKE receiver in UWB systems is that the number of
MPCs that can be utilized in a typical RAKE combiner is limited by the power
consumption budget, design complexity, and the channel estimation [11]. Aside
from being in large number, each MPC undergoes a different channel in UWB
systems, which causes distortion in the received pulse shape and makes the use
of a single LOS path signal as a suboptimal template [12]. The coherent RAKE
receiver also requires the knowledge of the channel impulse response and needs
to achieve the pulse-level synchronization with accuracy on the order of tens of
picoseconds [41].
Additionally, a major issue with the RAKE is that its full digital implementation requires high-sampling frequency (of the order of several GHz) ADCs, which
makes it expensive to implement [8]. In order to use low-sampling frequency
ADCs, [42] proposes that the received UWB signal can be correlated with a
symbol length template signal, and the correlator output can be sampled once
per symbol, i.e., symbol rate sampling. Problem with this approach is that the
generation of symbol length template signals increases receiver complexity and
power consumption. Moreover, an accurate estimation of the channel is also a
challenging task and requires a large number of training symbols. To dilute the
complexity to some extent, a moderately high-sampling frequency ADC or several parallel lower-speed ADCs may be used to enable chip rate sampling in the
RAKE receiver.
Due to the reasons discussed above, an optimal implementation of the RAKE
receiver for UWB system is impractical. Alternatively, research in sub-optimal
UWB receivers took off as they provide a trade-off between performance and
complexity to achieve a low power and low cost receiver [11, 12]. Especially, the
sub-optimal TR receiver got attention as it is able to collect most of the signal
energy by exploiting multipath diversity inherent in the environment without the
need for stringent timing and synchronization and channel estimation [12, 28, 47,
48, 55, 56]. On the down side, it suffers a 3 dB penalty because half of the pulses
are unmodulated [8]. The performance of the TR receiver is also limited by the
25
noise in the correlator due to the noisy reference template [8, 48]. In addition,
in order to avoid inter-pulse interference (IPI), the TR receiver requires accurate
long and wideband analog delay lines for its implementation.
Like the TR, the ED is also able to gather multipath energy without channel knowledge. Sine the ED is blind to the phase information and utilizes equal
gain combining, low complexity detection in this receiver is achieved at the expense of performance degradation [44, 45]. To enhance the performance of the
ED, weighted energy detectors (WEDs) employing high-speed ADCs have been
proposed and efficient weight estimation schemes are being explored [57–61].
Additionally, to ease the implementation of the TR and to minimize the degradation caused by the ED, the FSR and the CM-TR systems have been introduced.
While the FSR architecture greatly simplifies the receiver design [49], the detection of FSR signals still requires generation of a carrier signal at the receiver and
its performance also degrades as the data rate increases [51, 52]. As compared
to the time and frequency domain TR receivers, the promising CM-TR receiver
has a low implementation complexity as it neither needs analog delay lines nor a
carrier generator, see Fig. 14. Besides low complexity, BER performance of the
CM-TR is also better than the FSR and the TR systems [50]. On the down side,
since CM-TR UWB system is essentially an energy detection receiver based on
code-multiplexing, its performance is also greatly affected by the integration interval and the low SNR of the decision statistic. However, like other non-coherent
solutions, the main performance limiting feature of this receiver, which requires
consideration, is strong MUI and IFI.
In this context, effective modulation schemes, robust channel estimation algorithms and low-complexity receiver structures need to be explored in order to
meet the challenges hindering the widespread deployment of low cost, low data
rate WPANs and sensor networks. Though non-coherent solutions essentially
suffer from the noise enhancement, a largely analog implementation of a noncoherent IR-UWB receiver provides a receiver well-suited for the intended set of
applications. Thus, in this thesis, mainly sub-optimal receivers are studied and
codesign of signalling scheme and receiver architecture is addressed as this approach is common to solve the challenges in the transceiver design for UWB [43].
The objective is to develop efficient modulation and detection schemes, and to
enhance and evaluate performance of the sub-optimal receivers to be used in low
data rate wireless sensor networks.
7
Author’s Contributions
The thesis consists of five stand-alone parts. The following subsections highlight
the contributions of individual parts.
26
Introduction
7.1
Part I: Performance Evaluation of Coherent and
Non-coherent Receivers for IR-UWB Systems using
Multipath Channels for Industrial Environments
In this part, the performance of coherent RAKE and non-coherent ED and TR
receivers is evaluated, using measured channel responses in an industrial environment, with the aim to identify the receivers that offer a good compromise between implementation complexity and performance. The industrial environment
is considered as it is expected that UWB devices will be deployed in industrial
buildings management [62]. In the past, performance evaluations for coherent
and non-coherent receivers using UWB channels has been performed only for
office or residential environments [64–68] and, in addition, real channel measurement data has not been used in the previous performance evaluations of IR-UWB
receivers. In line with this, performance of coherent and non-coherent receivers is
evaluated for a single user system using non-line-of-sight (NLOS) channels [69].
The main contributions and outcomes of Part I are:
• A unified analysis of coherent RAKE and non-coherent ED and TR receiver
is presented and and BER performance evaluation is performed using real
channels measured in an industrial environment.
• The performance of partial RAKE (PRake), selective RAKE (SRake) and
all RAKE (ARake) is compared and the number of RAKE fingers required
to achieve a specific BER is determined.
• It is observed that, in the high SNR region, the SRake receiver with few
(about five) fingers has 5 − 6 dB gain over the PRake having same number
of fingers.
• It is found that the PRake receiver may be used if the channel has a decreasing PDP with embedded strong components at shorter delays.
• It is also concluded that, due to the saturation effects, employing more than
ten fingers of the SRake and twenty fingers of the PRake is not useful as
the rest of the MPCs do not carry significant energy.
• RAKE combining scheme, maximal ratio combining (MRC) and equal gain
combining (EGC), are compared and it is found that the difference in the
performance of MRC and low-complexity EGC combining scheme is not
that significant for SRake.
• It is found that low-complexity ED receivers may perform better than a
practical moderate finger coherent RAKE in the high SNR region.
27
• It is concluded that the ED receivers provide the best complexity/performance
trade-off for intended application.
7.2
Part II: Recursive and Doublet-Based Transmitted
Reference Schemes for Ultra Wideband Communications
The conventional TR schemes suffer from a noisy reference template and the
noise averaging schemes described in the literature, such as presented in [12],
have a high implementation complexity. In addition, there is a 50% energy/rate
loss associated with the conventional TR and implementation of the analog delay
lines in the TR receiver also poses challenges. Addressing these issues, this part
of the thesis mainly uses codesign of signalling scheme and receiver architecture
approach, and presents several TR based schemes with the aim to improve the
performance of conventional TR [70–72].
The main contributions and outcomes of Part II are:
• First of all, recursive TR (R-TR) and recursive averaged (R-ATR) receivers
are presented which recursively estimate the reference template for the correlator in order to achieve noise reduction in the reference template pulse.
A modified TR signaling sequence, in which all the reference pulses of a
symbol are transmitted together and their corresponding data-modulated
pulses follow after a delay, is used for the ATR and R-ATR receivers; the
use of slightly modified TR signaling requires shorter delays for averaging.
The BER analysis and simulations are performed; the simulation results
show that R-TR and R-ATR receivers exhibit different gains over the conventional TR and ATR receivers depending on the received signal SNR and
the value of recursive averaging weight parameter.
• Dual-doublet TR (DDTR) signaling is proposed, which transmits two bits
per symbol by using two TR doublets in each frame, and the DDTR receiver is presented for detection in which each modulated pulse is correlated
with two reference pulses, as opposed to the conventional TR scheme which
correlates each modulated pulse with only one reference pulse. It has been
validated by the simulation results that the proposed DDTR scheme requires 3 dB less energy per bit and recovers 50% rate loss of conventional
TR scheme, while giving similar BER performance.
• Doublet-shift TR (DSTR) signaling is proposed, which transmits two TR
doublets within a frame duration by using closely-spaced pulses and shifting
the positions of the pulses in the latter doublet. To detect these signals,
the DSTR-I receiver is the same as the TR receiver, whereas the twobranch DSTR-II structure is equipped with an extra delay and correlation
28
Introduction
operation. The performance improvement of the DSTR signaling over the
TR signaling shown by the BER analysis is validated by the simulation
results.
• Lastly, the DSTR scheme is extended to BPPM/DSTR scheme with the aim
to reduce the complexity of the DSTR-II receiver. The proposed ED/DSTR
receiver does not require a long analog delay as it is replaced by a squarelaw device in the first branch and a very short delay element is needed
in the second branch. It is verified by simulation results that the use of
closely-spaced pulses in the modulation and the proposed receiver leads to
better performance than the conventional ED and TR receivers.
7.3
Part III: Non-coherent Detectors Based on Fourth Order
Statistics of Impulse Radio UWB Signals: Empirical
evaluation using Channel Measurements
For detection of received signals in low data rate IR-UWB systems, conventional
ED is an ideal candidate in terms of implementation complexity and low power
consumption. However, due to equal gain combining of received MPCs, SNR of
the decision statistic is very low. Owing to the impulsive nature of UWB signals
and motivated by the fact that the cumulants are characterizing the distribution [73], the cumulants or higher-order moments are employed as a quantifying
measure for distinguishing two regions of signals with different distributions. This
part of the thesis presents a non-coherent kurtosis detector (KD) and a fourthorder detector (FD), which can discriminate between Gaussian noise signals and
non-Gaussian IR-UWB signals by directly estimating the fourth-order moment
of the received signal [74, 75].
The main contributions and outcomes of Part III are:
• A non-coherent KD receiver based on the normalized fourth central moment
(kurtosis) and an FD receiver based on estimation of the fourth moment
about zero, of the received IR-UWB signal, are proposed.
• Empirical evaluation and performance comparison of the detectors is performed considering real channels measured in a corridor, an office and a
laboratory environment.
• It is concluded that the KD receiver is better than the ED receiver only
under AWGN conditions, whereas in a multipath channel, the KD receiver
performance degrades as the non-Gaussianity of an IR-UWB signal decreases in this condition.
29
• It is found that the proposed FD receiver is slightly better than the ED in
the low SNR region and its performance improves as the SNR increases.
• It is also observed that the FD receiver performance is better on the channels having strong first arriving MPCs and very few clusters of MPCs carrying most of the energy.
• Finally, a rule of thumb for selection of integration time of the proposed FD
receiver is suggested, which states that the integration time which captures
all the MPCs within 10 dB of the strongest path of the worst set of channels,
in the available realizations, may be selected.
7.4
Part IV: Robust Weighted Non-Coherent Energy
Detection Receiver for Impulse Radio UWB PPM Signals
ED receiver performance strongly depends on the integration interval (window
size) of the integrator and the window position. At the expense of high speed
and high power ADCs, weighted EDs (WEDs) have been proposed in [57–61].
However, the weight estimation schemes in the WEDs are either complex or
require large number of training symbols. Part IV is along these lines, where
this problem is addressed in this part and a robust weight estimation scheme for
BPPM IR-UWB signals using the WED is proposed [76].
The main contributions and outcomes of Part IV are:
• A robust WED scheme is proposed, which is non-data-aided (NDA), adaptive and robust to channel variations and requires no a priori knowledge of
the channel and the noise.
• At first, a single-stage robust WED estimates the weighting coefficients
adaptively based on the received stochastic data and, in the second-stage,
the weight estimation process is refined using a decision directed approach.
• According to the results obtained from simulations, the robust WED weight
estimation method is close to that of an training symbol based data-aided
(DA) weight estimation scheme and a maximum eigenvector based NDA
scheme.
7.5
Part V: Weighted Code-Multiplexed
Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
This part deals with multi-user environment and investigates ways to enhance the
performance of a CM-TR system. Though a CM-TR UWB system complies with
30
Introduction
the requirements of multi-user sensor networks, it is not energy efficient as one
half of the energy is used to transmit reference pulses and, even at low-to-medium
data rates, it suffers from strong MUI and IFI. To this end, a weighted CM-TR
(WCM-TR) and a combined BPPM/CM-TR UWB system are presented in this
part [77].
The main contributions and outcomes of Part V are:
• Firstly, an adaptive robust weight estimation scheme, originally proposed
for the WED, is developed for the WCM-TR detector. The proposed
scheme estimates the weighting coefficients adaptively based on the received
stochastic data and is also robust to channel variations. It neither requires
training symbols nor a priori knowledge of the channel and the noise.
• Secondly, a combined BPPM/CM-TR UWB system transmits two bits
within the duration of one bit and the core idea is to achieve longer silent
periods between the pulses to minimize the deteriorating effects of IFI and
MUI. Besides being 3 dB energy efficient, BER of the multiuser BPPM/CMTR is better than the multiuser CM-TR system in the high SNR region and
improves as the SNR increases. While it effectively combats IFI/MUI in the
high SNR regime, it is not expected to work well in the low SNR case and
single-user scenario. This issue may be resolved by employing a dual-mode
BPPM/CM-TR system, which normally operates in the BPPM/CM-TR
mode if the current SNR level is above a certain threshold and multipleusers are active in the network, else it switches to the CM-TR mode.
Bibliography
[1] P. E. Mogensen, T. Koivisto, K.I. Pedersen, I. Z. Kovacs, B. Raaf, K. Pajukoski, M. J. Rinne, “LTE Advanced: The Path towards Gigabit/s in Wireless Mobile Communications,Wireless Communication”, 1st International
Conference on Vehicular Technology, Information Theory and Aerospace and
Electronic Systems Technology, Wireless VITAE 2009, pp. 147–151
[2] 3GPP Technical Report 36.913 “Requirements for further advancements for
E-UTRA (LTE-Advanced)”, June 2008.
[3] S. Chia, T. Gill, L. Ibbetson, D. Lister, A. Pollard, R. Irmer, D. Almodovar,
N. Holmes, S. Pike, “3G evolution” IEEE Microwave Magazine, Aug. 2008,
vol. 9, no. 4, pp. 52–63
[4] A. Doufexi, S. Armour, “Design considerations and physical layer performance results for a 4G OFDMA system employing dynamic subcarrier allocation”, IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2005, vol. 1, pp. 357–361
[5] S. Nanda, R. Walton, J. Ketchum, M. Wallace, and S. Howard, “A highperformance MIMO OFDM wireless LAN”, IEEE Communications Magazine, vol. 43, no. 2, pp. 101–109
[6] D. Porcino and W. Hirt, “Ultra-wideband radio technology: potential and
challenges ahead”, IEEE Communications Magazine, 2003, vol. 41, no. 7,
pp. 66–74
[7] M.-G. di Benedetto, T. Kaiser and N. Schmidt UWB – State of the Art,
Journal of Applied Signal Processing Editorial, EURASIP publishing, March
2005
[8] J. H. Reed et. al. An Introduction to Ultra Wideband Communication Systems, Prentice Hall, 2005
[9] R. C. Qiu, H. Liu, and X. Shen,“Ultra-wideband for multiple access communications,” IEEE Comm. Magazine, vol. 43, no. 2, pp. 80–87, Feb. 2005
[10] A. F. Molisch UWB Propagation Channels, Book chapter 1, pp.1, 2005
31
32
BIBLIOGRAPHY
[11] D. Cassioli, M. Z. Win, F. Vatalaro, and A. F. Molisch, “Performance of
low-complexity Rake reception in a realistic UWB channel”, Proc. IEEE
Int. Conf. on Commun., pp. 763–767, May 2003
[12] D. J. Choi and W. E. Stark, “Performance of ultra-wideband communications with suboptimal receivers in multipath channels,” IEEE Journal of
Sleceted Areas Communications, vol. 20, no. 9, pp. 1754–1766, Dec. 2002
[13] J. G. Proakis Digital Communications, McGraw-Hill, 1995
[14] T. S. Rappaport Wireless Communications: Principles and Practice, Prentice Hall PTR, Upper Saddle River, NJ, USA, 2nd edition, 2002
[15] R. A. Scholtz, D. M. Pozar and W. Namgoong, Ultra-Wideband Radio, Journal of Applied Signal Processing, EURASIP publishing, 2005:3, pp. 252–272
[16] R. A. Scholtz, “Multiple access with time-hopping impulse modulation”,
Proceedings Military Communications Conference, vol. 2, pp. 447–450
[17] M. Z. Win, R. A. Scholtz and L. W. Fullerton, “Time-hopping SSMA techniques for impulse radio with an analog modulated data subcarrier”, Proceedings IEEE International Symposium on Spread Spectrum Techniques and
Applications, vol. 1, pp. 359–364
[18] M. Z. Win and R. A. Scholtz, “On the robustness of ultra-wide bandwidth
signals in dense multipath environments”, IEEE Commun. Lett., vol. 2, no.
2, pp. 51–53, Feb. 1998
[19] M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spreadspectrum impulse radio forwireless multiple-access communications”,IEEE
Transactions on Communications, vol. 48, no. 4, pp. 679–689, April 2000
[20] U. S. Federal Communications Commission (FCC), “Revision of part 15 of
the commission’s rules regarding ultra-wideband transmission systems” First
Report and Order, ET Docket 98–153, FCC 02–48; Adopted: February 2002;
Released: April 2002
[21] L. Yang and G. B. Giannakis,“Ultra-wideband communications,” IEEE Signal Process. Magazine, vol. 21, no. 6, pp. 26–54, Nov. 2004
[22] W. Hirt, “Ultra-wideband radio technology: overview and future research”,
Elsevier Computer Communications vol. 26, no. 1, pp. 46–52, 1 January 2003
[23] A. Batra, J. Balakrishnan, G. R. Aiello, J. R. Foerster and A. Dabak, “Design of a Multiband OFDM System for Realistic UWB Channel Environments”, IEEE transactions on Microwave Theory and Techniques, vol. 52,
no. 9, Sept. 2004
BIBLIOGRAPHY
33
[24] M. Z. Win and R. A. Scholtz, “Impulse radio: How it works”, IEEE Commun. Lett., vol. 2, no. pp. 36–38, Feb. 1998
[25] Durisi,G., Benedetto,S., “Comparison between coherent and noncoherent
Receivers for UWB Communications,” EURASIP Journal on Applied Signal
Processing, 2005, vol. 3, pp. 359–368.
[26] J. T. Conroy, J. L. LoCicero, D. R. Ucci, “Communication techniques using
monopulse waveforms” IEEE Military Communications Conference Proceedings, MILCOM 1999, vol. 2, pp. 1181–1185
[27] M. Ghavami, L. B. Michael, S. Haruyama, R. Kohno, “A Novel UWB Pulse
Shape Modulation System”, Wireless Personal Communications, 2002 Springer, vol. 23, no. 1, pp. 105–120
[28] R. Hoctor and H. Tomlinson, “Delay-hopped transmitted-reference RF communications,” IEEE UWBST, pp. 265–269, Baltimore, MD, 2002
[29] R. T. Hoctor and H.W. Tomlinson, “An overviewof delay-hopped,
transmitted- reference RF communications,” in Technical Information Series: G.E. Research and Development Center, Jan. 2002, pp. 1–29.
[30] G. Durisi, S. Benedetto, “Performance evaluation and comparison of different modulation schemes for UWB multiaccess systems”, IEEE International
Conference on Communications, 2003. ICC ’03., vol. 3, pp. 2187–2191
[31] Bo Hu, N. C. Beaulieu, “Accurate performance evaluation of time-hopping
and direct-sequence UWB systems in multi-user interference”, IEEE Transactions on Communications, vol. 53, no. 6, pp. 1053–1062, June 2005
[32] D. Cassioli, M. z. Win and A. f. Molisch, “The ultra-wide bandwidth indoor
channel: from statistical model to simulations”, IEEE Journal of Selected
Areas in Communications, vol. 20, no. 6, pp. 1247–1257, 2002
[33] S. Ghassemzadeh, R. Jana, C. Rice, W. Turin and V. Tarokh, “A statistical
path loss model for in-home UWB channels”, Proceedings of IEEE Conf. on
Ultra Wideband Systems and Tech. 2002, pp. 59–64
[34] J. Kunisch and J. Pamp, “An ultra-wideband space-variant multipath indoor radio channel model”, Proceedings of IEEE Conf. on Ultra Wideband
Systems and Tech. 2003, pp. 290–294
[35] A. F. Molisch, “Ultrawideband propagation channels- theory, measurement,
and modelling”, IEEE Transactions Vehicular Technology Conf. 2005, vol.
54, no. 5, pp. 1528–1545
34
BIBLIOGRAPHY
[36] A. F. Molisch et al., “IEEE 802.15.4a channel model - final report,” Tech.
Rep. Document IEEE 802.15-04-0662-02-004a, 2005
[37] R. C. Qiu and I.-T. Lu, “Wideband wireless multipath channel modeling with
path frequency dependence,” in IEEE International Conference on Communications (ICC’96), 1996
[38] R. C. Qiu and I.-T. Lu, “Multipath resolving with frequency dependence for
broadband wireless channel modeling,” IEEE Trans.Veh. Tech., 1999
[39] A. Saleh and R. Valenzuela, “A statistical model for indoor multipath propagation,” IEEE Journal on Select. Areas Commun., vol. SAC-5, no. 2, pp.
128–137, Feb. 1987
[40] R. Price, P. E. Green, “A Communication Technique for Multipath Channels”, Proceedings of the IRE, vol. 46, no. 3, pp. 555–570
[41] Ning He, C. Tepedelenlioglu, “Performance analysis of non-coherent UWB
receivers at different synchronization levels”, IEEE Global Telecommunications Conference, 2004. GLOBECOM ’04., vol. 6, pp. 3517–3521
[42] A. F. Molisch et al., “An efficient low cost time-hopping impulse radio for
high data rate transmission,” Proc. IEEE 6th International Symposium on
Wireless Personal Multimedia Communications (WPMC 2003), Yokosuka,
Kanagawa, Japan, Oct. 19–22, 2003
[43] K. Witrisal, G. Leus, G. J. M. Janssen, M. Pausini, F. Troesch, T. Zasowski,
and J. Romme, “Noncoherent ultra-wideband systems”, IEEE Signal Processing Magazine, July 2009, vol. 26, no. 4, pp. 48–66
[44] S. Paquelet, L. M. Aubert, and B. Uguen, “An impulse radio asynchronous
transceiver for high data rates”, in Proc. IEEE Ultrawideband Syst. Technol.
(UWBST), Kyoto, Japan, pp. 1–5, May 2004
[45] M. Weisenhorn and W. Hirt, “Robust noncoherent receiver exploiting UWB
channel properties”, in Proc. IEEE Conference on UWB Systems and Technologies, pp. 156–160, May 2004
[46] M.E. Sahin, I. Guvenc, H. Arslan, “Optimization of energy detector receivers
for UWB systems”, IEEE 61st Vehicular Technology Conference, 2005. VTC
2005-Spring., vol. 2, pp. 1386–1390
[47] T. Q. S. Quek, M. Z. Win, “Ultrawide bandwidth transmitted-reference
signaling”, Communications, 2004 IEEE International Conference on, vol.6,
pp. 3409–3413
BIBLIOGRAPHY
35
[48] F. Tufvesson and A. F. Molisch, “Ultra-wideband communication using hybrid matched filter correlation receivers,” Proc. IEEE Veh. Technol. Conf.,
vol. 3, pp. 1290–1294, May 2004
[49] D. Goeckel and Q. Zhang, “Slightly frequency-shifted reference ultrawideband (UWB) radio,” IEEE Trans. Commun., vol. 55, no. 3, pp. 508–519,
Mar. 2007.
[50] A.A. D’amico and U. Mengali, “Code-multiplexed UWB transmittedreference radio,” IEEE Trans. on Comm., vol. 56, 2008, p. 2125–2132.
[51] J. Zhang, H.-Y. Hu, L.-K. Liu, and T.-F. Li, “Code-orthogonalized
transmitted-reference ultra-wideband (UWB) wireless communication systems,” in Proc. International Conf. Wireless Commun., Netw. Mobile Comput., Sep. 2007, pp. 528–532.
[52] H. Nie, Z. Chen, “Code-shifted reference ultra-wideband (UWB) radio communication” 6th Annual Networks and Services Research Conf. (CNSR),
May 2008, pp. 385–389.
[53] S. Gezici, “Coded-reference ultra-Wideband systems”, Proc. IEEE Inter.
Conf. on UWB, 2008, vol. 3. pp. 117–120.
[54] A. A. D’Amico, and U. Mengali, “Code-multiplexed transmitted-reference
UWB systems in a multi-user environment,” IEEE Trans. on Comm., March
2010, vol. 58, no. 3, pp. 966–974.
[55] Y.-L. Chao and R. A. Scholtz “Optimal and suboptimal receivers for
ultra-wideband transmitted reference systems,”IEEE Global Telecommun.
Conf.’03, vol. 2, pp. 759–763, 1-5 Dec. 2003
[56] W. M. Gifford and M. Z. Win, “On transmitted-reference UWB communications,”Asilomar Conference on Signals, Systems and Computers, 2004., vol.
2, pp. 1526–1531, Nov. 2004
[57] Z. Tian and B.M. Sadler, ”Weighted energy detection of ultra-wideband signals,” Proc. IEEE 6th Workshop on Signal Processing Advances in Wireless
Communications, 2005, pp. 1068–1072.
[58] J. Wu, Q. Liang, and H. Xiang, ”Adaptive Weighted Noncoherent Receiver
for UWB-PPM Signal in Multipath Channels,” Proc. ICWMMN Conference,
2006.
[59] J. Wu, H. Xiang, and Z. Tian, ”Weighted Noncoherent Receivers for UWB
PPM Signals,” IEEE Commun. Lett, vol. 10, no. 9, 2006, pp. 655–657.
36
BIBLIOGRAPHY
[60] A.A. D’Amico, U. Mengali, and E. Arias-de-Reyna, ”Energy-Detection
UWB Receivers with Multiple Energy Measurements,” IEEE Transactions
on Wireless Communications, 2007, vol. 6, no. 7, pp. 2652–2659.
[61] S. Bin, Y. Rumin, C. Taiping, and K. Kyungsup, ”Non-data-aided Weighted
Non-coherent Receiver for IR-UWB PPM Signals,” ETRI Journal, vol. 32,
no. 3, Jun. 2010, pp. 460–463.
[62] M. G. Khan, A. A. Ashraf, J. Karedal, F. Tufvesson, and A. F. Molisch,
“Measurements and Analysis of UWB Channels in Industrial Environments,” in Proc. Wireless Personal Multimedia Communications (WPMC),
Aalborg, Denmark, Sept. 2005
[63] J. Karedal, S. Wyne, P. Almers, F. Tufvesson, and A. F. Molisch, “UWB
channel measurements in an industrial environment”, in Proc. IEEE Globecom, 2004
[64] A. Rajeswaran, V.S. Somayazulu, J. R. Foerster, “RAKE performance for a
pulse based UWB system in a realistic UWB indoor channel,” Proc. IEEE
International Conference on Communications (ICC ’03) , vol.4, pp. 2879 2883, 11-15 May 2003
[65] B. Mielczarek, M. Wessman, and A. Svensson, “Performance of coherent
UWB RAKE receivers with channel estimators,” Proc. IEEE Vehicular
Technology Conference, vol. 3, pp. 1880-1884, Oct. 2003
[66] G. Durisi, S. Benedetto, “Performance of coherent and noncoherent receivers
for UWB communications ,” Proc. IEEE International Conference on Communications (ICC 2004), vol. 6, pp. 3429-3433, June 20-24, 2004
[67] S. Gezici, H. Kobayashi, H. V. Poor and A. F. Molisch, “Optimal and suboptimal linear receivers for time-hopping impulse radio systems,” Proc. IEEE
Wireless Communications and Networking Conference (WCNC 2004), vol.
2, pp. 908-913, Atlanta, GA, March 2004
[68] M. A. Rahman, S. Sasaki, Z. Jie, S. Muramatsu, H. Kikuchi, “Performance
evaluation of RAKE reception of ultra wideband signals over multipath
channels from energy capture perspective,” International Workshop on Ultra
Wideband Systems, 2004. Joint with Conference on Ultrawideband Systems
and Technologies, pp. 231-235, May 2004
[69] M. G. Khan, J. Nordberg, A. Mohammed, and I. Claesson, “Performance
evaluation of RAKE receiver for UWB systems using measured channels
in industrial environments,” in Proceedings of AusWireless’06, March 2006,
Sydney, Australia.
BIBLIOGRAPHY
37
[70] M. G. Khan, J. Nordberg, and I. Claesson, “Detection of Impulse Radio ultra
wideband Signals using Recursive Transmitted Reference Receivers”, in Proceedings of ICUWB’07, IEEE International Conference on ultra wideband,
September 24-26, 2007, Singapore.
[71] M. G. Khan, J. Nordberg, and I. Claesson, “Signaling and Detection of
UWB Signals based on a Dual-Doublet Transmitted Reference Scheme”, in
Proceedings of RVK’08, The twentieth Nordic Conference on Radio Science
and Communications, June 9-11, 2008, Växjö, Sweden.
[72] M. G. Khan, J. Nordberg, and I. Claesson, “A Doublet-Shift Transmitted
Reference Scheme for ultra wideband Communication Systems”, in Proceedings of ICUWB’07, IEEE International Conference on ultra wideband,
September 24-26, 2007, Singapore.
[73] Hyvärinen, A., Karhunen, J., Oja, E., 2001. Independent Component Analysis. John Wiley & Sons, Inc.
[74] M. G. Khan, B. Sällberg, J. Nordberg, and I. Claesson, “Non-coherent detection of impulse radio UWB signals based on fourth order statistics”, in
Proceedings of IEEE International Conference on UWB, ICUWB 2009 pp.
824–828, Canada.
[75] M. G. Khan, B. Sällberg, J. Nordberg, F. Tufvesson and I. Claesson, “NonCoherent Fourth-Order Detector for Impulse Radio Ultra Wideband Systems: Empirical evaluation using Channel Measurements”, published in
Springer Journal of Wireless Personal Communications, Online First on
November 01, 2011.
[76] M. G. Khan, B. Sällberg, J. Nordberg, and I. Claesson, “Robust Weighted
Non-Coherent Receiver for Impulse Radio UWB PPM Signals” IEEE Journal of Communications Letters, vol. 15, no. 6, pp. 614-616, June 2011
[77] M. G. Khan, B. Sällberg, J. Nordberg, and I. Claesson, “Energy Efficient Binary PPM/Code-Multiplexed Transmitted-Reference Multi-user UWB System, in Proceeding of IEEE International Conference on UWB, ICUWB
2011, pp. 615–619, Bologona, Italy.
Part I
Performance Evaluation of Coherent and
Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for
Industrial Environments
This Part is based on the following publications:
M. G. Khan, J. Nordberg and I. Claesson, “Performance Evaluation of RAKE
Receiver for Low Data Rate UWB Systems using Multipath Channels for Industrial Environments”, Research report, Blekinge Institute of Technology, 2008,
Issue: 4, ISSN: 1103–1581.
M. G. Khan, J. Nordberg and I. Claesson, “Performance evaluation of RAKE
receiver for UWB systems using measured channels in industrial environments,”
in Proceedings of AusWireless’06, March 2006, Sydney, Australia.
Performance Evaluation of Coherent and Non-coherent
Receivers for IR-UWB Systems using Multipath
Channels for Industrial Environments
November 22, 2011
Abstract
For UWB communication systems, industrial environments are an important scenario. However, the multipath offered by UWB channels is dense
and many multipath components have significant energy and, thus, it important to evaluate performance of UWB receivers using real channel characteristics. In line with this, performance of coherent and non-coherent receivers is evaluated for a single user system using non-line-of-sight (NLOS)
channels measured in a medium-sized industrial environment. The performance is compared for partial RAKE (PRake), selective RAKE (SRake),
transmitted reference (TR) and energy detector (ED) in terms of uncoded
bit-error-rate (BER). In addition, the effect of different number of fingers
on BER of PRake and SRake is studied and the performance of maximal ratio combining (MRC) and equal gain combining (EGC) is compared for the
RAKE receivers. From the comparison of the RAKE combining schemes,
it is observed that the difference in performance of the MRC and the EGC
is not that significant for the SRake, while the PRake has a considerably
better performance using the MRC. It is concluded that only few fingers of
the SRake (i.e., about five fingers) with EGC combining may be preferred
over a large number of the PRake (i.e., about twenty fingers) with MRC
combining. The results show that the low-complexity ED receivers perform
better than a practical moderate finger coherent PRake in the high SNR
region. Additionally, for the channels having strong components at shorter
delays and for higher SNRs, the ED receivers may perform better than even
a moderate finger SRake receiver.
43
44
1
Part I
Introduction
The transmission of UWB signals over a wireless channel results in multipath
components (MPCs) arriving at the receiver with high delay resolution due to its
wide bandwidth and thus, the receiver is able to resolve many MPCs. A RAKE
receiver can be used to combine these MPCs as it exploits the time-diversity
inherent in multipath and attempts to collect the signal energy coherently from
the received signal paths that fall within its span [1]. However, as the number
of resolved MPCs is very high in the case of UWB systems, the combining of
hundreds of MPCs using RAKE receivers is not realistic. It becomes important
to focus upon a subset of the received MPCs using a specific selection criteria,
for instance, by selecting a number of dominant MPCs.
The IEEE 802.15.4a group, which has developed a physical layer standard for
low data rate systems, has recognized the fact that a considerable amount of UWB
devices will be deployed in industrial buildings, factories and warehouses [2]. The
application set includes, e.g., sensor networks for process control, supervision
of storage halls, asset tagging and management. For such environments like a
factory hall with possibly multiple metallic reflectors, the multipath environment
is dense and almost all resolvable delay bins contain significant energy [3]. In
this case, a RAKE receiver needs to capture a large number of (on the order
of hundred) MPCs to collect a significant amount of the received energy [2, 4].
The RAKE receiver design is in this case a challenging task and performance
evaluation of the receivers under realistic channel conditions becomes important.
Previously, the performance of coherent RAKE and non-coherent receivers
for UWB systems has been evaluated, e.g., in [5–9]; however, most of these
evaluations have been performed using UWB channels for office or residential environments. Moreover, as most of the evaluations are based on simulated channel
models, it is necessary to evaluate the system performance considering realistic
channel characteristics of the environment. Thus, this part of the thesis investigates and analyzes the performance of the RAKE, ED and TR receivers in
terms of uncoded BER for industrial environments using measured channel responses. The objective here is not to suggest one receiver over the other, but
rather to provide a realistic performance comparison and draw conclusions considering performance/complexity trade-off. In this context, the relationship of
BER and various types of RAKE, the number of RAKE fingers and the RAKE
combining schemes is evaluated. In addition, performance of the coherent PRake
and SRake receivers is compared with the non-coherent TR and ED receivers.
Based on the simulation results, conclusions are drawn considering performance
and complexity issues.
This part is organized as follows: the system model of a typical UWB system
is described in Section 2. Section 3 describes the UWB channels used for the
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
s(t)
Data
r(t)
Multipath
Channel
Modulation
45
Receiver
h(t)
Decision
n(t)
Figure 1: Block diagram of the system model.
performance evaluation of the system. In Section 4, architecture of the RAKE
receiver, types of RAKE receiver, RAKE combining schemes and BER analysis
of the coherent RAKE is discussed. Section 5 and Section 6 present architecture
and BER analysis of the TR and the ED receivers, respectively. The simulation
parameters and results are discussed in Section 7, and conclusions are summarized
in Section 8.
2
System Model
IR-UWB systems employ different modulations such as binary phase shift keying
(BPSK) which is also known as antipodal pulse amplitude modulation (A-PAM),
binary pulse position modulation (BPPM) and on-off keying (OOK). It is wellknown that, to achieve the same level of noise immunity, the bipolar BPSK or
A-PAM modulation has a 3 dB advantage in terms of required power over the
unipolar BPPM modulation. Though BPSK modulation can not used with the
ED as it removes the phase information, its use is by far the most common with
the RAKE and the TR receiver. In the sequel, it is assumed that the RAKE
and TR receivers detect BPSK modulated signals, while the ED is used to detect
BPPM modulated signals.
The transmitted IR-UWB signal using BPSK, TR and BPPM modulation are
written, respectively, as
sBPSK (t)
∞ NX
f −1
X
p
Ep
bi p(t − iTs − jTf − cj Tc ),
=
(1)
i=−∞ j=0
sTR (t)
=
∞ NX
f −1
X
p
Ep
p(t − iTs − jTf − cj Tc )
i=−∞ j=0
+bi p(t − iTs − jTf − cj Tc − Td ) ,
sBPPM (t)
f −1
∞ NX
p X
=
Ep
p(t − iTs − jTf − cj Tc − di TBP P M ),
i=−∞ j=0
(2)
(3)
46
Part I
RT
where p(t) is a normalized UWB pulse of duration Tp , i.e., 0 p [p(t)]2 dt = 1, Ep
is the energy of each pulse, Ts is the symbol duration, Tf is the frame duration,
Tc is the chip duration, TBP P M is the BPPM shift and Nf is the number of
frames per symbol. Each frame of the BPSK and BPPM modulations contains a
single pulse, while each frame of the TR contains two pulses separated by a fixed
delay of duration Td . Moreover, the energy per symbol Es is equal to the energy
per bit Eb . For BPPM, each frame is divided in two halves and the position
of the pulse in one of these two halves is determined as di = (bi + 1)/2 ∈ {0, 1}.
Thus, one binary information symbol is transmitted by a stream of Nf pulses
in BPSK and BPPM signals, while 2Nf pulses are used in the TR signal. The
pseudo-random time-hopping (TH) sequences {cj } are assigned to each user that
share the UWB media to avoid collisions among the pulses of different users. If
the number of chips in a frame is denoted as Nc , then the chip interval is chosen
to satisfy Tc ≤ Tf /Nc , which avoids pulses of different users from overlapping.
The signals are transmitted over a multipath channel. It is assumed that the
impulse response of the channel is modeled by a typical tapped-delay line as
h(t) =
K−1
X
k=0
αk δ(t − τk ),
(4)
where δ(t) is the Dirac delta function, while αk are the channel tap weights, K
is the number of MPCs and τk is the delay associated with the k th multipath
component. The received signals for BPSK, TR and BPPM modulation are
given, respectively, by
rBPSK (t) =
f −1
∞ NX
X
p
Ep
bi g(t − iTs − jTf − cj Tc ) + n(t),
(5)
i=−∞ j=0
rTR (t) =
f −1
∞ NX
X
p
Ep
g(t − iTs − jTf − cj Tc )
(6)
i=−∞ j=0
+bi g(t − iTs − jTf − cj Tc − Td ) +n(t),
rBPPM (t) =
∞ NX
f −1
X
p
Ep
g(t − iTs − jTf − cj Tc − di TBP P M )
i=−∞ j=0
+n(t),
(7)
where n(t) is additive white Gaussian noise (AWGN) with zero mean and σn2 =
No /2 variance, and g(t) is interpreted as the aggregate channel after convolving
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
Modulated Pulse
Position
Symbol i = 0 ;
Unmodulated Pulse
Position
Bit b0 = −1
Pulse
Symbol i = 1 ;
47
Channel Delay
Spread
Bit b1 = 1
(a)
Tf
Ts
2Ts
Ts
2Ts
Ts
2Ts
(b)
Td
Tf
(c)
TBP P M
Tf
Figure 2: An example of transmitted sequences for two symbols, where b0 = −1,
b1 = 1, Nf = 2, and TH is not considered, (a) BPSK IR-UWB system (b) TR IRUWB system, where Td is the delay between reference and modulated pulses (c)
BPPM IR-UWB system, TBP P M is the BPPM shift between two pulse positions.
48
Part I
the multipath channel with the transmitted pulse, i.e.,
g(t) =
=
p(t) ∗ h(t)
K−1
X
k=0
αk p(t − τk ).
(8)
The duration of g(t) is defined as Tg = Tp + Tmds , where Tp is the pulse duration
and Tmds is the maximum delay spread, usually called maximum excess delay, of
the channel. Since delay spread should be taken into account to avoid inter-frame
interference (IFI) and inter-pulse interference (IPI), it can be achieved if BPPM,
BPSK and TR modulations comply with the conditions Tg ≤ TBP P M , Tg ≤ Tf
and Tg ≤ Td , respectively. Fig. 1 shows the system model, and Fig. 2 (a), (b)
and (c) show examples of transmitted sequences using the BPSK, TR and BPPM
modulations, respectively. It should be noted the BPSK modulation is able to
achieve twice the data rate if the separation between the possible positions is
kept equal for the three modulations.
3
UWB Channel
In the following subsections, the measurement procedure of the UWB channels
measured in an industrial environment and characteristics of these channels are
given briefly.
Measurement Procedure
The UWB channel measurement campaign1 had been conducted in MAX-Lab,
Lund, Sweden, in a medium-sized industrial environment depicted in Fig. 3. The
hall has a floor area of 94 × 70 m and a ceiling height of 10 m. The hall contains
many metallic objects, e.g., pipes, pumps and cylinders. The measurements were
performed in the frequency domain using a vector network analyzer (VNA) in
conjunction with virtual antenna arrays. The frequency range measured was from
3.1 to 8.0 GHz and 2001 frequency points were measured, resulting in a delay
resolution of 0.2 ns, and a maximum delay of 408 ns corresponding to a 122 m
path delay. Omnidirectional conical monopole antennas were used at transmitter
and receiver, respectively. The use of virtual antenna arrays allows to create a
virtual MIMO system of 7 × 7 antenna positions. The antenna separation was 50
mm, i.e., more than half a wavelength at the minimum frequency in order to obtain spatially independent channels. A total of sixteen peer-to-peer (P-P) NLOS
1 The measurement campaign was performed as a part of my master thesis, under the
supervision of Dr. Fredrik Tufvesson, at Lund University, Sweden.
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
49
Figure 3: A view of the industrial environment for UWB channel measurements.
positions were measured at four different locations with TX-RX separations of 2
m, 4 m, 8 m and 16 m at each location. Thus, for each measurement, 49 independent realizations of the channel were measured over a local area resulting in a
total of 49 × 16 independent NLOS channel realizations. A complete description
of the measurement setup and an analysis of the model parameters is given in [2].
Channel Delay Profiles
The measured transfer functions are transformed to the delay domain using inverse Fourier transformation with a Hanning window applied. The power delay
profiles (PDPs) calculated from the measurements on one antenna pair of the
virtual array are called instantaneous PDPs, where the PDP from the nth transmitter to the mth receiver is defined as [2]
P DP (τ, m, n) = |h(τ, m, n)|2 .
(9)
Averaged power delay profiles (APDPs) are obtained from 49 instantaneous
PDPs corresponding to different combinations of transmitter and receiver positions on the virtual array for each of the measurement positions. Thus, APDPs
50
Part I
−5
−10
[dB]
−15
−20
−25
−30
−35
0
20
40
60
80
100
120
140
160
180
200
Delay [ns]
Figure 4: Averaged power delay profiles of MG1 averaged over all channel realizations.
−5
−10
[dB]
−15
−20
−25
−30
−35
0
20
40
60
80
100
120
140
160
180
200
Delay [ns]
Figure 5: Averaged power delay profiles of MG2 averaged over all channel realizations.
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
51
are obtained as [2]
AP DP (τ ) =
M
N
1 XX
P DP (τ, m, n).
M N m=1 n=1
(10)
The analysis of APDPs for P-P NLOS measurements has shown the following
effects [2]:
1. For shorter distances (and a few of longer distance measurements), the first
component is the strongest. A similar observation was also made in the
measurement results presented in [3] for industrial environments.
2. The strong first component is followed by a minimum in the APDP indicating that the MPCs arrive in clusters.
3. For many of the measurements at larger distances, the strongest component
arrives 10 − 40 ns after the first arriving component.
4. For longer distances, APDPs have “soft-onset” shape as also seen in [3].
5. It has been observed that some specific MPCs carry significant power for
larger TX-RX separations.
6. It is also observed that nearly all resolvable delay bins contain significant
energy
The measured channel responses are divided into two groups based on the TXRX separation. The Measurement Group 1 (MG1) covers the measured channel
responses over the distances in the range of 2 to 8 m, while the Measurement
Group 2 (MG2) incorporates the measured channel responses with TX-RX separation from 10 to 16 m, as shown in Figs. 4 and 5, respectively. The total number
of independent realizations for MG1 and MG2 are 490 and 294, respectively.
4
4.1
RAKE Receiver
RAKE Architecture
A RAKE receiver consists of a bank of correlators, also called fingers, and each
finger is matched (synchronized) to a particular multipath component to combine the received multipaths coherently [10], see Fig. 6. Since a large number of
MPCs impinge on the UWB receiver, the number of MPCs that can be utilized in
a typical RAKE combiner is limited by the device’s power consumption budget,
hardware resources, and the channel estimation [12]. Secondly, each multipath
52
Part I
R
(·)dt
vtemp (t − τ0 )
R
rBPSK (t)
P
(·)dt
vtemp (t − τ1 )
R
β0
zi
bi
β1
(·)dt
vtemp (t − τK−1 )
βK−1
Figure 6: Architecture of the RAKE receiver for IR-UWB system.
component undergoes a different channel in UWB systems, which causes distortion in the received pulse shape and makes the use of a single LOS path signal
as a suboptimal template [13].
Due to wide bandwidth of UWB signals, the sampling rate at the RAKE
receiver is crucial for both performance and implementation complexity. An alldigital implementation requires Nyquist rate sampling using high speed analog
to digital converters (ADCs), which not only increases the complexity but also
power consumption. On the other hand, in order to enable symbol (or frame)
rate sampling, the received signal is correlated with a symbol (or frame) length
template signal [14]. However, implementation complexity of the RAKE is still
high as it requires generation of a long analog template signal matched to the
received signal. Alternatively, RAKE receiver my be realized using chip rate
sampling, see Fig. 7, and a sample-spaced correlator template is used in which the
channel is assumed to have taps at an integer multiple of the chip duration [10,15].
In order to accomplish channel estimation, [15] has proposed a technique in which
the sample-spaced projections of the received components are estimated to be
used in the RAKE combiner.
4.2
RAKE Types
A tapped-delay line channel with K number of delays provides us with K replicas of the same transmitted signal at the receiver [10]. Hence, a receiver that
processes the received signal in an optimum manner will achieve the performance
of an equivalent K th order diversity system [10]. In practice, only a subset of the
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
53
total number of resolved MPCs is used in the RAKE receivers [12]. The RAKE
types based on the number of MPCs used are given as follows [12]
• All-RAKE (ARake): The RAKE receiver which combines all the K resolved
MPCs is called an All-RAKE.
• Selective RAKE (SRake): The SRake receiver searches for the M best paths
out of K resolved MPCs to use them as RAKE fingers.
• Partial RAKE (PRake): The PRake receiver uses the M first arriving paths
out of K resolvable MPCs.
4.3
RAKE Combining Schemes
The outputs of the RAKE correlators (fingers) are passed to the combiner to add
up the signal coherently using the available channel state information. The RAKE
receiver uses well-known combining schemes such as maximal ratio combining
(MRC) and equal gain combining (EGC).
Maximal Ratio Combining (MRC)
If MRC technique is used, it is essential to estimate the amplitudes of the received MPCs to weigh each finger. The performance and optimality of the
MRC consequently depend upon the receiver’s estimate of the channel [13]. Let
β = [β0 , β1 , · · · , βK−1 ] be the RAKE combining weights which may be different
for different RAKE types.
• In the case of an ARake, the combining weights are chosen equal to the
fading coefficients of the channel, α̃ = [α̃0 , α̃1 , · · · , α̃K−1 ], i.e.,
β = α̃
(11)
• For SRake, if the set of indices of the M best fading coefficients with largest
amplitude is denoted by S, then the combining weights β are chosen as
follows [16]
α̃k ,
k∈S
β=
(12)
0,
k 6∈ S
• For PRake, using the first M MPCs, the weights of the MRC combining
are given by [16]
α̃k ,
k = 0, · · · , M − 1
β=
(13)
0,
k = M, · · · , K − 1
where M ≤ K.
54
Part I
rBPSK (t)
R
(·)dt
vCS-temp (t)
Tc
Tc
βK−1
βK−2
β1
β0
P
bi
Figure 7: Architecture of the RAKE receiver for a discrete-time channel using
chip rate sampling.
Equal Gain Combining (EGC)
In case of EGC scheme, all the tracked MPCs are weighed with their corresponding signs and combined [5]. This implies that the EGC combining scheme only
requires the phase of the fading channel [5, 17]. In a carrier-less UWB system,
determining the phase is even simpler because the phase is either 0 or π, to account for pulse inversion [18]. In a practical system, performing EGC is simpler
than MRC but there is a performance trade-off [17].
4.4
BER Performance Analysis
All fingers (correlators) of the RAKE use a delayed version of the template signal
with a delay chosen as an integer multiple of the chip duration. Assuming a
discrete-time channel with chip spaced channel taps, an equivalent single correlator RAKE with chip rate sampling and a sample-spaced template signal may
be employed. Considering the ith symbol of the received signal, the chip rate
samples obtained at the output of the correlator are written as
yi,j,k =
Z
(i+1)Ts +jTf +cj Tc +(k+1)ts
rBPSK (t)vCS-temp (t)dt,
(14)
iTs +jTf +cj Tc +kts
where ts is the sampling interval, and vCS-temp (t) is assumed to be a normalized
chip-spaced or sample-spaced template signal and it is represented for the ith
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
55
information symbol as
vCS-temp (t) =
s
1
Nf Nc
(i+1)Nf −1 Nc −1
X
j=iNf
X
k=0
p(t − jTf − cj Tc − kts ),
(15)
and rBPSK (t) is the received BPSK signal, i.e.,
∞ NX
f −1
X
p
rBPSK (t) =
Ep
bi g(t − iTs − jTf − cj Tc ) + n(t).
(16)
i=−∞ j=0
It is assumed that all paths are resolvable, that is, the minimum time between any two paths is larger than the pulse width [10]. Let us define the crosscorrelation function between g(t) and p(t) as [13]
Z ∞
α̃(τ ) =
g(t)p(t − τ )dt,
(17)
−∞
where α̃(τ ) = 0 if τ ≤ −Tp or τ ≥ Tg . If there is a perfect match of the received
signal with the reference signal, zero inter-frame and inter-symbol interference,
then the output of the k th finger for j th frame of the ith symbol is written, in
discrete time, as
p
(18)
yi,j,k = Ep bi α̃i,j,k + ηi,j,k ,
(19)
where the last term ηi,j,k is the noise at the output of the correlator.
Further, the diversity combining using the weight vector β and summation
over Nf frames yields the decision statistic for the ith symbol as
ZRAKE,i
=
Nf −1 K−1
Nf −1 K−1
X X
X X
p
Ep bi
βk α̃i,j,k +
βk ηi,j,k .
j=0 k=0
(20)
j=0 k=0
For ARake receiver with MRC combining and under perfect channel estimation,
the decision statistics is approximated as
ZRAKE,i =
K−1
K−1
X
X
p
Nf Ep bi
α̃2k +
α̃k ηk .
k=0
(21)
k=0
To determine the BER at the output of the RAKE, the conditional mean and
variance of the decision statistic at the output of the RAKE are evaluated from
Eq. (21) as
K−1
X
p
E{ZRAKE |(α, τ )} = Nf Ep
α̃2k ,
(22)
k=0
56
Part I
Var{ZRAKE |(α, τ )} = σn2
K−1
X
α̃2k .
(23)
k=0
In case of BPSK modulation, according to [1,13], the BER expression conditioned
on a particular channel realization is given by
s
!
E{ZRAKE |(α, τ )}2
Pe,RAKE |(α, τ ) = Q
Var{ZRAKE |(α, τ )}
v
u
P
2 
u
K−1 2
N E

u
k=0 α̃k
t f p

= Q
P
K−1


σn2 k=0 α̃2k
v

u
u 2Nf Ep K−1
X
= Q t
α̃2k 
No
k=0
v

u
u 2Es K−1
X
= Q t
α̃2k  ,
No
(24)
k=0
√ R∞
2
where Q(·) is the standard function Q(x) = 1/ 2π x e−t /2 dt [13].
5
5.1
Conventional TR Receiver
TR Architecture
In a TR receiver, the received signal is passed through a bandlimiting filter with
impulse response f (t), which is proportional to p(−t). Hence, if free-space propagation is assumed, the bandlimiting filter corresponds to a matched filter [19].
For simplicity, it is assumed that the shape of the received pulse is the same as the
transmitted pulse. However, in practice, as the propagation and antenna effects
may distort the received pulses, a bandlimiting filter of sufficiently wide bandwidth is usually used to remove the out-of-band noise from the received signal.
The resulting signal after passing through a bandpass filter is the convolution of
f (t) with rTR (t), i.e., r̃TR (t) = f (t) ∗ rTR (t), and it is written as
r̃TR (t) =
∞ NX
f −1
X
p
Ep
g̃(t − iTs − jTf − cj Tc )
i=−∞ j=0
+bi g̃(t − iTs − jTf − cj Tc − Td ) + ñ(t),
(25)
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
rTR (t)
BPF
r̃TR (t)
R t+TI
f (t)
t
j=0
Timing
Delay
Td
b̂i
PNf −1
(·)dt
57
r̃TR (t − Td )
Figure 8: Architecture of the conventional TR receiver.
Frame 2
Frame 1
r̃TR (t)
Ts
Tf
Td
r̃TR (t − Td )
Ts
SR
NOR
SR
NOR
TI
TI
Figure 9: An illustration of the correlation in the TR receiver, where SR and
NOR stand for signal region and noise-only region, respectively, while for symbol
i = 0, bit b0 = −1 and Nf = 2.
where g̃(t) and ñ(t) are filtered versions of g(t) and n(t), respectively.
Subsequently, the received signal is delayed by Td using an analog delay element branch. The signal r̃TR (t) and a delayed version of this signal are correlated and the outputs of the correlator are summed over Nf frames to acquire
the decision statistic, see Fig. 8. The decision statistic for the ith bit of TR
signaling [20–22] is written as
ZTR,i =
(i+1)Nf −1 Z jT +cj Tc +T +TI
f
d
X
j=iNf
jTf +cj Tc +Td
r̃TR (t)r̃TR (t − Td )dt,
(26)
where TI is the integration interval in each frame, 0 < TI ≤ Tg . The integration
interval determines the actual number of MPCs Kp (≤ K) captured by the TR
receiver [20].
58
Part I
The correlation process is depicted in Fig. 9, where the additive noise is excluded for simplicity in the presentation [23]. The figure shows that the output of the correlator is divided into signal regions (SR) and noise-only regions
(NOR) [23]. Thus, the choice of integration interval becomes a crucial parameter
as the integration should be performed only over the signal regions. It is observed
that, increasing the integration time improves performance up to a certain point,
after which the energy capture saturates and only noise is added [10]. It means
that the selection of an optimum integration interval can avoid the accumulation
of noise in the decision variable. The bit decision is made using conventional
detection as b̂i = sgn(ZTR,i ), where sgn(·) stands for the sign function.
5.2
BER Performance Analysis
The decision statistic for the ith symbol given in Eq. (26) is written as a sum of
the terms as [20]
ZTR,i = Z1,i + Z2,i + Z3,i + Z4,i ,
(27)
where the terms Z1 , Z2 , Z3 and Z4 are given by
Z1,i
(i+1)Nf −1 Z jT +cj Tc +T +TI
f
d
X
=
j=iNf
jTf +cj Tc +Td
Ep bi g̃(t − jTf − cj Tc )g̃(t − jTf − cj Tc − Td )dt,
Z2,i
=
(i+1)Nf −1 Z jT +cj Tc +T +TI
f
d
X
j=iNf
jTf +cj Tc +Td
p
Ep bi g̃(t − jTf − cj Tc )ñ(t − jTf − cj Tc − Td )dt,
Z3,i
=
(29)
(i+1)Nf −1 Z jT +cj Tc +T +TI
f
d
X
j=iNf
jTf +cj Tc +Td
p
Ep g̃(t − jTf − cj Tc − Td )ñ(t − jTf − cj Tc )dt,
Z4,i
(28)
=
(i+1)Nf −1 Z jT +cj Tc +T +TI
f
d
X
j=iNf
(30)
jTf +cj Tc +Td
ñ(t − jTf − cj Tc )ñ(t − jTf − cj Tc − Td )dt.
(31)
PKp −1 2
The signal component Z1,i in Eq. (28) is approximated as Nf Ep bi k=0
αk ,
where Kp is the number of captured MPCs within the integration window. The
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
59
noise is zero mean Gaussian and independent of g̃(t), so the noise-signal terms
Z2,i and Z3,i in Eq. (29) and Eq. (30) are considered as zero mean Gaussian
random variables. The noise signal terms are combined together and the variance
PKp −1 2
of this linear noise term is Nf Ep No k=0
αk . The noise-by-noise product term
Z4,i in Eq. (31) is the sum of Nf independent random variables for different
values of j. Using the central limit theorem, Z4,i is modeled as a Gaussian
random variable, assuming that the time-bandwidth product W TI is large [24].
If the noise is assumed to be uncorrelated, Z4,i is zero mean and its variance is
No2 Nf W TI /2. Hence, the decision statistic ZTR is a Gaussian random variable
under each channel realization [20,24]. The conditional mean and variance of the
decision statistic are given by [20]
E{ZTR |(α, τ )} = Nf Ep
Var{ZTR |(α, τ )} = No Nf Ep
Kp −1
X
α2k ,
(32)
k=0
Kp −1
X
α2k +
k=0
No2 Nf W TI
.
2
(33)
Thus, under the Gaussian approximation, the conditional BER of TR signaling
is written as [20–22]
Pe,TR |(α, τ ) =
=
=
=
s
Q

2
E {ZTR |(α, τ )} 
Var{ZTR |(α, τ )}
v
u
u
PKp −1 2 2
u
Nf Ep k=0 αk
u
t
Q
PKp −1

N 2N W T
 No Nf Ep k=0 α2k + o f2 I
v
u
u
u
u 1
t
Q
 2

v
u
u
u
u 1
t
Q
 2

2Nf Ep
No
2Nf Ep
No
Es
No
PKp −1
α2k

2









PKp −1 2

α
+
N
W
T
f
I
k=0
k
Es
No
k=0
PKp −1
α2k
2



.
PKp −1 2

k=0 αk + Nf W TI 
k=0
(34)
60
Part I
From Eq. (34), we see that the amount of received energy captured by the
TR receiver depends on the time-bandwidth product W TI , as Kp increases with
the increase in time-bandwidth product [20]. When Kp = K, increasing W TI
further only increases the noise in the receiver [20], as shown by the denominator
in Eq. (34). The instantaneous received SNR of TR signaling can be defined as
γTR
Kp −1
2Nf Ep X 2
=
αk .
No
(35)
k=0
Then, Eq. (34) can be written as
Pe,TR |(α, τ ) = Q
6
s
2
1
γTR
2 γTR + Nf W TI
!
.
(36)
Conventional Energy Detector
6.1
ED Architecture
In the conventional ED, the received signal is also passed through a bandlimiting
filter with impulse response f (t). The resulting signal after passing through a
bandpass filter is the convolution of f (t) with rBPPM (t), i.e., r̃BPPM (t) = f (t) ∗
rBPPM (t), and it is written as
f −1
∞ NX
X
p
Ep
g̃(t − iTs − jTf − cj Tc − di TBP P M ) + ñ(t), (37)
r̃BPPM (t) =
i=−∞ j=0
where g̃(t) is the bandlimited aggregate channel and ñ(t) is bandlimited noise
at the output of the filter. The output of the filter is passed through a squarelaw device and an integrator, see Fig. 10. The decision metrics for each of the
two pulse positions of orthogonal BPPM signal is obtained by integrating the
corresponding energy of pulse positions in the first and second half of each frame.
Without loss of generality, it is henceforth assumed that the detection of the ith
symbol is considered. The integrated energy is obtained by sampling the output
of the integrator twice per frame, i.e., after the two possible positions of the
symbol bi . The sampled energy estimates for the two positions of the ith symbol
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
BPF
r̃BPPM (t)
rBPPM (t)
R t+TI
(·)2
f (t)
t
(·)dt
2
r̃BPPM
(t)
+
PNf −1
61
b̂i
j=0
−
Timing
Figure 10: Architecture of the conventional ED receiver.
are written as
ZED,i0
=
(i+1)Nf −1 Z jT +cj Tc +TI
f
X
j=iNf
ZED,i1
=
[r̃BPPM (t)]2 dt,
(i+1)Nf −1 Z jT +cj Tc +TBP P M +TI
f
X
j=iNf
(38)
jTf +cj Tc
[r̃BPPM (t)]2 dt,
(39)
jTf +cj Tc +TBP P M
where the sub-indices “ED, i0” and “ED, i1” denote energy estimates for positions
“0” and “1”, respectively, of the ith symbol. The length of the integration interval
determines the amount of multipath energy and the amount of noise captured
by the receiver, and its value ranges between 0 < TI ≤ TBP P M . The decision
statistic in the conventional ED receiver is formed as
ZED,i = ZED,i0 − ZED,i1 ,
(40)
and a threshold circuit decides in favor of the pulse position which carries greater
energy, i.e.,
b̂i = sgn(ZED,i ).
(41)
6.2
BER Performance Analysis
The sampled values obtained from the integration over duration TI , for Nf
frames, can also be seen as sums of 2Nf W TI virtual samples due to the sampling theorem. The energy estimates for each of the two pulse positions are the
results obtained from the summation over 2Nf W TI virtual samples. Assuming that hypothesis H0 is true, i.e., bi = −1 (equivalently, di = 0), the decision
statistic variables, ZED,i0 |H0 incorporating signal-plus-noise region and ZED,i1 |H0
incorporating noise-only region, are approximated as Gaussian random variables
provided that 2Nf W TI is large. The mean and variance of the random variable
62
Part I
ZED,i0 |H0 are written as [25]
E{ZED,i0 |H0 } =
Var{ZED,i0 |H0 } =
No Nf W TI + Nf Ep
Kp −1
X
α2k ,
(42)
k=0
No2 Nf W TI
+ 2No Nf Ep
Kp −1
X
α2k .
(43)
k=0
Similarly, the mean and variance of the random variable ZED,i1 |H0 are written
as [25]
E{ZED,i1 |H0 }
Var{ZED,i1 |H0 }
= No Nf W T I ,
= No2 Nf W TI .
(44)
(45)
Thus, the conditional mean and variance of the decision statistic are given by
E{ZED |(α, τ )} = Nf Ep
Var{ZED |(α, τ )} =
2No2 Nf W TI
Kp −1
X
α2k ,
(46)
k=0
+ 2No Nf Ep
Kp −1
X
α2k .
(47)
k=0
and the conditional BER of BPPM signaling for the ED is written as [21, 22]
s

2
E {ZED |(α, τ )} 
Pe,ED |(α, τ ) = Q 
Var{ZED |(α, τ )}

v
u
u
PKp −1 2 2
u

Nf Ep k=0 αk
u

t


= Q
PKp −1 2

2
 2No Nf Ep k=0 αk + 2No Nf W TI 
v
u
u
u
u 1
t
= Q
 2

v
u
u
u
u 1
t
= Q
 2

N f Ep
No
Es
No
N f Ep
No
PKp −1
α2k

2



PKp −1 2

α
+
N
W
T
f
I
k=0
k
Es
No
k=0
PKp −1
α2k
2



.
PKp −1 2

k=0 αk + Nf W TI 
k=0
(48)
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
63
The instantaneous received SNR of the ED can be defined as
γED =
Kp −1
Nf Ep X 2
αk .
No
(49)
k=0
Then, Eq. (48) can be written as
Pe,ED |(α, τ ) = Q
s
2
γED
1
2 γED + Nf W TI
!
.
(50)
It is noteworthy that the BER expression of the BPPM ED is identical to that of
the BPSK TR receiver. This important result stems from the fact that, though
bipolar BPSK TR modulation has 3 dB advantage over unipolar BPPM, the
energy per pulse in the TR system is half. The reduced signal energy is compensated by a reduced noise energy in the TR receiver due to uncorrelated noise
terms in the correlation, which leads to its performance being equivalent to the
BPPM ED [13,21,22]. Obviously, if the energy per pulse in both systems is equal,
the TR receiver will exhibit 3 dB better performance.
In Table 1, comparison of the coherent and non-coherent receivers is presented
in terms of capability to detect bipolar modulation, channel estimation requirement, necessity to use analog delay element, sensitivity to synchronization errors
and implementation complexity of the receivers. As the conventional ED neither
requires analog delays and locally generated reference nor channel estimation, its
complexity is referred to as “Low”, and complexities of the other receivers are
described relative to it.
7
Performance Evaluation
In order to compare the performance of coherent and non-coherent receivers, the
IR-UWB systems are simulated for an indoor NLOS industrial environment. As
described in previous sections, BPSK modulation is used for the RAKE and the
TR, while BPPM modulation is employed for the ED receiver. The second derivative of the Gaussian function is used for pulse shaping with Tp = 2 ns. Keeping
the separation between the possible positions equal, an uncoded data rate of
Rb = 1 Mbps is achieved by setting Nf = 10 and Tf = 100 ns for BPSK, whereas
Rb = 0.5 Mbps is achieved with Nf = 10 and Tf = 200 ns for the BPPM and the
TR modulation. In addition, TI = 50 ns for all the receivers, TBP P M = 100 ns for
the ED, and Td = 100 ns for the TR receiver. For each level of SNR, i.e., Eb /No ,
performance over the NLOS channels is evaluated using 490 and 294 available
channel realizations of MG1 and MG2 channels, respectively. Moreover, for fair
comparison, energy assigned per symbol is kept equal for all the systems. The
64
Part I
Table 1: Comparison of the coherent and non-coherent receivers
Bipolar
ARake
PRake
SRake
TR
ED
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No
No
No
No
No
Yes
No
Sensitive
Sensitive
Sensitive
Less
Less
Sensitive
Sensitive
High
Low
Modulation
Channel
Estimation
Analog
Delay
Synchronization
Error
Implementation
Very
Complexity
High
Medium
High
P 2
energy of each channel impulse response is normalized as
αl = 1. The system
is assumed to be synchronized and there is no IFI in the received signal. The
sample-spaced projections of the received components are estimated [15] for the
RAKE with chip rate sampling assuming a perfect knowledge of the channel.
7.1
PRake versus SRake
Figs. 11 and 12 present the results of PRake and SRake receivers with MRC
combining implementing a different number of fingers utilizing the channels MG1
and MG2, respectively. It is depicted in the figures that the BER is very high with
five PRake fingers (referred to as PRake-5) and a single finger SRake (referred
to as SRake-1) shows better performance particularly over MG2. To further
improve the BER, PRake need to use on the order of twenty fingers, and this
increases the complexity of the receiver significantly. The results demonstrate
a 3 − 6 dB performance improvement using five finger SRake over five finger
PRake. The results for MG1 indicate that it is possible to achieve a BER of 10−3
with Eb /No = 16 dB using the SRake-5; while it provides the same BER with
Eb /No = 13.5 dB for channel MG2. Moreover, the performance of SRake-10 and
SRake-20 is also 2−3 dB better than corresponding PRake-10 and PRake-20 over
both MG1 and MG2. It should be noted that the BER of twenty finger SRake
approaches the BER of the ARake receiver, which uses fifty fingers to combine
all the sample-spaced components of the received signal. These results depict
a significant performance improvement associated with the SRake. However, it
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
65
0
10
−1
BER
10
−2
10
PRake-1
SRake-1
PRake-5
SRake-5
PRake-10
SRake-10
PRake-20
SRake-20
ARake
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 11: BER curves of the ARake and 1, 5, 10, and 20 finger PRake and
SRake receivers using MRC combining on MG1 channel.
0
10
−1
BER
10
−2
10
PRake-1
SRake-1
PRake-5
SRake-5
PRake-10
SRake-10
PRake-20
SRake-20
ARake
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 12: BER curves of the ARake and 1, 5, 10, and 20 finger PRake and
SRake receivers using MRC combining on MG2 channel.
66
Part I
0
10
−1
BER
10
−2
10
PRake-5 EGC
PRake-5 MRC
SRake-5 EGC
SRake-5 MRC
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 13: BER curves of PRake-5 and SRake-5 using MRC and EGC combining
on MG1 channel.
should be mentioned that the complexity of the SRake stems from the fact that
it needs accurate channel estimation to search for the best fingers that carry the
maximum energy.
The results in Figs. 11 and 12 demonstrate that the performance of a PRake
receiver largely depends on the shape of the channel delay profile. As the PRake
captures only the first arriving components, the performance severely degrades
on the MG2 channel as compared to the MG1. This is quite intuitive as PDP of
the MG2 has a shape of first increasing and then decreasing PDP, see Fig. 5. In
addition, there are some strong components in the PDP of the MG2 indicating
the arrival of MPCs in clusters. On the other hand, the MG1 channel has a
decreasing PDP with embedded strong components at shorter delays indicating
the onset of clusters of MPCs. In addition, the saturation effects are observed
by using more than ten fingers of the SRake and twenty fingers of the PRake
owing to the fact that the rest of the components do not carry significant energy.
It can be concluded that any further increase in the number of fingers increases
complexity of the system, while providing only marginal SNR gain.
7.2
EGC versus MRC
The effect of RAKE combining scheme is studied in Figs. 13 to 16 for both MG1
and MG2 channels. The BER is compared using five and twenty fingers of both
types of RAKE using EGC and MRC combining schemes. The results show that
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
67
0
10
−1
BER
10
−2
10
PRake-5 EGC
PRake-5 MRC
SRake-5 EGC
SRake-5 MRC
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 14: BER curves of PRake-5 and SRake-5 using MRC and EGC combining
on MG1 channel.
0
10
PRake-20 EGC
PRake-20 MRC
SRake-20 EGC
SRake-20 MRC
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 15: BER curves of PRake-20 and SRake-20 using MRC and EGC combining on MG1 channel.
68
Part I
0
10
PRake-20 EGC
PRake-20 MRC
SRake-20 EGC
SRake-20 MRC
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 16: BER curves of PRake-20 and SRake-20 using MRC and EGC combining on MG1 channel.
performance of the MRC combining is about 1 − 2 dB better than the EGC for
the PRake receiver. Moreover, the MRC performs better than the EGC as the
number of PRake fingers increase. In contrast, the BER using the EGC and the
MRC is equivalent in case of the SRake. This observation leads to an important
conclusion that the complexity of the SRake may be minimized to some extent,
without a significant performance degradation, by replacing the MRC with the
EGC combining.
7.3
Coherent versus Non-Coherent
To compare coherent and non-coherent receivers, Figs. 17 and 18 show the BER
results of the ED and the TR with the PRake and the SRake using measured
channels MG1 and MG2, respectively. It should be mentioned that, in order
to consider practical RAKE receivers of moderate implementation complexity,
five fingers of the PRake and the SRake are used to conduct these evaluations.
Figures illustrate that the BER curves of the BPPM ED and the BPSK TR
resemble, which verifies the BER analysis presented previously. Compared to the
five finger PRake receiver, the non-coherent ED and TR receivers show better
performance in the high SNR region, while opposite is true in the low SNR region.
In addition, the non-coherent ED and TR receivers outperform five finger SRake
in the high SNR region; however, this is only true for MG1 channel which has a
decreasing PDP with embedded strong components at shorter delays. The reason
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
69
0
10
ED
TR
PRake-5
SRake-5
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 17: BER curves of ED, TR, PRake-5 and SRake-5 using MRC combining
on MG1 channel.
0
10
ED
TR
PRake-5
SRake-5
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 18: BER curves of ED, TR, PRake-5 and SRake-5 using MRC combining
on MG2 channel.
70
Part I
lays in the fact that the coherent receivers use clean locally generated reference
signals in the correlator, which enables them to beat the non-coherent receivers
in the low SNR regime. On the other hand, as the effect of multipath becomes
dominant in the high SNR region, the non-coherent receivers are able to collect
the received energy effectively. Due to the same reason, increasing the length
of the integration interval of the non-coherent receivers is effective to improve
the BER in the high SNR region, whereas the opposite is valid in the low SNR
region.
8
Conclusions
The BER analysis and performance evaluation of the RAKE receivers and the
non-coherent ED and TR receivers is presented. The results using measured
NLOS channels in an industrial environment show that only a moderate number
of fingers of the SRake (i.e., about five fingers) are required to achieve an acceptable BER (i.e., about 10−3 ). On the other hand, the PRake requires at least 20
fingers to achieve the same BER performance, which makes it impractical for such
scenarios. The results demonstrate that the SRake receivers always outperform
the PRake receivers using the same number of fingers and the same combining
scheme. In addition, it is observed that a large number (i.e., about twenty) of
RAKE fingers do not provide gain as additional MPCs do not carry significant
energy. It is also observed that the performance of the RAKE receivers highly depends on the TX-RX separation. From the comparison of the RAKE combining
schemes, it is concluded that the difference in performance of the MRC and the
EGC is not that significant for the SRake, while the PRake has a considerably
better performance using the MRC. However, if the first arriving components
are not the strongest, which is typical for larger TX-RX separations, only the
SRake receiver with either the EGC or the MRC combining gives acceptable
performance.
Finally, comparison between the ED and TR receivers with the PRake and
SRake receivers demonstrates that BER curves of the non-coherent ED and TR
receivers surpass even five finger SRake in the high SNR region if the channels
have strong multipath components at shorter delays. Hence, the low-complexity
non-coherent receivers may be used as a promising alternative to the complex
coherent RAKE receivers for low power low-data rate IR-UWB systems. The
comparative evaluations also show that performance of the receivers depends to
a large extent on the shape of the power delay profile of the underlying channel.
This conclusion also emphasizes the importance of using realistic channels for
system design and evaluation.
Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB
Systems using Multipath Channels for Industrial Environments
71
Acknowledgment
The author would like to acknowledge and thank Dr. Fredrik Tufvesson and
Dr. Johan Kåredal from Lund University, Sweden, and Mr. Asim Ali Ashraf, for
their collaboration and support in the measurement campaign.
Bibliography
[1] J. G. Proakis Digital Communications, 4th ed. Boston: McGraw-Hill, 2001
[2] M. G. Khan, A. A. Ashraf, J. Karedal, F. Tufvesson, and A. F. Molisch,
“Measurements and Analysis of UWB Channels in Industrial Environments,” in Proc. Wireless Personal Multimedia Communications (WPMC),
Aalborg, Denmark, Sept. 2005
[3] J. Karedal, S. Wyne, P. Almers, F. Tufvesson, and A. F. Molisch, “UWB
channel measurements in an industrial environment”, in Proc. IEEE Globecom, 2004
[4] J. Karedal, S. Wyne, P. Almers, F. Tufvesson, and A. F. Molisch, “Statistical
analysis of the UWB channel in an industrial environment,” in Proc. IEEE
Vehicular Technology Conference, fall 2004
[5] A. Rajeswaran, V. S. Somayazulu, J. R. Foerster, “RAKE performance for a
pulse based UWB system in a realistic UWB indoor channel,“ Proc. IEEE International Conference on Communications (ICC ’03) , vol.4, pp. 2879–2883,
11-15 May 2003
[6] B. Mielczarek, M. Wessman, and A. Svensson, “Performance of coherent
UWB RAKE receivers with channel estimators,” Proc. IEEE Vehicular
Technology Conference, vol. 3, pp. 1880–1884, Oct. 2003
[7] G. Durisi, S. Benedetto, “Performance of coherent and noncoherent receivers
for UWB communications ,” Proc. IEEE International Conference on Communications (ICC 2004), vol. 6, pp. 3429–3433, June 20-24, 2004
[8] S. Gezici, H. Kobayashi, H. V. Poor and A. F. Molisch, “Optimal and suboptimal linear receivers for time-hopping impulse radio systems,” Proc. IEEE
Wireless Communications and Networking Conference (WCNC 2004), vol.
2, pp. 908–913, Atlanta, GA, March 2004
[9] M. A. Rahman, S. Sasaki, Z. Jie, S. Muramatsu, H. Kikuchi, “Performance
evaluation of RAKE reception of ultra wideband signals over multipath
channels from energy capture perspective,” International Workshop on Ultra
Wideband Systems, 2004. Joint with Conference on Ultrawideband Systems
and Technologies, pp. 231–235, May 2004
73
74
BIBLIOGRAPHY
[10] J. H. Reed et. al. An Introduction to Ultra Wideband Communication Systems, Prentice Hall, 2005
[11] A. F. Molisch UWB Propagation Channels, Book chapter 1, pp.1, 2005
[12] D. Cassioli, M. Z.Win, F. Vatalaro, and A. F. Molisch, “Performance of lowcomplexity Rake reception in a realistic UWB channel,” Proc. IEEE ICC’03,
vol.2, pp.763–767, 2003
[13] D. J. Choi and W. E. Stark, “Performance of ultra-wideband communications with suboptimal receivers in multipath channels,”IEEE Journal of
Sleceted Areas Comm., vol. 20, no. 9, Dec. 2002, pp. 1754–1766
[14] A. F. Molisch et al., “An efficient low cost time-hopping impulse radio for
high data rate transmission,” Proc. IEEE 6th International Symposium on
Wireless Personal Multimedia Communications (WPMC 2003), Yokosuka,
Kanagawa, Japan, Oct. 19–22, 2003
[15] V. Lottici, A. D’Andrea, U. Mengali, “Channel estimation for ultrawideband communications,” IEEE Journal on Selected Areas in Communications, 2002, vol. 20, no. 9, pp. 1638–1645
[16] S. Gezici, H. Kobayashi, H. V. Poor and A. F. Molisch, “Performance evaluation of impulse radio UWB systems with pulse-based polarity randomization
in asynchronous multiuser environments,” Proc. IEEE Conference on Ultra
Wideband Systems and Technologies (UWBST 2004), Kyoto, Japan, May
18–21, 2004
[17] F. Rajwani, N. C. Beaulieu, “Simplified bit error rate analysis of PAPMUWB with MRC and EGC in lognormal fading channel,” Proc. IEEE
ICC’05, vol. 5, pp. 2886–2889, May 2005
[18] J. R. Foerster, “The effects of multipath interference on the performance
of UWB systems in an indoor wireless channel,” in Proc. IEEE Vehicular
Technology Conf., Rhodes, Greece, May, 2001, pp. 1176–1180
[19] Weisenhorn, M., Hirt, W., Robust noncoherent receiver exploiting UWB
channel properties InProc. IEEE Conference on UWB Systems and Technologies 2005; 156–160.
[20] T. Q. S. Quek and M. Z. Win, “ Analysis of UWB transmitted-reference
communication systems in dense multipath channels,” IEEE Journal on Select. Areas in Communications vol. 23, no. 9, September 2005
BIBLIOGRAPHY
75
[21] S. Dubouloz, B. Denis, S. de Rivaz, L. Ouvry, “Performance analysis of
LDR UWB non-coherent receivers in multipath environments” IEEE International Conference on Ultra-Wideband, ICU 2005, 5-8 Sept. 2005, pp.
491-496
[22] K. Witrisal, G. Leus, G. J. M. Janssen, M. Pausini, F. Troesch, T. Zasowski,
and J. Romme, “Noncoherent ultra-wideband systems”, IEEE Signal Processing Magazine, July 2009, vol. 26, no. 4, pp. 48–66
[23] N. He and C. Tepedelenlioglu, “Performance analysis of non-coherent UWB
receivers at different synchronization levels,” Proc. IEEE Globecom, pp.
3517–3521, 2004
[24] Y.-L. Chao and R. A. Scholtz “Optimal and suboptimal receivers for
ultra-wideband transmitted reference systems,”IEEE Global Telecommun.
Conf.’03, vol. 2, pp. 759–763, 1–5 Dec. 2003
[25] Urkowitz H. Energy detection of unknown deterministic signals Proc. of the
IEEE, 1967, vol.55, pp.523–531
Part II
Recursive and Doublet-Based
Transmitted Reference Schemes for Ultra
Wideband Communications
This Part is based on the following publications:
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Recursive
Transmitted Reference Receivers for Impulse Radio UWB Systems”, Research
report, Blekinge Institute of Technology, 2008 Issue: 5, ISSN: 1103–1581.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Signaling
and Detection of UWB Signals based on a Dual-Doublet Transmitted Reference
Scheme”, in Proceedings of RVK’08 The twentieth Nordic Conference on Radio
Science and Communications, June 9–11, 2008, Växjö, Sweden.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “Detection
of Impulse Radio ultra wideband Signals using Recursive Transmitted Reference
Receivers”, in Proceedings of ICUWB’07, IEEE International Conference on ultra
wideband, September 24–26, 2007, Singapore.
Muhammad Gufran Khan, Jörgen Nordberg, and Ingvar Claesson, “A DoubletShift Transmitted Reference Scheme for ultra wideband Communication Systems”, in Proceedings of ICUWB’07, IEEE International Conference on ultra
wideband, September 24–26, 2007, Singapore.
Recursive and Doublet-Based Transmitted Reference
Schemes for Ultra Wideband Communications
November 22, 2011
Abstract
Transmitted reference (TR) schemes have gained attention for IR-UWB
communications as they bypass the complex task of channel estimation.
However, low-complexity detection in these schemes is achieved at the expense of a loss in performance due to noisy reference signals. In addition,
the conventional TR scheme is not energy-efficient as half of the energy
is used in transmitting the reference pulses. To remedy the drawbacks
of TR, recursive TR (R-TR), dual-doublet TR (DDTR), doublet-shift TR
(DSTR) and binary pulse position modulation (BPPM)/DSTR schemes
are presented. The proposed R-TR estimates the reference template for
the correlator recursively and it requires shorter delays for averaging. Secondly, the proposed DDTR scheme utilizes 3 dB less energy per bit and
recovers 50% rate loss of conventional TR scheme. Thirdly, the proposed
DSTR scheme achieves 2 dB better BER performance by using closelyspaced pulses and an extra correlation branch in the receiver. In addition,
the DSTR scheme is extended to BPPM/DSTR scheme, which reduces the
receiver complexity by using an energy detector (ED) branch. The simulation results validate that the proposed TR schemes and receivers have
better performance than the conventional TR system in terms of BER performance, energy efficiency and/or implementation complexity.
1
Introduction
The UWB technology offers many promising applications but research and development of UWB has to cope with formidable challenges that limit their bit-errorrate (BER) performance, capacity, throughput, and network flexibility [1]. The
IR-UWB utilizes short duration pulses for the transmission and has the ability to
resolve individual multipath components (MPCs) [2]. However, the large number
81
82
Part II
of MPCs impinging on the receiver makes it unrealistic to employ the traditional
RAKE receiver to capture a significant portion of the energy contained in the
received signal [2,3]. A RAKE receiver that implements tens or even hundreds of
correlation operations may be required to take full advantage of the available signal energy [4,5]. Providing a receiver with a large number of correlators (fingers),
however, increases the receiver complexity [6].
The TR scheme proposed by Hoctor et. al. [8] is an alternative simple autocorrelation receiver scheme for the demodulation of IR-UWB signals. The TR
communication systems operate by transmitting a pair of an unmodulated and a
modulated signal and employing the former to demodulate the latter [9]. Since
the reference signal and data signal are transmitted within the coherence time
of the channel, it is assumed that the channel responses to the two signals are
the same [10]. This scheme does not require expensive path-by-path channel
estimation as the reference signal is used to demodulate the data signal, hence,
the channel information is implicitly embedded in the demodulation. Besides
implicit channel estimation, this scheme has the advantage that receiver timing
and synchronization requirements are substantially reduced; by transmitting a
reference along with the data, it is possible to eliminate the need for a locally
generated reference and the complicated issue of locally generated reference synchronization [11].
Aside from the advantages mentioned above, a drawback of the TR receiver is
the significant performance degradation associated with employing noisy received
signals as the reference signals for data detection [2]. Second drawback of the
TR scheme stems from a reduced signal-to-noise ratio, which is partly due to
“wasting” energy on the reference pulses that are non-information-bearing [7].
In this part of the thesis, employing codesign of signalling schemes and receivers
architectures approach, a recursive TR (R-TR), a dual-doublet TR (DDTR), a
doublet-shift TR (DSTR) and a BPPM/DSTR signaling and detection scheme
are proposed with the aim to enhance the performance of the conventional TR
scheme.
The outline of rest of Part II is as follows. In Section 2, the signal model
and receiver architectures of the recursive TR systems are presented. Sections
3, 4 and 5 describe the signal model and receiver architecture of the DDTR, the
DSTR and the BPPM/DSTR systems, respectively. The performance evaluation
and simulation results are discussed in Section 6 and conclusions are presented
in Section 7.
2
Recursive Transmitted Reference System
The following subsections present the motivation, signal model and receiver architectures of the recursive TR IR-UWB systems.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
83
2.1
Motivation
In [10, 12], an averaged TR (ATR) system, which performs averaging of all the
reference pulses in a previous symbol interval, has been proposed to remedy the
problem of noisy reference pulses. However, the suppression of noise by averaging previously received reference pulses requires the implementation of precise
long and wideband analog delays which may be burdensome [12]. Alternatively,
the averaging process might need to be done using digital signal processing; in
this situation, the receiver must have a high sampling frequency ADC, and the
receiver architecture is no longer considered “simple” [13]. Moreover, a decision
directed autocorrelation receiver and its recursive solution is proposed in [14] for
pulsed ultra wideband systems. The decision directed scheme decreases the signaling overhead but relies on the past symbol decisions which can lead to error
propagation.
In order to achieve a low-complexity solution for reference signal averaging,
the recursive TR (R-TR) and the recursive averaged TR (R-ATR) signaling and
detection schemes are investigated. The R-TR receiver estimates the reference
template for the correlator frame-by-frame recursively from the previous template and the newly received reference pulse. The R-ATR receiver estimates the
reference template symbol-by-symbol recursively from the previous template and
the average over the reference pulses within the current symbol. The R-TR receiver has a low-complexity as the delays are short and the correlation can be
performed in the analog domain thereby avoiding the high sampling rate requirement. However, the R-ATR receiver requires a long delay element, corresponding
to the duration of one bit, to accomplish recursion. The comparison of the proposed receivers has been performed with the conventional TR and ATR receivers.
2.2
Signal Model
The transmitted signal for the TR and the R-TR systems is given by
f −1
∞ NX
X
p
sTR (t) =
Ep
p(t − iTs − jTf )
(1)
i=−∞ j=0
+bi p(t − iTs − jTf − Td ) ,
RT
where p(t) is a normalized UWB pulse of duration Tp i.e., 0 p [p(t)]2 dt = 1, Ep
is the energy of each pulse, Tf is the frame duration. Each symbol bi ∈ {−1, 1}
contains Nf frames and each frame of the TR contains two pulses separated by a
fixed delay of duration Td , thus energy per symbol Es is equal to energy per bit
Eb . Fig. 1 (a) shows an example of the transmitted sequence in the conventional
TR and R-TR systems.
84
Part II
The proposed transmitted signal for the ATR and the R-ATR systems is
slightly modified and is given by
∞ NX
f −1
X
p
sATR (t) =
Ep
p(t − iTs − jTf /2)
i=−∞ j=0
+bi p(t − iTs − jTf /2 − Nf Td ) ,
(2)
which shows that each symbol is transmitted by a stream of Nf reference pulses
followed by Nf data-modulated pulses. Fig. 1 (b) shows an example of the transmitted sequence in the ATR and R-ATR systems. The figure illustrates that all
the reference pulses in a bit interval are transmitted together and their corresponding data-modulated pulses follow after a delay equal to Nf Td . The IR-UWB
systems typically use time-hopping (TH) and polarity scrambling to obtain processing gain, to combat multiple access interference (MAI), and to smooth the
signal spectrum [15]. For simplification, the recursive schemes described above
assume that TH is absent. The TH and pulse-based polarity scrambling, which
can be easily undone at the the receiver [15], can be used with the recursive
schemes.
It is assumed that the signals are transmitted over a multipath channel with
the impulse response
K−1
X
h(t) =
αk δ(t − τk ),
(3)
k=0
where δ(t) is the Dirac delta function, while αk are the channel tap weights, K
is the number of MPCs and τk is the delay associated with the k th multipath
component. The received signals, after passing through the tapped-delay line
multipath channel, are expressed as
f −1
∞ NX
X
p
rTR (t) =
Ep
g(t − iTs − jTf )
i=−∞ j=0
+bi g(t − iTs − jTf − Td ) + n(t),
rATR (t) =
(4)
∞ NX
f −1
X
p
Ep
g(t − iTs − jTf /2)
i=−∞ j=0
+bi g(t − iTs − jTf /2 − Nf Td ) + n(t),
(5)
where n(t) is an additive Gaussian noise with zero mean and variance σn2 = No /2,
and g(t) is interpreted as the aggregate channel after convolving the multipath
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
85
Bit b0 = −1
Symbol i = 0 ;
Symbol i = 1 ;
Bit b1 = 1
(a)
Td
Ts
2Ts
Ts
2Ts
Ts
2Ts
Ts
2Ts
Tf
(b)
Td = Tf /2
Nf T d
(c)
Td
δTd
T̄f
(d)
δTd
∆Td
TBP P M
T̄f
Symbol i = 0 ; Bits b0,1 = −1, b0,2 = 1 Symbol i = 1 ; Bits b1,1 = 1, b1,2 = 1
(e)
Td1
Ts
2Ts
Td2
T̄f
Figure 1: An example of the transmitted sequence for two symbols, (a) TR and
R-TR scheme, for Nf = 2 (b) ATR and R-ATR scheme, for Nf = 2 (c) DSTR
scheme, for N̄f = 1 (d) BPPM/DSTR scheme, for N̄f = 1 (e) DDTR scheme, for
N̄f = 1.
86
Part II
channel with the transmitted pulse, i.e.,
g(t) =
K−1
X
k=0
αk p(t − τk ).
(6)
The duration of g(t) is defined as Tg = Tp + Tmds , where Tp is the pulse duration
and Tmds is the maximum delay spread of the channel.
2.3
Recursive Transmitted Reference Receiver
First, as in the TR receiver, the received signal rTR (t) is passed through a filter
f (t) which is matched to the transmitted pulse and the output signal is denoted as r̃(t), where the subscript TR is dropped for clarity. Then, the reference
template is estimated in a recursive manner to enable the receiver to capture adequate multipath diversity, see Fig. 2. This averaging process gives an estimate
of the aggregate analog channel g(t). The previously estimated template and the
current reference pulse in the newly received frame are pre-multiplied with appropriate weights and then added to obtain a new template. The previous estimated
template is obtained using a delay Tf , since the template estimation process assumes that the delay between two subsequent reference pulses is Tf , see Fig. 1
(a). Thus, the template update essentially requires the weighting and alignment
of the previous template estimate and the newly received reference pulse. The
complexity of the R-TR is less than the ATR but more than conventional the TR
receiver. The recursion process, which is equivalent to exponentially weighted
averaging, in the R-TR receiver is expressed as
g(R-TR) j (t) = (1 − µ)g(R-TR) j−1 (t − Tf ) + µr̃j (t),
(7)
where the frame index j is used for the j th template to emphasize that the
update is performed frame-by-frame; g(R-TR) j (t) is the new template and the
term g(R-TR) j−1 (t−Tf ) is the previous template estimate at the (j−1)th iteration.
The parameter µ ∈ [0, 1] is suggested to be µ = L1 , where L is the approximative
number of previous estimated templates used in the average. This weighting
factor is associated with the channel and may be adjusted if the knowledge of
channel variations is available. The parameter 1 − µ can also be interpreted as
the forgetting factor of the previous template estimates and the value of µ may
help the estimated template to adapt the channel variations. If the channel is
fast time-varying, a large value of the parameter (i.e., µ → 1) assigns more weight
to the current observation, thus, any change to the channel is rapidly tracked,
whereas a small value (i.e., µ → 0) minimizes the fluctuations due to noise but
rapid channel variations cannot be tracked.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
87
In the signal, the part of the frame which holds the estimated template is the
signal region (SR), and this part of the signal is used in the correlation operation.
The estimated reference template in the R-TR is written as
p
g(R-TR) j (t) = Ep g̃(t) + n̂j (t),
(8)
where t ∈ [0, Tf /2], n̂j (t) is residual noise in the estimated template g(R-TR) j (t).
A delayed version of the newly estimated template g(R-TR) j (t) is obtained by
using a delay of Td and correlation is performed with the modulated pulse. In
this case, the decision statistic for the ith symbol is formed at the output of the
correlator after summation over Nf frames and is given by
ZR-TR,i =
(i+1)Nf −1 Z jT +T +TI
f
d
X
j=iNf
jTf +Td
r̃(t)g(R-TR) j (t − Td )dt.
(9)
For the R-TR receiver, the bit decision is also made using as b̂i = sgn(ZR-TR,i ).
The decision statistic of the R-TR is expressed as a sum of four terms as
ZR-TR,i = Z1,i + Z2,i + Z3,i + Z4,i ,
(10)
where the terms Z1 , Z2 , Z3 and Z4 are given by
Z1,i
=
(i+1)Nf −1 Z jT +T +TI
f
d
X
j=iNf
Z2,i
=
(i+1)Nf −1 Z jT +T +TI
f
d
X
j=iNf
Z3,i
=
=
jTf +Td
(i+1)Nf −1 Z jT +T +TI
f
d
X
j=iNf
Z4,i
jTf +Td
jTf +Td
(i+1)Nf −1 Z jT +T +TI
f
d
X
j=iNf
jTf +Td
Ep bi g̃(t − jTf )g̃(t − jTf − Td )dt,
p
Ep bi g̃(t − jTf )n̂(t − jTf − Td )dt,
p
Ep g̃(t − jTf − Td )ñ(t − jTf )dt,
ñ(t − jTf )n̂(t − jTf − Td )dt.
(11)
(12)
(13)
(14)
Following [16], the first term Z1,i corresponds to a signal term and is approxiPKp −1 2
mated as Nf Ep bi k=0
αk . The variance of the noise in the noise-signal term
Z2,i decreases due to recursive averaging;
mean Gaussian random
it is a zero
No PKp −1 2
1
variable and its variance tends to 2L−1 Nf Ep 2
k=0 αk as L tends to infinity [14, 18]. The noise-signal term Z3,i is also a zero mean Gaussian random
88
Part II
PKp −1 2
αk . In addition, the noise-by-noise prodvariable with variance Nf Ep N2o k=0
uct term Z4,i is also a zero mean Gaussian random variable, assuming that the
N 2N W T
I
f
o
time-bandwidth product W TI is large [24], and its variance tends to 2(2L−1)
as L tends to infinity [14, 18]. The conditional mean and variance of decision
statistic are given by [14, 16, 18]
E{ZR-TR |(α, τ )} = Nf Ep b
Kp −1
X
α2k ,
(15)
k=0
Kp −1
No X 2 No2 Nf W TI
1 Nf Ep
αk +
,
Var{ZR-TR |(α, τ )} = 1 +
2L − 1
2
2(2L − 1)
(16)
k=0
and the conditional BER of the R-TR receiver is approximated as
s

2
E {ZR-TR |(α, τ )} 
Pe,R-TR |(α, τ ) = Q 
Var{ZR-TR |(α, τ )}
v
u
2
u
2Nf Ep PKp −1 2
u
k=0 αk
No
u
u1 = Q
t
 21
2Nf Ep PKp −1 2
N WT

1+ 1
α + f I
2
2L−1
No
k=0
k
2L−1
Since the instantaneous received SNR of the TR receiver is defined as
γTR =
Kp −1
2Nf Ep X 2
αk ,
No



 . (17)


(18)
k=0
then, in order to compare the BER expression with the TR, Eq. (17) can be
written as


v
u
2
γ

u 1
TR
(19)
Pe,R-TR |(α, τ ) = Q t .
Nf W TI
2 1+ 1
2L−1 γTR + 2L−1
As opposed to the TR receiver, since the R-TR receiver uses a recursively averaged estimated template in the correlator, the residual noise in the estimated
reference template of the R-TR is less than the noise in the reference template
of the TR receiver. Hence, the instantaneous received SNR of the R-TR is also
higher than the TR receiver, which results in a lower BER for the R-TR receiver.
The BER expression also shows its dependence on the parameter µ. In practice,
the value µ is suggested to be set adaptively according to an estimate of the
channel variation rate to achieve robustness in a dynamic channel environment.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
89
R t+TI
BPF
rTR (t)
f (t)
t
r̃(t)
(·)dt
PNf −1
b̂i
j=0
Delay
Td
Timing
g(R-TR)j (t)
Delay
Tf
µ
1−µ
Figure 2: Architecture of the R-TR receiver.
2.4
Averaged Transmitted Reference Receiver
The performance of the TR receiver is limited by the fact that the reference signal
used in the correlator is noisy. The performance of the TR system is usually
improved using the ATR, as shown in Fig. 3, which performs averaging over the
Nf previous reference pulses prior to demodulation, as also described in [10, 12].
As previously mentioned, this averaging process is not trivial to perform as it
requires long and precise analog delays.
The received signal rATR (t) at the output of the filter f (t) is also denoted
as r̃(t) by dropping the subscript ATR for clarity. The transmitted sequence of
pulses has been slightly modified for the ATR and the R-ATR, as shown in Eq.
(2), such that all the reference pulses in a bit interval are transmitted together
and their corresponding data-modulated pulses follow with a delay Td = Nf Tf /2.
Its advantage is this that it needs shorter delays for averaging and also requires
that the channel remains invariant only over one symbol duration. Using this
signaling scheme, the averaged template denoted as g(ATR) (t) is formed over Nf
reference pulses previously received within the current symbol duration, as
g(ATR)i (t)
=
=
1
Nf
(i+1)Nf −1
X
j=iNf
r̃(t + (Nf − j)Tf /2),
p
1
Ep g̃(t) +
Nf
(i+1)Nf −1
X
j=iNf
ñ(t + (Nf − j)Tf /2).
(20)
The decision statistic for the ith symbol is formed by correlating and combining all the Nf modulated pulses within the current symbol duration with the
90
Part II
BPF
rATR (t)
f (t)
R t+TI
t
r̃(t)
Delay
Td
Noise
Averaging
PNf −1
(·)dt
b̂i
j=0
Timing
gATRi (t)
Figure 3: Architecture of the conventional ATR receiver.
appropriately delayed averaged template g(ATR) (t), and it is written as
ZATR,i =
(i+1)Nf −1 Z jT /2+N T +TI
f
f d
X
j=iNf
jTf /2+Nf Td
r̃(t)g(ATR) (t − Td )dt.
(21)
Under the Gaussian approximation, the conditional mean and variance of the
decision statistic are given by [16, 17]
E{ZATR |(α, τ )} = Nf Ep b
Kp −1
X
α2k ,
(22)
k=0
Kp −1
1 No X 2 No2 W TI
Var{ZATR |(α, τ )} = 1 +
Nf Ep
αk +
.
Nf
2
2
(23)
k=0
Then, the conditional BER of the ATR receiver is written as
v

u
2
u
P
K
−1
2N
E
p
f p
2
u

k=0 αk
No
u

1
u

,
Pe,ATR |(α, τ ) = Q t P

K
−1
2N
E
p
f p
2
 2 12 1 + N1
k=0 αk + W TI 
No
f

v
u
u 1 = Q t
2 1 1+
2
1
Nf
2
γTR
γTR + W TI


.
(24)
Compared to the TR and the R-TR, the instantaneous received SNR of the ATR
is higher due to less noise variance, which results in a lower BER for the R-TR
receiver.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
91
2.5
Recursive Averaged Transmitted Reference Receiver
The conventional ATR scheme is extended to generate a recursive architecture
called recursive averaged TR (R-ATR), as depicted in Fig. 4. First, like the ATR,
the proposed R-ATR receiver performs the averaging by appropriately delaying
Nf received reference pulses within the current symbol. Further, the resulting averaged waveform and the previously estimated template are pre-multiplied
with appropriate weights and added to obtain the new template. The previous template estimate is kept in a memory with delay Nf Td to be utilized in
the recursion process. It is noteworthy that the template update is performed
symbol-by-symbol in case of the R-ATR, which means that there is an increase
in complexity as compared to the ATR.
In a similar fashion as Eq. (7), the template estimation process is expressed
as
g(R-ATR) i (t) = (1 − µ)g(R-ATR) i−1 (t − Nf Td ) + µg(ATR) i (t),
(25)
where the symbol index i is used for the ith template to emphasize that the update
is performed symbol-by-symbol; g(R-ATR) i (t) is the new template and the term
g(R-ATR) i−1 (t−Nf Td ) is the previous template estimate at the (i − 1)th iteration.
The term g(ATR) i (t) represents the average over Nf received reference pulses
within the current symbol duration, see Eq. (20). The newly estimated template
g(R-ATR) (t) is used in the correlator for demodulation of all the subsequent Nf
data-modulated pulses over a bit interval to form the decision statistic for the ith
symbol, i.e.,
ZR-ATR,i =
(i+1)Nf −1 Z jT /2+N T +TI
f
f d
X
j=iNf
jTf /2+Nf Td
r̃(t)g(R-ATR) i (t − Td )dt.
(26)
As the estimated template undergoes both simple and recursive averaging in
the R-ATR, the conditional mean and variance of the decision statistic are given
by [16–18]
E{ZR-ATR |(α, τ )} = Nf Ep b
Var{ZR-ATR |(α, τ )} = 1 +
Kp −1
X
α2k ,
(27)
k=0
Kp −1
1
No X 2
No2 Nf W TI
Nf Ep
αk +
.
Nf + 2L − 1
2
2(Nf + 2L − 1)
k=0
(28)
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Part II
R t+TI
BPF
rATR (t)
f (t)
t
r̃(t)
(·)dt
PNf −1
b̂i
j=0
Delay
Td
Noise
Averaging
Timing
gATRi (t)
gR-ATRi (t)
Delay
Nf T d
µ
1−µ
Figure 4: Architecture of the R-ATR receiver.
The conditional BER of the R-ATR receiver is approximated as
v
u
2
u
2Nf Ep PKp −1 2
u
α
k=0
k
No
u
u1 Pe,R-ATR |(α, τ ) = Q 
t
P
 21
Kp −1 2
2Nf Ep
1

k=0 αk +
2 1 + Nf +2L−1
No

v
u
u 1 = Q t
2 1 1+
2
2
γTR
1
Nf +2L−1
γTR +
Nf W TI
Nf +2L−1


.



,
Nf W TI 

Nf +2L−1
(29)
which shows that the SNR of the decision statistic in the R-ATR is higher than its
simple averaging counterpart, i.e., the ATR receiver. This result is also intuitive
as the R-ATR receiver incorporates the ATR receiver as well.
If TH is used in conjunction with TR signaling, averaging of the template
estimates in the proposed R-TR scheme should be performed by selecting the
required delay according to the TH sequence. It requires a bank of delay elements,
however, the delays are relatively short i.e., on the order of a frame duration.
In addition, the complexity of the proposed R-ATR scheme can be reduced by
repeating the TH sequence after a symbol duration. The recursion process in the
R-ATR scheme requires only a fixed symbol long delay element.
3
Dual-Doublet TR System
The following subsections present the motivation, signal model and receiver architecture of the DDTR IR-UWB system.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
93
3.1
Motivation
In [10], optimal and suboptimal UWB TR receivers are analyzed and a differential
TR system is presented in which no reference pulses are transmitted. However,
the differential TR system suffers from the noisy reference template as do the
TR. A differential TR detector and its iterative solution is also considered and
analyzed in [19]. In [13], a generalized model of the TR scheme, which combines
the conventional TR and the differential TR techniques, has been presented to
increase the power efficiency and to improve BER. Further, some other schemes
have been proposed to improve the energy efficiency of the conventional TR UWB
system, for instance, an energy efficient modulation scheme is presented in [20],
in which the reference pulse also carries information. In [21], a reference sharing
TR scheme, which achieves energy-efficiency by sharing a single reference pulse
among modulated pulses and varying its amplitude, is presented. To recover
energy/rate loss of conventional TR scheme, a dual-doublet TR (DDTR) signaling
and detection scheme for IR-UWB systems is proposed. The DDTR transmits
two bits in a symbol by sharing reference pulses of two TR doublets within each
frame. The receiver architecture for DDTR scheme is similar to the conventional
TR receiver and requires only an extra delay, a correlator and two adders.
3.2
Signal Model
The proposed DDTR scheme exploits the repetition of non-information-bearing
reference pulses by transmitting two bits using two consecutive TR doublets
within each frame. The transmitted signal in the proposed DDTR signaling is
written as
∞ N̄X
f −1
X
p
s̄DDTR (t) =
Ep
bi,1 p(t − iT̄s − j T̄f ) + p(t − iT̄s − j T̄f − Td1 )
i=−∞ j=0
+p(t − iT̄s − j T̄f − Td2 ) + bi,2 p(t − iT̄s − j T̄f − Td1 − Td2 ) , (30)
where p(t) is the normalized transmitted pulse Ep is the pulse energy, N̄f is the
number of frames, T̄f is the frame duration and the symbol energy is Es = 4N̄f Ep .
Fig. 1 (e) illustrates that two bits in the DDTR scheme are transmitted in a
symbol using N̄f frames and each frame contains four pulses. Thus, a symbol
consists of two bits bi,1 ∈ {−1, 1} and bi,2 ∈ {−1, 1} and the frame duration in
DDTR is twice the frame duration of the equivalent conventional TR scheme (i.e.
T̄f = 2Tf ). The four pulses per frame can be divided into two TR doublets, with
each doublet carrying two pulses. In the first doublet, the first pulse is modulated
with the first bit bi,1 and the second pulse is the reference pulse. In the second
doublet, the first pulse is the reference pulse, while the second pulse is modulated
94
Part II
with the second bit bi,2 . The pulses within a doublet are separated by a fixed
delay Td1 and the doublets are separated by a fixed delay of duration Td2 .
It is evident from the comparison of Fig. 1 (a) and (e) that the DDTR does
not incur the 50% rate/energy loss of the conventional TR scheme if N̄f = Nf /2.
The received signal, after passing through the multipath channel, is written as
r̄(t) =
f −1
∞ N̄X
X
p
Ep
bi,1 g(t − iT̄s − j T̄f ) + g(t − iT̄s − j T̄f − Td1 )
i=−∞ j=0
+ g(t − iT̄s − j T̄f − Td2 ) + bi,2 g(t − iT̄s − j T̄f − Td1 − Td2 ) + n̄(t).
(31)
For simplification, r̄(t) is expressed as a linear combination of the two signals
r̄1 (t) and r̄2 (t), such that
r̄(t) = r̄1 (t) + r̄2 (t),
(32)
where
r̄1 (t) =
∞ N̄X
f −1
X
p
Ep
bi,1 g(t − iT̄s − j T̄f )
i=−∞ j=0
+ g(t − iT̄s − j T̄f − Td1 ) + n̄1 (t),
r̄2 (t)
(33)
∞ N̄X
f −1
X
p
=
Ep
g(t − iT̄s − j T̄f − Td2 )
i=−∞ j=0
+ bi,2 g(t − iT̄s − j T̄f − Td1 − Td2 ) + n̄2 (t),
(34)
i.e., r̄1 (t) carries the first TR doublets and r̄2 (t) consists of the second TR doublets, n̄1 (t) and n̄2 (t) are Gaussian processes with zero mean and variance σn2 . In
this case, the IPI within a doublet can be avoided if Td1 > Tg and the interference
between any two doublets can be avoided by keeping the delay (Td1 + Tg ) ≤ Td2
and 2Td2 ≤ T̄f .
3.3
Dual-Doublet TR Receiver
In a similar manner as in the conventional TR receiver, the output of the bandpass
filter f (t) of the DDTR receiver is written as
r̄˜(t)
= r̄˜2 (t) + r̄˜1 (t).
(35)
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
95
r̄(t)
BPF
˜r̄ (t)
R t+TI
f (t)
t
(·)dt
PN̄f −1
b̂i,1
PN̄f −1
b̂i,2
j=0
˜r̄(t − Td1 )
Timing
Delay
Td1
R t+TI
t
(·)dt
j=0
˜r̄(t − Td2 )
Timing
Delay
Td2
Figure 5: Architecture of the DDTR receiver.
Frame 1
r̃(t)
Ts
Td1
r̃(t − Td1 )
SR
SR
NOR
Ts
NOR
TI
TI
(a)
r̃(t)
Ts
r̃(t − Td2 )
Td2
SR
NOR
SR
NOR
Ts
TI
TI
(b)
Figure 6: An illustration of the correlation in DDTR for symbol i = 0 consisting
of N̄f = 1 frames. The first and last pulse are modulated with bits b0,1 = −1
and b0,2 = 1, respectively, (a) first branch (b) second branch.
96
Part II
For the detection, the architecture of the receiver referred to as the DDTR receiver
is shown in Fig. 5. As the reference pulses are shared among the two bits; the
receiver architecture is modified to perform correlation of each data-modulated
pulse with two reference pulses. In the first delay and correlator branch of the
DDTR receiver, after delaying the received signal by Td1 , the first (modulated)
and third (reference) pulse of a frame are correlated with the second (reference)
and fourth (modulated) pulse, respectively. In the second delay and correlator branch, after delaying the signal by Td2 , the first (modulated) and second
(reference) pulse of a frame are correlated with the third (reference) and fourth
(modulated) pulse, respectively. It means that the integration in both correlators is performed over two intervals per frame and the outputs of the correlators
are also sampled twice per frame. In this scheme, each modulated pulse is being
correlated with both reference pulses in a frame, as opposed to the conventional
TR scheme which correlates each modulated pulse with only one reference pulse.
The correlation process in the DDTR is illustrated in Fig. 6.
The outputs of the first correlator branch after summation over N̄f frames,
denoted as YI−b̂i,1 and YI−b̂i,2 for bits bi,1 and bi,2 respectively, are written as
YI−b̂i,1
(i+1)N̄f −1 Z j T̄ +T +TI
f
d1
X
=
j=iN̄f
j T̄f +Td1
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − Td1 ) + r̄˜2 (t − Td1 ) dt
(i+1)N̄f −1 Z j T̄f +Td1 +TI X
=
j=iN̄f
j T̄f +Td1
r̄˜1 (t)r̄˜1 (t − Td1 ) + r̄˜1 (t)r̄˜2 (t − Td1 )
+r̄˜2 (t)r̄˜1 (t − Td1 ) + r̄˜2 (t)r̄˜2 (t − Td1 ) dt,
YI−b̂i,2
=
(i+1)N̄f −1 Z j T̄ +T +T +TI
f
d1
d2
X
=
(36)
j=iN̄f
j T̄f +Td1 +Td2
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − Td1 ) + r̄˜2 (t − Td1 ) dt
(i+1)N̄f −1 Z j T̄f +Td1 +Td2 +TI X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜1 (t)r̄˜1 (t − Td1 ) + r̄˜1 (t)r̄˜2 (t − Td1 )
˜
˜
˜
˜
+r̄2 (t)r̄1 (t − Td1 ) + r̄2 (t)r̄2 (t − Td1 ) dt,
(37)
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
97
where r̄˜(t) is written as a linear combination of two signals r̄˜1 (t) and r̄˜2 (t), and
TI is the integration interval for each correlation which satisfies 0 < TI ≤ Tg . As
the integrations are performed only over the signal regions and assuming there
is no interference between the pulses, i.e., Td2 ≥ (Td1 + Tg ) and 2Td2 ≤ T̄f , Eq.
(36) and Eq. (37) reduce to a simplified form as
YI−b̂i,1
=
(i+1)N̄f −1 Z j T̄ +T +TI
f
d1
X
j=iN̄f
YI−b̂i,2
=
j T̄f +Td1
r̄˜1 (t)r̄˜1 (t − Td1 )dt,
(i+1)N̄f −1 Z j T̄f +Td1 +Td2 +TI
X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜2 (t)r̄˜2 (t − Td1 )dt,
(38)
(39)
where Eq. (38) and Eq. (39) illustrate that, in each frame, the first (modulated)
and third (reference) pulse are delayed by Td1 and correlated with the second
(reference) and fourth (modulated) pulse, respectively.
The outputs of the second correlator branch after summation over N̄f frames,
denoted as YII−b̂i,1 and YII−b̂i,2 for bits bi,1 and bi,2 respectively, are written as
YII−b̂i,1
=
(i+1)N̄f −1 Z j T̄ +T +TI
f
d2
X
=
j=iN̄f
j T̄f +Td2
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − Td2 ) + r̄˜2 (t − Td2 ) dt
(i+1)N̄f −1 Z j T̄f +Td2 +TI X
j=iN̄f
j T̄f +Td2
r̄˜1 (t)r̄˜1 (t − Td2 ) + r̄˜1 (t)r̄˜2 (t − Td2 )
+r̄˜1 (t − Td2 )r̄˜2 (t) + r̄˜2 (t)r̄˜2 (t − Td2 ) dt,
YII−b̂i,2
=
(40)
(i+1)N̄f −1 Z j T̄ +T +T +TI
f
d1
d2
X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − Td2 ) + r̄˜2 (t − Td2 ) dt
=
(i+1)N̄f −1 Z j T̄f +Td1 +Td2 +TI X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜1 (t)r̄˜1 (t − Td2 ) + r̄˜1 (t)r̄˜2 (t − Td2 )
˜
˜
˜
˜
+r̄1 (t − Td2 )r̄2 (t) + r̄2 (t)r̄2 (t − Td2 ) dt,
(41)
98
Part II
Again, assuming that there is no interference between pulses, i.e., Td2 ≥ (Td1 +Tg )
and 2Td2 ≤ T̄f , Eq. (40) and Eq. (41) reduce to a simplified form as
YII−b̂i,1
=
(i+1)N̄f −1 Z j T̄ +T +TI
f
d2
X
j=iN̄f
YII−b̂i,2
=
j T̄f +Td2
r̄˜2 (t)r̄˜1 (t − Td2 )dt,
(i+1)N̄f −1 Z j T̄ +T +T +TI
f
d1
d2
X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜2 (t)r̄˜1 (t − Td2 )dt,
(42)
(43)
where Eq. (42) and Eq. (43) illustrate that, in each frame, the first (modulated)
and second (reference) pulse are delayed by Td2 and correlated with the third (reference) and fourth (modulated) pulse, respectively. Finally, the decision statistic
for the first bit is formed by adding the outputs obtained from the summation
of the first integration interval of the two correlators, given in Eq. (38) and Eq.
(42), i.e.,
ZDDTR−b̂i,1
=
YI−b̂i,1 + YII−b̂i,1
=
(i+1)N̄f −1 Z j T̄ +T +TI
f
d1
X
j T̄f +Td1
j=iN̄f
+
r̄˜1 (t)r̄˜1 (t − Td1 )dt
(i+1)N̄f −1 Z j T̄f +Td2 +TI
X
j=iN̄f
j T̄f +Td2
r̄˜2 (t)r̄˜1 (t − Td2 )dt,
(44)
which shows that the pulse modulated with bit bi,1 is correlated with both reference pulses. The decision for the first bit is made as b̂i,1 = sgn(ZDDTR−b̂i,1 ).
In a similar manner, the decision statistic for the second bit is formed by
adding the outputs obtained from the summation of the second integration interval of the two correlators, given in Eq. (39) and Eq. (43), i.e.,
ZDDTR−b̂i,2
=
YI−b̂i,2 + YII−b̂i,2
=
(i+1)N̄f −1 Z j T̄f +Td1 +Td2 +TI
X
j=iN̄f
+
j T̄f +Td1 +Td2
r̄˜2 (t)r̄˜2 (t − Td1 )dt
(i+1)N̄f −1 Z j T̄ +T +T +TI
f
d1
d2
X
j=iN̄f
j T̄f +Td1 +Td2
r̄˜2 (t)r̄˜1 (t − Td2 )dt,
(45)
which shows that the pulse modulated with bit bi,2 is also correlated with both
reference pulses. Similarly, the decision in the second branch for the second bit
is made as b̂i,2 = sgn(ZDDTR−b̂i,2 ).
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
99
According to Eq. (44) and Eq. (45), assuming N̄f = Nf /2, the number of
correlations in the DDTR receiver for each modulated pulse are equal to the TR
receiver, the instantaneous received SNRs of the DDTR and the TR signaling are
equal. The conditional mean and variance of decision statistic are given by [16,17]
E{ZDDTR |(α, τ )}
= 2N̄f Ep
Kp −1
X
α2k
k=0
= Nf Ep
Kp −1
X
α2k ,
(46)
k=0
Kp −1
X
Var{ZDDTR |(α, τ )} = 2N̄f Ep No
= Nf Ep No
α2k +
k=0
Kp −1
X
α2k +
k=0
No2 2N̄f W TI
2
No2 Nf W TI
,
2
(47)
where αk are the MPCs with k = 0, ..., Kp −1, and Kp ≤ K is the total number of
captured MPCs by the DDTR receiver. Hence, the conditional BER expression
of the DDTR is written as
s

2
E
{Z
|(α,
τ
)}
DDTR

Pe,DDTR |(α, τ ) = Q 
Var{ZDDTR |(α, τ )}
v

u
u
PKp −1 2 2
u

Nf Ep k=0 αk
u

t
= Q
PKp −1 2 No2 Nf W TI 


 Nf Ep No k=0 αk +

2
=
=
v
u
u
u
u 1
t
Q
 2

Q
s
2Nf Ep
No
2Nf Ep
No
PKp −1
α2k
2



,
PKp −1 2

α
+
N
W
T

f
I
k=0
k
k=0
2
γTR
1
2 γTR + Nf W TI
!
.
(48)
Thus, the BER performance of both schemes is the same if N̄f = Nf /2 and
the DDTR system transmits two bits within a symbol duration, it recovers 50%
100
Part II
energy/rate loss. It is also evident from the BER expression that, if N̄f = Nf ,
the variance of the noise increases due to a higher number of frames but the
instantaneous received SNR of the DDTR receiver is also higher than that of the
TR receiver due to the higher energy assigned per symbol. Therefore, in this scenario, the DDTR system will have better BER performance but energy/rate loss
is equal to that of the conventional TR system. The BER simulations conducted
in the performance evaluation section confirm this result.
4
Doublet-Shift TR System
The following subsections present the motivation, signal model and receiver architecture of the DSTR IR-UWB system.
4.1
Motivation
A signal processing model for a TR UWB system is proposed in [22], for the case
where both pulses in a doublet are more closely spaced than the length of the
impulse response. In [23], a dual pulse transmission based on interleaved pulses
and an auto-correlation detection scheme for UWB communications has been
presented. In addition, a signaling scheme which uses multiple closely spaced
pulses, called pulse burst, has been adopted in the IEEE 802.15.4a standard.
The main benefit of pulse burst transmission is an increase in the integrated
signal energy at the receiver. In order to benefit from the use of closely spaced
pulses, a doublet-shift TR (DSTR) signaling and detection scheme is proposed.
The proposed scheme utilize the same energy per bit as the conventional TR
scheme and it has the potential to improve the data rate or system capacity. The
receiver architecture for the DSTR signaling is similar to the conventional TR
receiver, which means that the delay and correlation is performed in the analog
domain.
4.2
Signal Model
The transmitted signal in the proposed DSTR signaling scheme is written as
s̄DSTR (t) =
f −1
∞ N̄X
X
p
Ep
p(t − iT̄s − j T̄f ) + bi p(t − iT̄s − j T̄f − δTd )
i=−∞ j=0
+ bi p(t − iT̄s − j T̄f − Td ) + p(t − iT̄s − j T̄f − δTd − Td ) , (49)
where p(t) is a normalized transmitted UWB pulse, T̄f is the frame duration
and each symbol consists of one bit bi ∈ {−1, 1}. Fig. 1 (c) shows the signal-
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
101
ing sequence for the DSTR scheme. The figure illustrates that the transmitted
symbol contains N̄f (= Nf /2) successive frames (i.e., half of the conventional TR
scheme) and each frame contains four pulses. The four pulses are further divided
into two TR doublets, with each doublet carrying two pulses. The first doublet
transmits the reference pulse first and the data-modulated pulse follows. In the
second doublet, the order of the pulses within a doublet is shifted, i.e., the datamodulated pulse is transmitted before the reference pulse. It is illustrated by
Eq. (49) that the doublets are separated by a fixed delay of duration Td and the
pulses within a doublet are separated by a fixed shorter delay δTd . It is evident
from the comparison of Fig. 1 (a) and (c) that the amount of energy assigned per
symbol is the same as in the TR scheme. It should be noted the DSTR signaling
is able to achieve nearly twice the data rate if the separation between the TR
doublet positions is kept equal to the conventional TR.
The received DSTR signal, after passing through the multipath channel, is
written as
r̄(t)
f −1
∞ N̄X
X
p
=
Ep
g(t − iT̄s − j T̄f ) + bi g(t − iT̄s − j T̄f − δTd )
i=−∞ j=0
+ bi g(t − iT̄s − j T̄f − Td ) + g(t − iT̄s − j T̄f − δTd − Td ) + n̄(t)
= r̄1 (t) + r̄2 (t),
(50)
where r̄(t) is expressed as a linear combination of the two signals r̄1 (t) and r̄2 (t),
i.e.,
r̄1 (t) =
∞ N̄X
f −1
X
p
Ep
g(t − iT̄s − j T̄f ) +
i=−∞ j=0
bi g(t − iT̄s − j T̄f − δTd ) + n̄1 (t),
(51)
and
r̄2 (t)
=
f −1
∞ N̄X
X
p
Ep
bi g(t − iT̄s − j T̄f − Td )
i=−∞ j=0
+g(t − iT̄s − j T̄f − δTd − Td ) + n̄2 (t).
(52)
The signal r̄1 (t) carries the first TR doublets and r̄2 (t) consists of the second
shifted TR doublets, n̄1 (t) and n̄2 (t) are independent Gaussian processes with
zero mean and variance σn2 . In this case, the IPI within a doublet is allowed
102
Part II
to occur (δTd << Tg ), as interleaved pulses are used. However, the interference
between any two doublets is avoided by keeping the delay (δTd + Tg ) ≤ Td and
2Td ≤ T̄f .
4.3
Doublet-Shift TR Receiver
The received signal of the DSTR scheme at the output of the filter f (t) is written
as
r̄˜(t)
= r̄˜1 (t) + r̄˜2 (t).
(53)
For the detection of DSTR signals, the architecture of the DSTR receiver is shown
in Fig. 7. In order to compare complexity and performance of the receivers, an
architecture which uses only the first branch of the DSTR receiver is denoted as
DSTR-I receiver, which is the same as the conventional TR receiver. Similarly,
if both branches of the DSTR receiver are used, that architecture is denoted
as DSTR-II receiver. In the DSTR-I receiver, the first TR doublet is used as
a reference template for the second shifted TR doublet. First, the signal r̄˜(t)
is delayed by Td , which is the delay between two subsequent TR doublets and
then the correlation is performed. The decision statistic for the ith symbol of the
DSTR modulated signal is formed as
ZDSTR−I,i
=
(i+1)N̄f −1 Z j T̄ +T +T̄I
f
d
X
=
j=iN̄f
j T̄f +Td
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − Td ) + r̄˜2 (t − Td ) dt
(i+1)N̄f −1 Z j T̄ +T +T̄I f
d
X
j=iN̄f
j T̄f +Td
r̄˜1 (t)r̄˜1 (t − Td ) + r̄˜1 (t)r̄˜2 (t − Td )
+r̄˜1 (t − Td )r̄˜2 (t) + r̄˜2 (t)r̄˜2 (t − Td ) dt,
(54)
where r̄˜(t) is expressed as a linear combination of the two signals r̄˜1 (t) and r̄˜2 (t),
and T̄I is the integration interval which satisfies 0 < T̄I ≤ (δTd + Tg ). The output
of the correlator consists of signal regions and noise-only regions. However, the
integration is performed only overs the signal regions. Assuming Td ≥ (δTd + Tg )
and 2Td ≤ T̄f , Eq. (54) reduces to a simplified form as
ZDSTR−I,i =
(i+1)N̄f −1 Z j T̄ +T +T̄I
f
d
X
j=iN̄f
j T̄f +Td
r̄˜2 (t)r̄˜1 (t − Td )dt,
(55)
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
103
which illustrates that the signal r̄˜1 (t), consisting of the first TR doublets, is delayed and correlated with the signal r̄˜2 (t) that carries the second shifted TR
doublets. In the DSTR-I receiver, the output of the correlator is summed over
N¯f frames to acquire the decision statistic and the bit decision is made as
b̂i,DST R−I = sgn(ZDSTR−I,i ).
On the other hand, in the DSTR-II receiver, a second correlator is used in
the receiver to demodulate the data-modulated pulses within a doublet as each
TR doublet also contains a reference and an interleaved data-modulated pulse.
Hence, in the dual-branch DSTR, the detection is performed by combining the
outputs of both correlators. Fig. 7 shows that the received signal is delayed by
δTd and the integration in the second correlator is performed over 2N̄f intervals
within a bit duration, as the number of doublets is twice the number of frames.
The correlation process in DSTR-II is illustrated in Fig. 8. The decision statistic
δZDSTR,i is computed as
(i+1)N̄f −1Z j T̄ +δT +δ T̄I
f
d
X
δZDSTR,i =
j=iN̄f
+
Z
j T̄f +δTd
j T̄f +δTd +Td +δ T̄I
j T̄f +δTd +Td
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − δTd ) + r̄˜2 (t − δTd ) dt
r̄˜1 (t) + r̄˜2 (t) r̄˜1 (t − δTd + r̄˜2 (t − δTd dt, (56)
where δ T̄I is the integration interval within each doublet which satisfies the condition 0 < δ T̄I ≤ Tg . Assuming Td ≥ (δTd + Tg ) and 2Td ≤ T̄f , Eq. (56) reduces
to a simplified form as
δZDSTR,i
=
(i+1)N̄f −1Z j T̄ +δT +δ T̄I
f
d
X
j=iN̄f
+
Z
j T̄f +δTd
j T̄f +δTd +Td +δ T̄I
j T̄f +δTd +Td
r̄˜1 (t)r̄˜1 (t − δTd ) dt
˜
˜
r̄2 (t)r̄2 (t − δTd ) dt,
(57)
where the first term illustrates that the reference pulses in the first doublets are
delayed and correlated with their corresponding data-modulated pulses. Similarly, the second term shows that the data-modulated pulses of the second doublet are delayed and correlated with their corresponding reference pulses. In the
dual-branch receiver, the bit decision is made as
b̂i,DST R−II = sgn(ZDSTR−I,i + δZDSTR,i ).
(58)
Following the same approach as in the TR receiver [16,17], under the Gaussian
approximation and assuming N̄f = Nf /2, the conditional mean and variance of
104
Part II
r̄(t)
BPF
˜r̄ (t)
R t+T̄I
f (t)
t
PN̄f −1
(·)dt
j=0
˜r̄ (t − Td )
b̂i
Timing
Delay
Td
R t+δT̄I
t
PN̄f −1
(·)dt
j=0
˜r̄(t − δTd )
Timing
Delay
δTd
Figure 7: Architecture of the DSTR receiver.
Frame 1
r̃(t)
Ts
Td
r̃(t − Td )
Ts
SR
NOR
TI
(a)
r̃(t)
Ts
δTd
r̃(t − δTd )
Ts
SR
SR
NOR
NOR
TI
TI
(b)
Figure 8: An illustration of the correlation in DSTR for symbol i = 0 consisting
of N̄f = 1 frames. The second and third pulse are modulated with bit b0 = −1,
(a) first branch (b) second branch.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
105
decision statistic are given by
E{ZDSTR-II |(α, τ )}
=
2N̄f Ep
Kp −1
X
Kq −1
X
α2k + 2N̄f Ep
k=0
=
Nf Ep
Kp −1
X
k=0
α2k + Nf Ep
k=0
Var{ZDSTR-II |(α, τ )} = 2N̄f Ep No
= Nf Ep No
Kp −1
X
α2k + 2N̄f Ep No
X
Kq −1
k=0
X
α2k ,
α2k +
k=0
Kq −1
k=0
k=0
α2k +Nf Ep No
Kq −1
(59)
k=0
Kp −1
X
α2k
X
α2k +
No2 2N̄f W TI
2
No2 Nf W TI
, (60)
2
where Kp and Kq are the number of captured MPCs within the corresponding
integration windows in thr first and second branch, respectively. The conditional
BER of the DSTR-II receiver is written as
s

2
E {ZDSTR-II |(α, τ )} 
Pe,DSTR-II |(α, τ ) = Q 
Var{ZDSTR-II |(α, τ )}
v

u
u
PKp −1 2 PKq −1 2 2
u

Nf Ep ( k=0 αk + k=0 αk )
u

t


= Q
PKp −1 2 PKq −1 2
No2 Nf W TI 
 Nf Ep No ( k=0 αk + k=0 αk ) +

2
=
=
v
u
u
u
u 1
t
Q
 2

Q
s
2Nf Ep PKp −1
k=0
No (
PKq −1
2
2
αk )


α2k + k=0


PKq −1 2

2Nf Ep PKp −1 2
(
α
+
α
)
+
N
W
T
f
I
k=0
k
k=0
k
No
(γTR,Kp + γTR,Kq )2
1
2 γTR,Kp + γTR,Kq + Nf W TI
!
.
(61)
In the first branch of the DSTR-II receiver, as the correlation is performed only
over the signal region, the use of closely spaced pulses within a doublet significantly improves the SNR of the receiver due to higher integrated energy, which
translates into a lower BER. Secondly, as the two branch DSTR-II architecture
uses a second correlator branch in the receiver to demodulate the data-modulated
106
Part II
pulses within a doublet, the SNR of the decision statistic is improved further due
to the time diversity, which leads to a performance improvement of the DSTR-II
over the DSTR-I receiver. The BER simulations conducted in the performance
evaluation section confirm this result.
5
BPPM/DSTR System
The following subsections present the motivation, signal model and receiver architecture of the BPPM/DSTR IR-UWB system.
5.1
Motivation
In the proposed DSTR scheme, presented in the previous section, the first branch
of the receiver structure DSTR-II is the same as the conventional TR receiver and
the second branch requires a short delay element and a correlation operation to
demodulate the pulses within a doublet. The DSTR-II receiver improves the BER
performance but still it requires a long analog delay element in the first branch.
To circumvent the need of a long analog delay element, a BPPM/DSTR signaling
is presented and a combination of the ED and the DSTR receiver is proposed
for detection. The combined ED/DSTR receiver requires a square-law device
and a very short delay element, which significantly decreases the implementation
complexity, and it also provides better performance than the conventional ED
and TR receivers.
5.2
Signal Model
The transmitted signal in the proposed BPPM/DSTR signaling scheme is written
as
s̄BPPM/DSTR (t) =
∞ N̄X
f −1
X
p
Ep
p(t − iT̄s − j T̄f − di TBP P M )
i=−∞ j=0
+bi p(t − iT̄s − j T̄f − δTd − di TBP P M )
+bi p(t − iT̄s − j T̄f − ∆Td − di TBP P M )
+p(t − iT̄s − j T̄f − δTd − ∆Td − di TBP P M ) ,
(62)
where p(t) is the transmitted UWB pulse, and T̄f is the frame duration. Each
transmitted bit bi ∈ {−1, 1} contains N̄f successive frames. Due to BPPM,
each frame is divided in two halves and the position of the four pulses in one of
these two halves is determined as di = (bi + 1)/2 ∈ {0, 1}. Similar to the DSTR
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
107
r̄(t)
BPF
+
r̄˜(t)
t+T
RI
f (t)
(·)dt
t
PN̄f −1
j=0
−
b̂i
Timing
t+∆
R T̄I
(·)dt
t
+
−
Timing
Delay
∆Td
P
N̄f −1 j=0 r̄˜(t − ∆Td )
Figure 9: Architecture of the ED/DSTR receiver.
scheme, the four pulses are further divided into two shifted TR doublets. The
doublets are separated by a short fixed delay of duration ∆Td and the pulses
within a doublet are interleaved in time (i.e., δTd = Tp ). Moreover, the total
number of TR doublets utilized per symbol is the same as in for the conventional
TR scheme. In other words, the amount of energy assigned per symbol (and also
per bit) is the same in both the cases.
The received signal of the BPPM/DSTR, after passing through the multipath
channel, is written as
r̄(t) =
f −1
∞ N̄X
X
p
Ep
g(t − iT̄s − j T̄f − di TBP P M )
i=−∞ j=0
+bi g(t − iT̄s − j T̄f − δTd − di TBP P M )
+bi g(t − iT̄s − j T̄f − ∆Td − di TBP P M )
+g(t − iT̄s − j T̄f − δTd − ∆Td − di TBP P M ) + n̄(t),
(63)
where n̄(t) is AWGN noise with zero mean and variance σn2 = No /2.
5.3
ED/DSTR Receiver
The received signal of the BPPM/DSTR scheme is passed through a filter f (t)
which is matched to the transmitted pulse, and the output of the filter is denoted
as r̄˜(t). The first branch of the ED/DSTR receiver consists of a conventional
108
Part II
ED. In the conventional ED, the output of the filter is passed through a squarelaw device and an integrator, see Fig. 9. The decision metrics for each of the
two pulse positions of an orthogonal BPPM signal is obtained by integrating the
corresponding energy of pulse positions in the first and second half of each frame.
In each frame, the integrated energy is obtained by sampling the output of the
integrator twice per frame, i.e., after the two possible positions of the symbol bi .
The sampled energy estimates ZED,il for the ith symbol are written as
ZED,i0
=
(i+1)N̄f −1 Z j T̄f +T̄I
X
j=iN̄f
ZED,i1
=
[r̄˜(t)]2 dt,
(i+1)N̄f −1 Z j T̄ +TBP P M +T̄I
f
X
j=iN̄f
(64)
j T̄f
[r̄˜(t)]2 dt,
(65)
j T̄f +TBP P M
where the sub-indices “ED, i0” and “ED, i1” denote energy estimates for positions
“0” and “1” of the ith symbol, respectively. The length of the integration interval
determines the amount of multipath energy and the amount of noise captured by
the receiver, and its value ranges between 0 < TI ≤ Tf /2. The decision statistic
in first branch of the ED/DSTR receiver is formed as
ZED = ZED,i0 − ZED,i1 .
(66)
The second branch of the ED/DSTR receiver consists of a short delay element
as in the DSTR-II receiver, see Fig. 9. In the second branch, the first TR doublet
is used as a reference template for the second shifted TR doublet. First, the signal
r̄˜(t) is delayed by ∆Td , which is the delay between two subsequent TR doublets,
and then the correlation is performed. The output of the correlator is summed
over N¯f frames and absolute values are used to acquire the decision statistics.
It should be mentioned that the absolute values are used to estimate ∆ZDSTR,i0
and ∆ZDSTR,i1 as the decision is made based on the position information and not
on the phase information. The decision statistics for the possible bit positions
”0” and ”1”, respectively, are formed as
∆ZDSTR,i0
=
N̄f −1 Z
(i+1)
X
j=iN̄f
∆ZDSTR,i1
=
j T̄f +∆Td
N̄f −1 Z
(i+1)
X
j=iN̄f
j T̄f +∆Td +T̄I
r̄˜(t)r̄˜(t − ∆Td )dt,
j T̄f +TBP P M +∆Td +T̄I
j T̄f +TBP P M +∆Td
(67)
r̄˜(t)r̄˜(t − ∆Td )dt. (68)
This illustrates that, for each position, the signal consisting of the first TR doublets is delayed and correlated with the signal that carries the second shifted TR
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
109
Table 1: Comparison of TR, ATR, R-TR and R-ATR Schemes
TR
ATR
R-TR
R-ATR
Reference
Power
1/2
1/2
1/2
1/2
Data
Rb
Rb
Rb
Rb
High
Very
High
High
Very
High
Rate
Implementation
Complexity
Table 2: Comparison of TR, DDTR and DSTR Schemes
TR
Reference
Power
1/2
DDTR
0
DSTR
Data
Rb
2Rb
≥ Rb
High
High
High
1/2
Rate
Implementation
Complexity
doublets. The decision statistic in the second branch is formed as
ZDSTR = ∆ZDSTR,i0 − ∆ZDSTR,i1 .
(69)
In the ED/DSTR architecture, the decision statistics from the two receiver branches
are added and the symbol decision is made as
b̂i = sgn(ZED + ZDSTR ).
(70)
As the BER expressions for the ED and the TR are equal, the conditional
BER of ED/DSTR signaling can be written as
v

u 2
uE Z
ED/DSTR |(α, τ )


Pe,ED/DSTR |(α, τ ) = Q t

Var{ZED/DSTR |(α, τ )}
= Q
s
(γED,Kp + γTR,Kq )2
1
2 γED,Kp + γTR,Kq + Nf W TI
!
.
(71)
where Kp and Kq are the number of captured MPCs within the corresponding
integration windows in each branch. It should be noted that the BERs of the
110
Part II
Table 3: Comparison of dual-pulse TR, ED and ED/DSTR Schemes
Reference
TR
ED
ED/DSTR
1/2
0
0
Rb
Rb
Rb
High
Very
Low
Power
Data
Rate
Implementation
Complexity
Low
DSTR-II and ED/DSTR receivers are also expected to be similar, the simulations
conducted in the following section confirm this result.
In Table 1, 2, and 3, a comparison of the proposed TR schemes is presented
with respect to signal power used to transmit reference pulses, achieved data
rate and implementation complexity. The complexity is mainly considered in
terms of the length of analog delay elements required for implementation as it
is exceedingly difficult to build delay lines on the order of 10 − 100 ns (i.e.,
typical values for maximum channel delay spread) [24, 25]; thus, complexity of
the conventional TR which requires delays in this range is referred to as “High”
and complexities of the other receivers are described relative to it.
6
Performance Evaluation
To evaluate BER performance of the proposed receivers, an IR-UWB system is
simulated using the multipath channels proposed by IEEE 802.15.4a [26] for lowdata rate UWB systems. The second derivative of a Gaussian pulse is employed
with about 2 ns pulse duration. For TR and ATR signaling, the uncoded data
rate of Rb = 0.5 Mbps is achieved with Nf = 10, Tf = 200 ns and Td = 100 ns.
The channel model CM1 is used which covers line-of-sight (LOS) scenarios in residential environments with maximum delay spread of about 100 ns, which means
that a negligible amount of IFI occurs. The selection of integration interval is
crucial as the excess or lack of integration can degrade the receiver performance
significantly; the integration interval value TI = 50 ns is used as it collects most
of the energy in the
channels. The energy of the channel impulse responses
P CM1
is normalized as
α2l = 1 and the system is assumed to be perfectly synchronized. For all the receivers except the DDTR, BER versus Eb /No (as Eb = Es )
simulations are performed; whereas BER versus Es /No results are presented for
the DDTR receiver as it uses two bits per symbol.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
111
0
10
−1
BER
10
−2
10
−3
10
TR
ATR
R-TR
R-TR
R-TR
R-TR
µ = 0.5
µ = 0.2
µ = 0.1
µ = 0.05
4
6
−4
10
0
2
8
10
12
Eb /No [dB]
14
16
18
20
Figure 10: BER curves of the TR, the ATR and the R-TR receivers over CM1
channel.
0
10
−1
BER
10
−2
10
TR
ATR
R-ATR
R-ATR
R-ATR
R-ATR
−3
10
µ = 0.5
µ = 0.2
µ = 0.1
µ = 0.05
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 11: BER curves of the TR, the ATR and the R-ATR receivers over CM1
channel.
112
6.1
Part II
TR/ATR versus R-TR/R-ATR
The realistic indoor UWB channels usually have a long channel coherence time
Tco , so the channel coherence time for the channel is assumed to be 0.2 ms. For
recursive receivers, different values of the parameter µ are set, i.e., 0.5, 0.2, 0.1
and 0.05, in order to observe its effect on the BER performance. The simulated
BER curves are shown in Fig. 10 for the TR, the ATR and the R-TR receivers.
For µ = 0.2, the proposed R-TR receiver has 4 dB better performance than the
conventional TR and its BER curve approaches to that of the ATR receiver. The
results validate that, in general, the R-TR receiver performance improves as the
value of µ decreases. For a very small value of µ = 0.05, the R-TR has 2 − 3 dB
gain over the ATR for SNRs of less than 14 dB but its performance deteriorates
in the high SNR region. As smaller values of µ are effective against fluctuation
due to noise, better performance is observed in the low SNR region; on the other
hand, smaller value of µ makes the recently received signal less significant in the
high SNR case, which leads to performance deterioration.
Similar results are depicted in Fig. 11 for the TR, the ATR and the R-ATR
receivers. For µ = 0.5, the BER curves show that the R-ATR yields a 2 dB gain
in SNR over its simple averaging counterpart, i.e., the ATR receiver. The results
verify that the recursive averaging process helps to further alleviate the noise
effect, which in turn improves the BER performance. Though smaller values of
µ in the R-ATR provide at least 4 dB gain over the ATR for SNRs of less than
10 dB, the BER deteriorates significantly for SNRs higher than that. The BER
curves also reveal that, in comparison to the R-TR receiver, higher value of µ
should be used for the R-ATR as the the signals used in the recursive averaging of
the R-ATR are less noisy due to prior simple averaging. From the above results,
it is concluded that, in practice, the value of parameter µ should be set adaptively
depending on the channel variation rate and the SNR of the received signal.
6.2
TR versus DDTR
To evaluate the performance of the DDTR scheme, T̄f = 400 ns and the simulation is divided in two cases based on the value of N̄f . In the first case,
Rb = 1 Mbps if N̄f = Nf /2 = 5, the curves in Fig. 12 show that the DDTR
receiver has the same BER performance as the TR receiver. In addition, the
DDTR saves 3 dB energy and the bit rate is also two times the conventional
TR scheme. In the second case, Rb = 0.5 Mbps if N̄f = Nf = 10, the results in
Fig. 12 show that the DDTR outperforms the TR by about 1 − 1.5 dB. However,
in the second scenario, both schemes utilize equal energy and have the same bit
rate. It can also be explained intuitively that the DDTR receiver exhibits a better performance as it performs twice the number of correlations for each symbol
as compared to the conventional TR receiver.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
113
0
10
TR
DDTR Nf = 5
DDTR Nf = 10
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Es /No [dB]
14
16
18
20
Figure 12: BER curves of TR and DDTR receivers, for case A N̄f = Nf /2 and
for case B N̄f = Nf .
6.3
TR versus DSTR
Similarly, in order to evaluate the performance improvement using the DSTR signaling scheme, the simulation has been performed for Rb = 1 Mbps with N̄f = 5,
T̄f = 200 ns. The TR doublets are separated by Td = 100 ns and the pulses
within a doublet are interleaved in time i.e., δT d = 4 ns. The integration times
are set to be T̄I = 50 ns and δ T̄I = 16 ns and Fig. 13 depicts the BER curves.
The results validate that the DSTR-I structure performs approximately 1.5 dB
better than the conventional TR, while the DSTR-II structure further improves
the performance by providing an SNR gain of 2 dB over the TR receiver.
6.4
TR versus ED/DSTR
In last evaluation, parameters for the BPPM/DSTR are set to be Rb = 1 Mbps,
N̄f = 5, T̄f = 200 ns, ∆Td = 8 ns and δT d = 4 ns; and the integration times are
set to be T̄I = 50 ns and ∆T̄I = 32 ns. Fig. 14 depicts the BER curves for the
conventional single-pulse modulation and the proposed dual-pulse DSTR and
BPPM/DSTR modulations, which transmit two interleaved pulses. It is evident
from the BER evaluations of the TR receiver for single and dual-pulse modulations that about 1 dB SNR gain is achieved by utilizing closely-spaced pulses.
Aside from the dual-pulse gain, the results validate that the TR and the ED show
114
Part II
0
10
TR
DSTR-I
DSTR-II
−1
BER
10
−2
10
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 13: BER curves of conventional TR receiver, and DSTR-I, DSTR-II receivers for the DSTR signaling scheme.
0
10
−1
BER
10
−2
10
Conventional TR
Dual-pulse TR
Dual-pulse ED
DSTR-II
ED/DSTR
−3
10
−4
10
0
2
4
6
8
10
12
Eb /No [dB]
14
16
18
20
Figure 14: BER curves of conventional single-pulse TR, dual-pulse TR and ED,
DSTR-II and ED/DSTR receivers.
Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband
Communications
115
the same BER for dual-pulse modulated signals, while the proposed ED/DSTR
enhances the performance by about 0.5 dB. It should be noted that BER curves
of the low complexity ED/DSTR and resemble with the complex DSTR-II; this
result clearly shows the advantage of using multiple closely spaced pulses in conjunction with the proposed ED/DSTR receiver.
7
Conclusions
In this part, the BER analysis, receiver architectures and performance evaluations
of four TR based modulation and detection schemes have been presented. First
of all, the recursive scheme of the transmitted reference receiver structure for
the detection of impulse radio UWB signals is presented. The proposed R-TR
estimate the reference template for the correlator recursively by appropriately
weighting and aligning the received reference pulses and the previous estimated
templates. The R-TR receiver has a low-complexity compared to the ATR receiver as it requires shorter delays for the recursive averaging. Moreover, due to
the transmission of all the reference pulses of a symbol together in the modified
TR signaling for the ATR and the R-ATR receivers is especially of interest as it
also requires shorter delays for averaging. The performance evaluations indicate
that the R-TR and R-ATR have different SNR gains, depending on the value
of parameter µ, over the conventional TR and ATR receivers. In the low SNR
region, the R-TR and R-ATR receiver performance improves over the TR and
the ATR as the value of µ decreases, whereas higher values of µ are required
in the high SNR regime; this leads to the conclusion that the weight parameter
should be set adaptively in a dynamic channel environment.
Secondly, in the proposed DDTR, which shares non-information-bearing reference pulses by transmitting two TR doublets, each modulated pulse is correlated
with two reference pulses, as opposed to the conventional TR scheme which correlates each modulated pulse with only one reference pulse. The proposed DDTR
receiver structure for detection of DDTR signals requires an extra correlator and
two adders. With this signaling, the proposed DDTR requires 3 dB less energy
per bit and recovers 50% rate loss of the conventional TR scheme, while giving
the same BER performance. Additionally, the BER performance improvement
of about 1 − 1.5 dB can be achieved with the DDTR if the same energy/rate is
used for both scheme.
Thirdly, the proposed DSTR scheme transmits two TR doublets within a
frame duration and shifts the positions of the pulses in the latter doublet. The
amount of energy utilized by the proposed scheme is identical to the conventional
TR scheme. The DSTR scheme also has the potential to increase the data rate
as it uses closely-spaced pulses within a doublet. The DSTR-I receiver for the
proposed scheme is the same as the conventional TR receiver. However, the
116
Part II
improved DSTR-II structure requires a very short delay and correlation operation
to demodulate the pulses within a doublet. The simulation results validate that
the use of the DSTR signaling scheme improves the uncoded BER performance
over the conventional TR signaling scheme.
Finally, a BPPM/DSTR modulation is proposed and a combined ED/DSTR
receiver is used for detection. The ED/DSTR requires a very short delay element
and provides better performance than the conventional ED and TR receivers. In
comparison to to other proposed signaling and detection schemes, the ED/DSTR
receiver may provide best complexity/performance trade-off.
Bibliography
[1] L. Yang and G. B. Giannakis,“Ultra-wideband communications,” IEEE Signal
Process. Magazine, vol. 21, no. 6, pp. 26–54, Nov. 2004
[2] R. C. Qiu, H. Liu, and X. Shen,“Ultra-wideband for multiple access communications,” IEEE Comm. Magazine, vol. 43, no. 2, pp. 80–87, Feb. 2005
[3] M. G. Khan, J. Nordberg, A. Mohammed, and I. Claesson, “Performance
evaluation of RAKE receiver for UWB systems using measured channels in
industrial environments,” AusWireless’06, March 2006
[4] M. Z. Win and R. A. Scholtz, “On the energy capture of ultra-wide bandwidth
signals in dense multipath environments,” IEEE Commun. Lett., vol. 2, Sep.
1998, pp. 245–247
[5] M. G. Khan, A. A. Ashraf, J. Karedal, F. Tufvesson, and A. F. Molisch,
“Measurements and Analysis of UWB Channels in Industrial Environments,”
in Proc. WPMC’05, Aalborg, Denmark, Sept. 2005
[6] D. Cassioli, M. Z. Win, F. Vatalaro, and A. F. Molisch, “Performance of lowcomplexity Rake reception in a realistic UWB channel,” Proc. IEEE ICC’03,
vol.2, pp.763–767, 2003
[7] F. Tufvesson and A. F. Molisch, “Ultra-wideband communication using hybrid
matched filter correlation receivers,” Proc. IEEE Veh. Technol. Conf., vol. 3,
pp. 1290–1294, May 2004
[8] R. Hoctor and H. Tomlinson, “Delay-hopped transmitted-reference RF communications,” IEEE UWBST, pp. 265–269, Baltimore, MD, 2002
[9] R. T. Hoctor and H. W. Tomlinson, “An overviewof delay-hopped,
transmitted- reference RF communications,” in Technical Information Series:
G.E. Research and Development Center, Jan. 2002, pp. 1–29
[10] Y.-L. Chao and R. A. Scholtz “Optimal and suboptimal receivers for
ultra-wideband transmitted reference systems,”IEEE Global Telecommun.
Conf.’03, vol. 2, pp. 759–763, 1-5 Dec. 2003
117
118
BIBLIOGRAPHY
[11] W. M. Gifford and M. Z. Win, “On transmitted-reference UWB communications,”Asilomar Conference on Signals, Systems and Computers, 2004., vol.
2, pp. 1526–1531, Nov. 2004
[12] D. J. Choi and W. E. Stark “Performance of ultra-wideband communications
with suboptimal receivers in multipath channels,”IEEE Journal of Sleceted
Areas Comm., vol. 20, no. 9, pp. 1754–1766, Dec. 2002
[13] Y. -L. Chao and R. A. Scholtz “Novel UWB transmitted reference
schemes,”Asilomar Conference on Signals, Systems and Computers, 2004.,
vol. 1, pp. 652–656, 7-10 Nov. 2004
[14] S. Zhao, H. Liu, and Z. Tian, “Decision directed autocorrelation receivers
for pulsed ultra-wideband systems,” IEEE Trans. Wireless Communications,
vol. 5, no. 8, pp. 2175–2184, Aug. 2006
[15] S. Zhao, P. Orlik, A. F. Molisch, H. Liu, and J. Zhang “Hybrid Ultrawideband Modulations Compatible for Both Coherent and Transmit-Reference
Receivers,”IEEE Trans. on Wireless Communications.
[16] T. Q. S. Quek and M. Z. Win, “ Analysis of UWB transmitted-reference
communication systems in dense multipath channels,” IEEE Journal on Select. Areas in Communications vol. 23, no. 9, September 2005
[17] K. Witrisal, G. Leus, G. J. M. Janssen, M. Pausini, F. Troesch, T. Zasowski, and J. Romme, “Noncoherent ultra-wideband systems”, IEEE Signal
Processing Magazine, July 2009, vol. 26, no. 4, pp. 48–66
[18] J. Wu, Q. Liang, and H. Xiang, ”Adaptive Weighted Noncoherent Receiver
for UWB-PPM Signal in Multipath Channels,” Proc. ICWMMN Conference,
2006.
[19] G. Durisi and S. Benedetto, “Comparison between coherent and noncoherent receivers for UWB Communications,” UWB – State of the Art, Journal of Applied Signal Processing Editorial, EURASIP
[20] T. Zasowski, F. Althaus, and A. Wittneben, “An energy efficient
transmitted-reference scheme for ultra wideband communications,”in Proc.
of 2004 UWBST., Kyoto, Japan, May 2004
[21] Y. L. Chun and C. Toumazou, “Reference Sharing Ultra Wideband Communication System”, International Symposium on Circuits and Systems, ISCAS’04, vol. 4, pp. IV-121–4
BIBLIOGRAPHY
119
[22] Q. H. Dang, A. Trindade, and A.-J. van der Veen, “Signal Model and Receiver Algorithms for a Transmit-Reference Ultra-Wideband Communication
System,”IEEE Journal of Sleceted Areas Comm., vol. 24, no. 4, April 2006,
pp. 773–779
[23] X. Dong, A. C. Y. Lee, and L. Xiao, “A new UWB dual pulse transmission
and detection technique,”in Proc. IEEE ICC’05., May 2005
[24] S. Gezici, F. Tufvesson, and A. F. Molisch, “On the performance of
transmitted-reference impulse radio,” in Proc. of IEEE Globecom, Nov. 2004,
pp. 2874–2879.
[25] M. Casu and G. Durisi, “Implementation aspects of a transmittedreference
UWB receiver,” Journal of Wireless Communications and Mobile Computing,
pp. 537–549, May 2005.
[26] A. F. Molisch et al., “IEEE 802.15.4a channel model - final report,” Tech.
Rep. Document IEEE 802.15-04-0662-02-004a, 2005
Part III
Non-coherent Detectors Based on Fourth
Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using
Channel Measurements
This Part is based on the following publications:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Non-coherent detection of impulse radio UWB signals based on fourth order
statistics”, In Proc. of IEEE International Conference on UWB, ICUWB 2009
pp. 824–828, Canada.
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, Fredrik Tufvesson
and Ingvar Claesson, “Non-Coherent Fourth-Order Detector for Impulse Radio
Ultra Wideband Systems: Empirical evaluation using Channel Measurements”,
published in Springer Journal of Wireless Personal Communications, Online First
on November 01, 2011.
Non-coherent Detectors Based on Fourth Order
Statistics of Impulse Radio UWB Signals: Empirical
evaluation using Channel Measurements
November 22, 2011
Abstract
Low-complex and low power non-coherent energy detector (ED) is interesting for low data rate impulse radio (IR) ultra wideband (UWB) systems
but, compared to coherent receivers, it suffers from a loss in performance
due to low signal-to-noise ratio (SNR) at the detector. In addition, the performance of an ED strongly depends on the integration interval (window
size) of the integrator and the window position. A non-coherent kurtosis
detector (KD) and a fourth-order detector (FD), which can discriminate between Gaussian noise signals and non-Gaussian IR-UWB signals by directly
estimating the fourth-order moment of the received signal, are presented.
The performance of the detectors is evaluated using real channels measured in a corridor, an office and a laboratory environment. The results
show that bit-error-rate (BER) performance of the proposed KD receiver
is better than the ED receiver only under certain conditions, while the FD
receiver is slightly better than the ED in low SNR region and its performance improves as the SNR increases. In addition, the performance of the
FD receiver is less sensitive to overestimation of the integration interval
making it relatively robust to variations of the channel delay spread. Finally, a criteria for the selection of integration time of the proposed detector
is suggested.
1
Introduction
UWB systems have gained significant attention for high data rate wireless personal area networks (WPANs) as well as for low data rate WPANs and sensor networks. The IEEE 802.15.4a group has identified that IR-UWB systems are wellsuited for low cost, low power operation as well as location-based applications.
124
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
125
An IR-UWB system is based on the transmission of short (often subnanosecond)
pulses which occupy a wide frequency band. The commonly used pulse shapes
for UWB communications are the first derivative of the Gaussian pulse and the
second derivative of the Gaussian pulse, which are typically obtained by directly
driving an antenna with short-duration electrical signals [1].
Due to the very large bandwidth (usually several GHz), an implementation
of an all-digital UWB receiver requires high-sampling frequency ADCs, which
makes the receiver structure complex, expensive and especially power consumption increases, since the current consumption is proportionally quadratic to the
clock frequency. Alternatively, an analog implementation of the IR-UWB receiver
is capable to achieve a simple, low cost and low power receiver due to the lowfrequency ADC required therein. Hence, the analog domain implementation of
the IR-UWB receivers may be a preferable alternative for low data rate wireless
sensor networks.
Nevertheless, the coherent RAKE receiver implemented in the analog domain also requires a fairly complicated structure, with one despreader (correlator, RAKE finger) for each delay bin to be received [2]. As received UWB signals
may consist of hundreds of multipath components (MPCs) [3], a large number
of RAKE fingers are needed when the delay spread is large compared to the
pulse duration. The RAKE receiver also requires a locally generated reference
template [4, 5], accurate synchronization, and channel estimation. Hence, noncoherent detection of IR-UWB signals have gained popularity due to low-complex
and low power constraints of low data rate IR-UWB transceivers.
A non-coherent signaling and detection scheme in which a reference signal
and a delayed data-modulated signal are transmitted together [6, 7], is called
transmitted reference (TR). The reference and delayed data-modulated signals
are aligned and correlated at the TR receiver for detection. However, the TR
receiver requires long analog delay lines and its performance degrades as noisy
reference signals are used in the correlator for detection. Energy detection (ED)
is another non-coherent approach for IR-UWB signals, where a low-complexity
analog receiver is achieved at the expense of performance degradation due to low
SNR of the metric used for the decision [8, 9]. Moreover, an ED with a fixed
integration interval (window size) of the integrator is not robust against variations of channel delay spread and channel impulse response [8, 10]. To enhance
detection performance, weighted ED techniques using multiple integrator have
been proposed, see e.g., [11,12]. The drawback of these techniques is a higher implementation complexity as they also require high sampling rates and estimation
of the weighting coefficients.
Recently, a non-coherent kurtosis detector (KD) based on the normalized
fourth central moment (kurtosis) of the received IR-UWB signal was proposed
in [13]. In estimation theory, the cumulants, or higher-order moments, are used
126
Part III
to capture distinguishing characteristics of the probability distribution of the received signal. Through the Gram-Charlier expansion of a probability distribution
function, cumulants are characterizing the distribution [14]. The cumulants can
therefore be simply considered as quantifying measures for distinguishing two
regions of signals with different distributions, by comparing the values of the
cumulants of the regions. In [13], the presence of non-Gaussian-distributed IRUWB signals in Gaussian noise was detected by using the kurtosis. However, the
KD receiver is better than the ED receiver only under certain conditions such as
the unavailability of an optimum integration time and multipath channels having
very short delay spread, i.e., close to AWGN conditions.
In this paper, a fourth-order detector (FD) which is based on the fourth moment about zero, also called the fourth raw or crude moment, of the received
signal is proposed. The FD receiver does not require high sampling rates and
there is only a slight increase in receiver complexity as compared to the conventional ED receiver. To investigate the effects of realistic operating environments
on the detector performance, empirical evaluation and BER simulations are performed using the channels obtained from the measurements. In addition, the
problem of estimating a suitable integration time of the proposed detector is addressed. As the estimation of integration time should be performed using realistic
channel characteristics, the channels obtained from the measurements are used
to analyze the integration time of the proposed detector.
The organization of Part III is as follows. The model of an IR-UWB system
is presented in Section 2. Section 3 describes the conventional ED, the KD
and the proposed FD receivers. In Section 4, the UWB channel measurement
environment and the results of the measurement campaign are presented. In
Section 5, performance of the the three non-coherent receivers is evaluated and,
finally, conclusions are presented in Section 6.
2
System Model
The transmitted signal generated of an orthogonal binary pulse position modulated (BPPM) IR-UWB system is written as
u(t) =
∞
X
p
Es
p(t − iTs − di TBP P M ),
(1)
i=−∞
where p(t) is a normalized UWB pulse of duration Tp and bandwidth W , whereas
Es is the energy per symbol and it is equal to the energy per bit Eb . The symbol
duration Ts is divided into two subintervals of duration equal to the BPPM shift,
i.e., TBP P M = Ts /2. Each signal representing one binary information symbol bi
is transmitted using a low duty cycle pulse, i.e., Ts ≫ Tp . The bit bi ∈ {−1, 1}
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
127
determines the position of the signal as di = (bi + 1)/2 ∈ {0, 1}; i.e., the signal is
either at the beginning of a symbol at iTs or with an offset iTs + TBP P M . The
signal is transmitted over a multipath channel which is modeled as a tapped-delay
line with impulse response
h(t) =
K−1
X
k=0
αk δ(t − τk ),
(2)
where K is the number of MPCs, αk and τk are the weight and delay associated
with the k th multipath component, and δ(·) is the Dirac delta function. The
signal s(t) obtained at the output of the tapped-delay line multipath channel is
the convolution of u(t) and h(t), according to
s(t)
= u(t) ∗ h(t)
∞ K−1
X
X
p
=
Es
αk p(t − iTs − di TBP P M − τk )
i=−∞ k=0
∞
X
p
=
Es
g(t − iTs − di TBP P M ),
(3)
i=−∞
where g(t) is interpreted as the aggregate channel after convolving the multipath
channel with the transmitted pulse, i.e.,
g(t) =
=
p(t) ∗ h(t)
K−1
X
k=0
αk p(t − τk ).
(4)
The duration of g(t) is defined as Tg = Tp + Tmds , where Tmds is the maximum
delay spread of the channel. The delay spread effect of the multipath channel
may cause interference between two pulse positions. This interference between
two adjacent pulse positions can be avoided, i.e., orthogonality between the two
consecutive pulse positions can be maintained, by keeping TBP P M ≥ Tg . The
signal at the receiving antenna, denoted as r(t), is corrupted by additive white
Gaussian noise (AWGN), denoted as n(t), with two-sided PSD No /2, i.e.,
r(t) = s(t) + n(t).
3
(5)
Non-Coherent Detectors
Non-coherent detectors based on second-order (energy) and fourth-order (e.g.,
kurtosis) statistics of the received signal are discussed in the following subsections.
128
3.1
Part III
Conventional Energy Detector
In the conventional ED, the received signal is passed through a bandlimiting filter,
which removes the out-of-band noise from the received signal. The resulting signal
after passing through a bandpass filter is the convolution of f (t) with r(t), and
is written as
r̃(t) =
=
s̃(t) + ñ(t)
∞
X
p
Es
g̃(t − iTs − di TBP P M ) + ñ(t),
(6)
i=−∞
where g̃(t) is the bandlimited aggregate channel, ñ(t) is bandlimited noise at
the output of the filter. The output of the filter is passed through a squarelaw device and an integrator, see Fig. 1. The decision metrics for each of the
two pulse positions of orthogonal BPPM signal is obtained by integrating the
corresponding energy of pulse positions in the first and second half of each bit.
Without loss of generality, it is henceforth assumed that the detection of the
ith symbol is considered. In each frame, the integrated energy is obtained by
sampling the output of the integrator twice per frame, i.e., after the two possible
positions of the symbol bi . The sampled energy estimates for the two possible
positions of the ith symbol are written as
ZED,i0
ZED,i1
=
=
Z
(i+1)Ts +TI
[r̃(t)]2 dt,
iTs
Z (i+1)Ts +TBP P M +TI
[r̃(t)]2 dt,
(7)
(8)
iTs +TBP P M
where the sub-indices “ED, i0” and “ED, i1” denote energy estimates for positions
“0” and “1”, respectively, of the ith symbol. The length of the integration interval
determines the amount of multipath energy and the amount of noise captured
by the receiver, and its value ranges between 0 < TI ≤ TBP P M . The decision in
the conventional ED receiver is made in favor of the pulse position which carries
greater energy, i.e.,
b̂i = sgn(ZED,i0 − ZED,i1 ).
(9)
3.2
Kurtosis Detector (KD)
A non-coherent detector based on the normalized fourth central moment (kurtosis) of the received IR-UWB signal, proposed in [13], is called KD. The kurtosis
is a statistical quantity that can be used for indicating the non-Gaussianity of a
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
129
r(t)
BPF
r̃(t)
r̃2 (t)
(·)2
f (t)
R t+TI
t
+
(·)dt
b̂i
−
Timing
Figure 1: Architecture of conventional non-coherent energy detector (ED) receiver.
random variable [14]. The kurtosis for a zero-mean random variable x is defined
as
κx =
E{x4 }
,
E{x2 }2
(10)
where E{·} denotes the expected value of the variable. The kurtosis value for nonGaussian-distributed IR-UWB signals is larger than that for Gaussian distributed
signals. The kurtosis of a Gaussian distribution is 3 and the kurtosis value is
greater than 3 for so-called super-Gaussian distributions that have sharp peaks
and longer tails [14] such as the distribution of IR-UWB pulses. Thus, kurtosis
can be used as a quantitative measure of the non-Gaussianity of the received
IR-UWB signals at the receiver. The fourth standardized moment is also defined
in terms of excess kurtosis as
Kx = E{x4 } − 3E{x2 }2 .
(11)
The value of excess kurtosis for a Gaussian distributed random variable is zero
[14]. The KD receiver is obtained from a conventional ED receiver by adding
an extra square-law device, an integrator and a sampler, see Fig. 2. In the KD
receiver, like in the conventional ED, the integrated energy values, denoted as
zi0 and zi1 , for the two assumed pulse positions of the ith symbol are obtained
in the first branch
zi0
zi1
=
=
Z
(i+1)Ts +TI
[r̃(t)]2 dt,
iTs
Z (i+1)Ts +TBP P M +TI
iTs +TBP P M
[r̃(t)]2 dt.
(12)
(13)
130
Part III
r(t)
BPF
r̃(t)
(·)2
f (t)
r̃2 (t)
R t+TI
t
(·)dt
Timing
r̃4 (t)
(·)2
R t+TI
t
Kurtosis
Estimation
&Decision
b̂i
(·)dt
Timing
Figure 2: Architecture of the KD receiver obtained through the addition of an
extra square-law device, an integrator and a sampler in a conventional ED receiver.
In addition, the receiver estimates fourth moment values, denoted as yi0 and yi1 ,
for the two assumed pulse positions of ith symbol in the second branch, i.e.,
yi0
yi1
=
=
Z
(i+1)Ts +TI
[r̃(t)]4 dt,
iTs
Z (i+1)Ts +TBP P M +TI
[r̃(t)]4 dt.
(14)
(15)
iTs +TBP P M
The kurtosis for each of the two pulse positions is estimated, according to Eq.
(11), using the energy and fourth moment estimates as
ZKD,i0
ZKD,i1
=
=
yi0 − 3[zi0 ]2 ,
2
yi1 − 3[zi1 ] .
(16)
(17)
A decision that is based on the estimated kurtosis values is made in favor of the
pulse position with greater kurtosis value, i.e., b̂i = sgn(ZKD,i0 − ZKD,i1 ).
3.3
Fourth-Order Detector (FD)
Since kurtosis is a measure of non-Gaussianity of a signal, and non-Gaussianity
of a signal decreases after passing through a multipath channel with large delay
spread due to the central limit theorem, the performance of the KD receiver
degrades over multipath channels. An alternative receiver named FD which is
based on estimation of the fourth moment about zero of the received IR-UWB
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
131
r(t)
BPF
f (t)
r̃(t)
(·)2
(·)2
r̃4 (t) R t+T
I
r̃2 (t)
t
+
(·)dt
b̂i
−
Timing
r̃2 (t)
Figure 3: Architecture of the FD receiver obtained through the addition of an
extra square-law device in the conventional ED receiver.
signal is presented herein, see Fig. 3. The complexity of the FD receiver is less
than the KD receiver as it can be obtained from a conventional ED receiver by
employing only an extra square-law device. In the proposed FD receiver, the
decision metric is formed by estimating fourth moment values for positions “0”
and “1” of the ith symbol, identical to Eq. (14) and Eq. (15), respectively, i.e.,
ZFD,i0
ZFD,i1
=
=
Z
(i+1)Ts +TI
[r̃(t)]4 dt,
iTs
Z (i+1)Ts +TBP P M +TI
[r̃(t)]4 dt.
(18)
(19)
iTs +TBP P M
A decision that is based on the estimated fourth moment values is made according
to b̂i = sgn(ZFD,i0 −ZFD,i1 ). The rationale behind using the proposed FD receiver
instead of the KD receiver is given in the following analysis.
Under AWGN channel conditions, assuming that the IR-UWB signal and
Gaussian noise are independent (uncorrelated) and Gaussian noise is ergodic, the
received signal for the ith symbol is given by
r̃i,l (t) = s̃i,l (t) + ñi,l (t),
(20)
where l ∈ {0, 1}, stands for the two possible pulse positions of the received
ith symbol. Assuming that hypothesis H0 is true and dropping the index i for
simplification in the presentation, the received signal will have IR-UWB signalplus-noise corresponding to l = 0, i.e.,
r̃0 (t) = s̃0 (t) + ñ0 (t),
(21)
and corresponding to l = 1, the signal consists of the noise-only region, i.e.,
r̃1 (t) = ñ1 (t).
(22)
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Part III
For the KD receiver, it estimates one kurtosis value for the IR-UWB signalplus-noise region and the second value for the noise-only region and the KD
receiver then compares the two kurtosis values. According to Eq. (11), the
excess kurtosis value for the IR-UWB signal-plus-noise region is given by
Kr̃0 = E r̃0 (t)4 } − 3E r̃0 (t)2 }2
= E (s̃0 (t) + ñ0 (t))4 } − 3E (s̃0 (t) + ñ0 (t))2 }2
= E s̃0 (t)4 } + E ñ0 (t)2 }E s̃0 (t)2 } + 2E s̃0 (t)3 }E ñ0 (t)}
+E s̃0 (t)2 }E ñ0 (t)2 } + E ñ0 (t)4 } + 2E s̃0 (t)}E ñ0 (t)3 }
+2E s̃0 (t)3 }E ñ0 (t)} + 2E s̃0 (t)}E ñ0 (t)3 } + 4E s̃0 (t)2 }E ñ0 (t)2 }
2
−3 E s̃0 (t)2 } + E ñ0 (t)2 } + 2E s̃0 (t)ñ0 (t)} ,
(23)
since E ñ0 (t)} = 0 and E ñ0 (t)3 } = 0,
Kr̃0 = E s̃0 (t)4 } + E ñ0 (t)2 }E s̃0 (t)2 } + E s̃0 (t)2 }E ñ0 (t)2 } + E ñ0 (t)4 }
+4E s̃0 (t)2 }E ñ0 (t)2 } − 3E s̃0 (t)2 }2 − 3E ñ0 (t)2 }2
−6E s̃0 (t)2 }E ñ0 (t)2 }
= E s̃0 (t)4 } + E ñ0 (t)4 } + 6E s̃0 (t)2 }E ñ0 (t)2 } − 3E s̃0 (t)2 }2
−3E ñ0 (t)2 }2 − 6E s̃0 (t)2 }E ñ0 (t)2 }
= E s̃0 (t)4 } + E ñ0 (t)4 } − 3E s̃0 (t)2 }2 − 3E ñ0 (t)2 }2
=
Ks̃0 + Kñ0 ,
(24)
where Kr̃0 , Ks̃0 and Kñ0 are kurtosis values for the received signal r̃0 (t), the
IR-UWB signal s̃0 (t), and the Gaussian noise ñ0 (t), respectively. As the kurtosis
(or excess kurtosis) value for the Gaussian noise is zero [14], i.e., Kñ0 = 0, Eq.
(24) reduces to
Kr̃0
=
=
Ks̃0
E s̃0 (t)4 } − 3E s̃0 (t)2 }2 .
(25)
Kr̃1 = Kñ1 = 0,
(26)
In a similar manner, the kurtosis value for the noise-only region is
where Kr̃1 and Kñ1 are kurtosis values for the received signal r̃1 (t), and the
Gaussian noise ñ1 (t), respectively. Finally, a distance measure between the signalplus-noise region and the noise-only region for the KD receiver can be written
as
SKD
=
=
Kr̃0 − Kr̃1
E s̃0 (t)4 } − 3E s̃0 (t)2 }2 .
(27)
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
133
For the FD receiver, making similar assumptions as for the KD receiver, yields
that the estimated fourth moment value for the IR-UWB signal-plus-noise region
is
Fr̃0 = E (s̃0 (t) + ñ0 (t))4 }
= E s̃0 (t)4 } + E ñ0 (t)2 }E s̃0 (t)2 } + E s̃0 (t)2 }E ñ0 (t)2 } + E ñ0 (t)4 }
+4E s̃0 (t)2 }E ñ0 (t)2 }
= E s̃0 (t)4 } + E ñ0 (t)4 } + 6E s̃0 (t)2 }E ñ0 (t)2 },
(28)
where F denotes the fourth moment estimate. The estimated forth moment value
for the noise-only region is given by
Fr̃1 = E ñ1 (t)4 }.
(29)
A similar distance measure between the signal-plus-noise and the noise-only regions of the FD receiver is
SFD
=
=
=
Fr̃0 − Fr̃1
E s̃0 (t)4 } + E ñ0 (t)4 } + 6E s̃0 (t)2 }E ñ0 (t)2 } − E ñ1 (t)4 }
E s̃0 (t)4 } + 6E s̃0 (t)2 }E ñ0 (t)2 },
(30)
where the equivalent fourth-order noise terms are canceled as the Gaussian noise
is assumed to be ergodic. The above analysis shows that the separation measure
related to the FD receiver in Eq. (30) is greater than the separation measure
related to the KD receiver in Eq. (27), i.e., SFD > SKD . Hence, under AWGN
channel conditions and ideal detector parameters, it is believed that the larger
distance between the two regions in the FD receiver will provide a lower BER
than the corresponding KD receiver.
4
Channel Measurements
A channel measurement campaign is performed to evaluate the performance of
the proposed detector in realistic environments. The following subsections incorporate the measurement procedure, characteristics of the environments, and the
results.
4.1
Measurement Procedure
The channel measurements1 are performed in a corridor, in an office, and in a
medium-sized laboratory environment, at Lund University, Sweden. The laboratory room contain many metallic and wooden objects typically found in such
1 The measurement campaign was performed in collaboration with Dr. Fredrik Tufvesson,
at Lund University, Lund, Sweden.
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Part III
Figure 4: A view of the laboratory environment for UWB channel measurements.
environments as depicted in Fig. 4 . The corridor, office and laboratory have
floor areas of 2.1 × 30 m2 , 2.9 × 6 m2 and 6.2 × 6 m2 , respectively. The ceiling
height of all three environments is 3 m. Fig. 5(a) and (b) show the layout of the
office and laboratory, respectively.
The measurements are performed in the frequency domain using a vector network analyzer (VNA). The complex channel transfer function H(f ), estimated
by the VNA, covers the frequency range from 3.1 to 10.6 GHz. The number of
frequency points measured within the specified frequency range is 1601, which
results in a delay(or temporal) resolution of 0.133 ns. A maximum channel length
of 213 ns corresponding to a 64 m path delay can be measured. The antennas
used as transmitter and receiver are commercial meander line antennas from SkyCross, which are almost omnidirectional in the horizontal plane. A virtual MIMO
(multiple-input multiple-output) system of M × N = 5 × 5 antenna positions is
created by moving each antenna to five different positions along a rail using stepper motors. The antenna separation is 97 mm, i.e., more than half a wavelength
at the minimum frequency (i.e., 3.1 GHz).
In the corridor and office, three peer-to-peer (P-P) line-of-sight (LOS) measurements are performed in each environment. The TX was moved at three different positions keeping the RX fixed at one position in both the environments. In
Fig. 5(a), the measurements performed in the office are labelled, ‘TX01’, ‘TX02’
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
135
Figure 5: Layout of the (a) office environment (b) laboratory environment, with
distances given in [cm] and TX-RX antenna positions specified for UWB channel
measurements.
−10
−15
−20
−25
[dB]
−30
−35
−40
−45
−50
−55
−60
0
20
40
60
Delay [ns]
80
100
Figure 6: The averaged PDP of one measurement position (i.e. TX03-RX01) in
the corridor environment.
136
Part III
−10
−15
−20
−25
[dB]
−30
−35
−40
−45
−50
−55
−60
0
20
40
60
Delay [ns]
80
100
Figure 7: The averaged PDP of one measurement position (i.e. TX02-RX01) in
the office environment.
−10
−15
−20
−25
[dB]
−30
−35
−40
−45
−50
−55
−60
0
20
40
60
Delay [ns]
80
100
Figure 8: The averaged PDP of one measurement position (i.e. TX01-RX02) in
the laboratory environment.
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
137
and ‘TX03’ for three TX locations and fixed RX location is labelled as ‘RX01’.
Similarly, in the laboratory environment, a total of nine, mostly obstructed lineof-sight (OLOS), positions are measured. The measurements are performed with
three TX and three RX positions in the laboratory. The P-P OLOS measurements were performed at two locations of TX labelled ‘TX01’ and ‘TX02’ in
Fig. 5(b). In one of the measurements, the TX, labelled as ‘TX03’, was in an
elevated position, similar to a base station (BS) or an access point, at a height
of 2.2 m. The RX antenna positions are the same for all TX positions and their
locations are labelled in Fig. 5(b) as ‘RX01’, ‘RX02’ and ‘RX03’.
4.2
Channel Delay Profiles
The measured transfer functions H(f ) are transformed to the delay domain using
the inverse Fourier transform. The power delay profile (PDP) of each measurement is obtained from the impulse response of the channel, and the PDP from
the nth transmitter to the mth receiver on the virtual arrays is defined as
P DP (τ, m, n) = |h(τ, m, n)|2 .
(31)
The PDP calculated from the measurement on one antenna pair of the virtual
array is called instantaneous PDP. The average of all instantaneous PDPs corresponding to the different combinations of transmitter and receiver positions on
the virtual array is called an averaged PDP. Figs. 6 and 7 show the averaged
PDP, obtained from 25 instantaneous PDPs, of one measurement position in the
corridor and the office, respectively. For these measurements, the averaged PDPs
indicate that the first MPCs are the strongest and that the MPCs arrive in clusters. Similarly, the averaged PDP of one measurement position in the laboratory
environment is shown in Fig. 8. The averaged PDP indicates that the strongest
component arrives 10 − 20 ns after the first arriving component. The averaged
PDP results are used in the following section to obtain a rule of thumb for the
estimation of optimum integration time.
5
Performance Evaluation
In this section, the probability of error of the three detectors is evaluated empirically using the real multipath channels obtained from the measurement campaign,
and the BER performance of the detectors is compared using multipath channels.
5.1
Empirical Evaluation
In case of non-ideal (realistic) channel conditions, since the received signal is
subject to random fluctuations due to the (possibly) time-varying channel and the
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Part III
additive random noise, the estimated decision statistics also fluctuate randomly
and may cause erroneous decisions. Evaluation of the probability of error (Pe ) of
the detector structures requires knowledge of the statistical distributions of the
decision statistics. For binary pulse position modulation (BPPM) scheme, the
probability of a symbol (bit) detection error is given by
Pe = P (Zi,0 − Zi,1 < 0|bi = −1) = P (Zi,0 − Zi,1 ≥ 0|bi = 1),
(32)
where Zi,0 and Zi,1 represent the estimated decision statistics of orthogonal
BPPM signals for the detector structure at hand. The detector performance
is quantified by the probability distribution functions (PDFs) of the estimated
decision statistics as it provides information on how these estimated values are
distributed in the signal-plus-noise region and in the noise-only region. In particular, the amount of overlap between the signal-plus-noise PDF and the noise-only
PDF is proportional to the probability of bit-error of the detector. As the decision statistics are of order four for kurtosis/fourth-order detector, the derivation
to find a modeled PDF in multipath channel conditions will probably involve simplifications and assumptions. Therefore, an exact expression of the BEP of the
kurtosis/fourth-order detector can not be derived and the detector performance
must be assessed via empirical evaluation using the real multipath channels. Using the alternative approach, the PDFs of the decision statistics of the detectors
are estimated using the channel measurements. By estimating the PDFs using
real channels, the actual behavior of the decision statistics is captured instead
of some modeled behavior. In order to perform empirical evaluation, each decision statistic variable at the output of the integrator can be considered a sum
of N = 2W TI virtual samples, due to the sampling theorem, where W is the
bandwidth and TI is the integration time. For the ED receiver, under hypothesis
H0 , the sampled energy estimates ZED,i0 |H0 and ZED,i1 |H0 are obtained as
ZED,i0 |H0
∼
=
ZED,i1 |H0
∼
=
N
−1
X
tn =0
N
−1
X
tn =0
2
s̃i0 (tn ) + ñi0 (tn ) ∆t,
2
ñi1 (tn ) ∆t,
(33)
(34)
where ∆t is the sampling interval and tn = n∆t is the sampling time index.
Similar expressions for the decision statistics of the KD and the FD receiver can
be obtained using the sampling theorem. The random variables ZKD,i0 |H0 and
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
139
ZED,0
ZED,1
PDF
100
50
0
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
ZKD,0
ZKD,1
1500
PDF
0.065
1000
500
0
0
0.005
0.01
0.015
PDF
600
0.02
ZFD,0
ZFD,1
400
200
0
0.005
0.01
0.015
0.02
0.025
0.03
Decision statistic value
Figure 9: Estimated Probability Distribution Functions (PDFs) of the decision
statistic values for the ED (upper), the KD (middle) and the proposed FD (lower)
under hypothesis H0 , where Eb /No = 12 dB, and TI = 20 ns.
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Part III
ZKD,i1 |H0 are estimated as
ZKD,i0 |H0 ∼
=
ZKD,i1 |H0 ∼
=
N
−1
X
tn =0
N
−1
X
tn =0
NX
2
−1
4
2
s̃i0 (tn ) + ñi0 (tn ) ∆t −3
s̃i0 (tn )+ ñi0 (tn ) ∆t , (35)
tn =0
4
ñi1 (tn ) ∆t − 3
NX
−1
tn =0
2
2
ñi1 (tn ) ∆t .
(36)
For the FD receiver, the random variables ZFD,i0 |H0 and ZFD,i1 |H0 are estimated
as
ZFD,i0 |H0
∼
=
ZFD,i1 |H0
∼
=
N
−1
X
tn =0
N
−1
X
tn =0
4
s̃i0 (tn ) + ñi0 (tn ) ∆t,
4
ñi1 (tn ) ∆t.
(37)
(38)
The PDFs of these estimated decision statistic variables for the ED, the KD
and the proposed FD using the channels measured in the office environment are
presented in Fig. 9, for Eb /No = 12 dB and TI = 20 ns (i.e., an estimated
optimum value of TI for the office channels). Since the distributions are approximately known through estimation of the PDFs, the probability of bit-error can
be estimated by empirical evaluation of Pe = P (Zi,0 − Zi,1 < 0|bi = −1). For the
particular setting in Fig. 9, the estimated probability of bit-error (Pe ) is 0.66 %,
9 %, and 0.43 % for the ED, the KD, and the proposed FD, respectively. The
probability of bit-error (Pe ) is very high for the KD receiver as the optimum
value of TI is used for detection. For higher Eb /No values, the distribution of the
noise-only decision statistic tends towards the Dirac δ-function, and the signalplus-noise decision statistic distribution will tend towards the IR-UWB signal
distribution. As the amount of overlap between the signal-plus-noise PDF and
the noise-only PDF tends towards zero, it causes the probability of bit-error to
decrease proportionally. On the other hand, decreasing the Eb /No value broadens
the estimated PDFs, leading to a poor detection performance.
The decision statistic PDFs depicted in Fig. 9 also indicate that the PDFs
related to the ED show a high degree of similarity for signal-plus-noise region
and noise-only region. However, the PDFs related to the KD and the FD show
a high degree of disparity. The signal-plus-noise decision statistics for the KD
and the FD are skewed right due to the high kurtosis value of the UWB pulse
signal. In contrast, the corresponding noise decision statistics are symmetric and
significantly less spread. Further, it is noteworthy that the PDFs related to the
proposed FD has the least amount of overlap compared to the KD and the ED.
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
141
0
10
ED
KD
FD
−1
BER
10
−2
10
−3
10
0
20
40
60
80
100
TI [ns]
120
140
160
180
200
Figure 10: BER curves of the conventional ED receiver, the KD receiver and the
proposed FD receiver, for Eb /No = 12 dB, as a function of integration time TI
over AWGN channels, of the conventional ED receiver.
0
10
ED
KD
FD
−1
BER
10
−2
10
−3
10
0
20
40
60
80
100
TI [ns]
120
140
160
180
200
Figure 11: BER curves of the conventional ED receiver, the KD receiver and the
proposed FD receiver, for Eb /No = 12 dB, as a function of integration time TI
over the measured corridor multipath channels.
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Part III
This fact has been used in this research as an indicator that the decision statistics
provided by the proposed FD has higher performance, in terms of less overlap,
than the other two methods. The BER versus Eb /No evaluations conducted in
the following subsections confirm this result.
5.2
System Parameters and Design Rule
In all the evaluations, the second derivative of a Gaussian pulse having pulse duration of Tp = 0.5 ns is used in conjunction with the orthogonal BPPM. The symbol
duration Ts = 400 ns provides a BPPM shift of TBP P M = 200 ns to ensure the
orthogonality between two consecutive pulse positions after passing through the
multipath channels.
P 2 The energy of the channel impulse responses is normalized
to unity, i.e.,
αl = 1, and it is assumed that there is no interpulse interference
and that a perfect synchronization is achieved.
The key design parameter in non-coherent receivers is the integration time and
its selection is crucial as the excess or lack of integration can degrade the receiver
performance significantly. Since the integration time is strongly dependent upon
the current channel conditions, it might be beneficial to track the channel characteristics and then adapt the integration time in order to improve robustness of
the IR-UWB receivers. However, due to the low complex receiver constraint and
that it is difficult to implement an adaptive algorithm using analog devices, the
value of the integration time is often fixed during the design and implementation
of the receiver [15]. Thus, it is necessary to find a suitable integration time to
integrate the energy available in the signal-dominant region in order to maximize
the receiver performance.
In Figs. 10, 11, 12 and 13, the BER performance of all three receivers is
shown as a function of integration time TI using the AWGN, the corridor, the
office and the laboratory channels, respectively. The results show that the KD
receiver performs best only in AWGN channel conditions with non-optimum TI
values and its performance degrades significantly in the multipath environment.
From this observation, it can be conluded that the KD receiver is not suitable for
detection if the optimum integration time of the multipath channel is available.
Additionally, the results demonstrate that BER of the conventional ED and the
proposed FD receivers exhibit a local minima, i.e., an optimum value of TI ,
around 10 ns for the corridor channels. From the slopes of the curves after the
minimal values, it is also observed that performance of the ED receiver drops
rapidly as compared to the FD receiver as the integration time increases. It can
be concluded that the proposed FD receiver is less sensitive to the overestimation
of the integration time as opposed to the ED receiver.
Finally, a rule of thumb for the selection of integration time is obtained by
comparing the results obtained for the optimum integration times with the av-
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
143
0
10
ED
KD
FD
−1
BER
10
−2
10
−3
10
0
20
40
60
80
100
TI [ns]
120
140
160
180
200
Figure 12: BER curves of the conventional ED receiver, the KD receiver and the
proposed FD receiver, for Eb /No = 12 dB, as a function of integration time TI
over the measured office multipath channels.
0
10
ED
KD
FD
−1
BER
10
−2
10
−3
10
0
20
40
60
80
100
TI [ns]
120
140
160
180
200
Figure 13: BER curves of the conventional ED receiver, the KD receiver and the
proposed FD receiver, for Eb /No = 12 dB, as a function of integration time TI
over the measured laboratory multipath channels.
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Part III
140
120
Occurrences
100
80
60
40
20
0
0
5
10
15
20
25
Topt [ns]
30
35
40
Figure 14: Distribution of the optimum values of integration time Topt for FD
receiver with Eb /No = 12 dB using all 375 available channel realizations from the
measurement campaign.
eraged PDPs from the channel measurements. The distribution of the optimum
values of integration time Topt for the FD receiver is evaluated and presented in
Fig. 14 using all 375 available channel realizations from the measurement campaign. The mean value of Topt , which is distributed in the range of 5 to 40 ns,
is about 13 ns. According to a worst-case design approach suggested in [8], the
value of integration time should be around 40 ns. The averaged PDPs shown in
Figs. 6, 7, and 8 indicate that all the MPCs within 10 dB of the strongest path
are captured with an integration time between 10 − 15 ns for the channels measured in the corridor and in the office. However, for the channel measured in the
laboratory, it is observed that the integration time should be between 20 − 30 ns
to capture all MPCs within 10 dB of the strongest path. These observed values
of integration time are very close to the optimum integration times obtained from
the simulation results shown in Figs. 11, 12 and 14. Hence, a simple criteria for
selection of the integration time of the proposed FD receiver is to choose the
value of TI which captures all the MPCs within 10 dB of the strongest path of
the worst set of channels in the available realizations.
5.3
BER versus SNR Results
The BER curves of the receivers are evaluated as a function of the Eb /No , where
Es = Eb . For the ED, the KD and the FD receivers, BER results over the
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
145
0
10
−1
BER
10
−2
10
−3
10
ED, TI = 40 ns
KD, TI = 40 ns
FD, TI = 40 ns
ED, TI = 10 ns
KD, TI = 10 ns
FD, TI = 10 ns
−4
10
6
8
10
Eb /No [dB]
12
14
Figure 15: BER curves of the conventional ED, the KD and the proposed FD
receiver over multipath channel measured in the corridor environment.
0
10
−1
BER
10
−2
10
−3
10
ED, TI = 40 ns
KD, TI = 40 ns
FD, TI = 40 ns
ED, TI = 20 ns
KD, TI = 20 ns
FD, TI = 20 ns
−4
10
6
8
10
Eb /No [dB]
12
14
Figure 16: BER curves of the conventional ED, the KD and the proposed FD
receiver over multipath channel measured in the office environment.
146
Part III
0
10
−1
BER
10
−2
10
−3
10
ED, TI = 40 ns
KD, TI = 40 ns
FD, TI = 40 ns
ED, TI = 20 ns
KD, TI = 20 ns
FD, TI = 20 ns
−4
10
6
8
10
Eb /No [dB]
12
14
Figure 17: BER curves of the conventional ED, the KD and the proposed FD
receiver over multipath channel measured in the laboratory environment.
measured channels for the corridor, the office and the laboratory environments
are shown in Figs. 15, 16 and 17, respectively. The BER comparison of the
receivers over the corridor and the office channels shows that the proposed FD
receiver has an improvement of 0.5 dB to 1 dB over the ED receiver, depending
on the value of TI . Similarly, the FD receiver performance is about 0.5 dB better
than the ED receiver over the laboratory channels. In addition, the results show
that the KD BER degrades significantly as the performance is evaluated using
the estimated optimum TI values for the ED and the FD.
Comparison of low and high SNR regions show that the FD receiver suffers
from the same problem as the ED in the low SNR region. As mentioned in
Section 3, the motivation behind the use of fourth order detectors is mainly the
non-Gaussian nature of the IR-UWB signals which stands out from the Gaussian
nature of the interfering noise. The non-Gaussian nature of IR-UWB signals
is dominant only for higher SNRs, while IR-UWB signal statistics can not be
distinguished from the Gaussian noise in the low SNR region. Figs. 15, 16 and
17 verify that FD and ED receivers have nearly equal BER in the low SNR region,
while BER performance of the FD improves over the ED performance as the SNR
increases. However, for the channels with very short delay spread, BER of the
FD is slightly better than the ED even in the low SNR case.
Considering the results of the three environments, it is concluded that the FD
Non-coherent Detectors Based on Fourth Order Statistics of Impulse Radio UWB
Signals: Empirical evaluation using Channel Measurements
147
receiver has better performance in the corridor and in the office environment as
compared to the laboratory environment. The performance degradation of the
FD in the laboratory environment can be explained by examining the averaged
PDPs of the channel measurements. It is depicted in Fig. 8 that the measured
channels in the laboratory environment consist of many clusters of MPCs and
that their energy is spread over a large number of MPCs, which makes the signal
statistics close to Gaussian. In contrast, as illustrated by the averaged PDPs
given in Figs. 6 and 7, performance of the FD is better on the corridor and the
office channels as the IR-UWB signal characteristics are maintained, to some
extent, due to the strongest first arriving MPCs and very few clusters of MPCs
carrying most of the channel energy in these channels.
6
Conclusions
A non-coherent fourth-order detector (FD) based on estimation of the fourth
moment of the received signal is proposed as an alternative to the conventional
energy detector (ED). The performance of the receivers has been evaluated using
real channels obtained from the measurements. The results show that, in terms of
required SNR, the proposed FD receiver gives an improvement over the conventional ED of about 0.5 − 2 dB depending on the SNR, channel conditions and the
value of integration time. Moreover, it is observed that the KD receiver is better
than the ED receiver only under AWGN conditions. It should be mentioned that
the FD receiver suffers from the same problem as the ED in the low SNR region,
however, BER performance of the FD improves over the ED performance as the
SNR increases. Secondly, the proposed FD receiver is more robust to variations
in channel delay spread than the ED since the BER of the FD receiver is less
sensitive to overestimation of the integration interval. Finally, a rule of thumb for
selection of integration time of the proposed FD receiver is suggested, i.e., choose
the value of TI which captures all the MPCs within 10 dB of the strongest path
of the worst set of channels in the available realizations.
Acknowledgment
The author would like to acknowledge and thank Dr. Fredrik Tufvesson and
Dr. Johan Kåredal from Lund University, Sweden, for their collaboration and
support in the measurement campaign.
Bibliography
[1] Durisi,G., Benedetto,S., “Comparison between coherent and noncoherent Receivers for UWB Communications,” EURASIP Journal on Applied Signal
Processing, 2005, vol. 3, pp. 359–368.
[2] Tufvesson, F., Molisch, A.F., “Ultra-wideband communication using hybrid
matched filter correlation receivers,” in Proc. IEEE Veh. Technol. Conf., 2004,
vol. 3, pp. 1290–1294.
[3] Molisch, A.F., “Ultrawideband propagation channels- theory, measurement,
and modelling,” in Proc. of IEEE Transactions Vehicular Technology Conf.,
2005, vol. 54 no. 5, pp. 1528–1545.
[4] Gezici, S., Kobayashi, H., Poor, H.V., Molisch, A.F., “Optimal and suboptimal linear receivers for time-hopping impulse radio systems,” in Proc. of IEEE
Wireless Communications and Networking Conference (WCNC) , Atlanta, GA,
2004, vol. 2, pp. 908–913.
[5] Ning He, Tepedelenlioglu, C., “Performance analysis of non-coherent UWB
receivers at different synchronization levels,” in Proc. of IEEE Global Telecommunications Conference, 2004, vol. 6, pp. 3517–3521.
[6] Hoctor, R., Tomlinson, H., “Delay-hopped transmitted-reference RF communications,” in Proc. of IEEE UWBST Baltimore, MD, 2002, pp. 265–269.
[7] Choi, D.J., Stark, W.E., “Performance of ultra-wideband communications
with suboptimal receivers in multipath channels,” IEEE Journal of Sleceted
Areas Communications, 2002, vol. 20, no. 9, pp. 1754–1766.
[8] Weisenhorn, M., Hirt, W., “Robust noncoherent receiver exploiting UWB
channel properties,” in Proc. IEEE Conference on UWB Systems and Technologies, 2005, pp. 156–160.
[9] Sahin ME, Guvenc I, Arslan H., “Optimization of energy detector receivers
for UWB systems,” in Proc. of IEEE 61st Vehicular Technology Conference,
2005, vol. 2, pp. 1386–1390.
149
150
BIBLIOGRAPHY
[10] Song, N., Wolf, M., Haardt, M., “Low-complexity and energy efficient noncoherent receivers for UWB communications”, in Proc. IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications,
PIMRC, 2007, 1–4.
[11] Tian Z, Sadler BM., “Weighted energy detection of ultra-wideband signals,”
in Proc. of IEEE 6th Workshop on Signal Processing Advances in Wireless
Communications, 2005, 1068–1072.
[12] D’Amico AA, Mengali U, Arias-de-Reyna E., “Energy-detection UWB receivers with multiple energy measurements,” IEEE Transactions on Wireless
Communications, 2007, vol. 6 no. 7, pp. 2652–2659.
[13] Khan, M.G., Sällberg, B., Nordberg, J., Claesson, I., “Non-coherent detection of impulse radio UWB signals based on fourth order statistics,” in Proc.
of IEEE International Conference on UWB, ICUWB, 2009, pp. 824–828.
[14] Hyvärinen, A., Karhunen, J., Oja, E., 2001. Independent Component Analysis. John Wiley & Sons, Inc.
[15] Chao, Y.-L., “Optimal integration time for UWB transmitted reference correlation receivers,” in Asilomar Conference on Signals, Systems and Computers, 2004, pp. 647–651.
Part IV
Robust Weighted Non-Coherent Energy
Detection Receiver for Impulse Radio
UWB PPM Signals
This Part is based on the following publication:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Robust Weighted Non-Coherent Receiver for Impulse Radio UWB PPM
Signals” IEEE Journal of Communications Letters, vol. 15, no. 6, pp. 614–616,
June 2011
Robust Weighted Non-Coherent Energy Detection
Receiver for Impulse Radio UWB PPM Signals
November 22, 2011
Abstract
An energy detection based robust weight estimation scheme for pulseposition modulated (PPM) impulse radio ultra wideband (IR-UWB) signals
using weighted energy detector (WED), also referred to as weighted noncoherent receiver (WNCR), is proposed. Conventional data-aided WED
(DA WED) schemes estimate the weighting coefficients, or channel state
information (CSI), using a number of training symbols over time-varying
channels. In contrast, the proposed robust WED scheme is non-data-aided
(NDA), adaptive and robust to channel variations. The proposed robust
WED estimates the weighting coefficients adaptively based on the received
stochastic data, and the weight estimation process is refined using a decision
directed approach.
1
Introduction
Though unable to fully exploit the UWB potential, conventional non-coherent
receivers (NCRs) have gained attention due to low complexity and low power constraints of low data rate impulse radio ultra wideband (IR-UWB) transceivers.
Recently, at the expense of an increase in complexity, weighted non-coherent
receivers (WNCRs) or weighted energy detectors (WEDs) using either a single integrator with a high-speed analog-to-digital converter (ADC) or multiple
integrators using many low-speed ADCs have been proposed to improve the performance of the conventional ED receiver [1–4].
For the WEDs, the optimal weighting coefficients are derived in [1, 3, 4]. In
addition, a data-aided (DA) weight estimation method based on the transmission
of training symbols is presented in [4]. In practical channel conditions, the performance of this method may degrade if the channel coherence time is less than the
154
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
155
period between training data retransmission. As an alternative to the data-aided
approach, a decision-directed WED (DD WED) has been presented in [2]. The
main drawback of the DD scheme is that previous erroneous decisions can lead
to error propagation and hence poor detection performance over time-varying
channels. In a recent work, an eigenvector based non-data-aided WED (NDA
WED), which is a completely blind scheme as it requires no a priori knowledge
of the channel and noise statistics, is proposed in [5]. However, the NDA WED
has a higher implementation complexity as it needs to perform singular value
decomposition (SVD) of the recursively estimated data autocorrelation matrix
for estimation of the weight vector.
To remedy the drawbacks of existing schemes, an adaptive, non-data-aided
robust WED weight-setting scheme is presented in this part. The robust WED
is a low-complexity and suboptimal scheme which requires no a priori knowledge
of the channel and the noise. Unlike the DA WED, the proposed robust WED
can track the channel variations with little system overhead. The remaining of
Part IV is organized as follows. The signal model of the BPPM IR-UWB system
is presented in Section 2. Section 3 describes the architecture and detection
strategy for the WED receiver. Section 4 presents weight estimation methods
for the WED receiver. In Section 5, performance evaluation of the IR-UWB
systems and simulation results are presented and, finally, conclusions are drawn
in Section 6.
2
System Model
For a single-user BPPM IR-UWB system, the modulated signal s(t), generated
by the transmitter, is written as
f −1
∞ NX
X
p
u(t) = Ep
p(t − iTs − jTf − di TBP P M ),
(1)
i=−∞ j=0
RT
where p(t) is a normalized UWB pulse of duration Tp , i.e., 0 p [p(t)]2 dt = 1.
Ts , Tf and Ep are the symbol duration, frame duration and energy per pulse,
respectively. Each binary symbol contains Nf frames and each frame is divided
into two slots each of length TBP P M = Tf /2, thus energy per symbol is Es =
Nf Ep and it is equal to energy per bit Eb . The position of a pulse in the j th s
frame is determined, to be either at the beginning of the frame or with an offset
TBP P M , by di ∈ {0, 1} which is evaluated from the binary information symbol
bi ∈ {−1, 1} as di = (bi + 1)/2.
TheP
modulated signal is passed through a tapped-delay line multipath channel
L−1
h(t) = l=0 αl δ(t − τl ), where δ(t) is the Dirac delta function, while αl and τl are
156
Part IV
Adaptive
Weight
Estimation
+
wm
r(t)
r̃(t)
BPF
f (t)
(·)2
t+T
R I
Nf −1 M
P P
(·)dt
t
(kd )
yi,j,m
b̂i
j=0 m=1
−
Timing
Figure 1: Architecture of the robust weighted ED (WED) receiver.
the fading coefficients and delays of the MPCs, respectively. The signal received
at the output of multipath channel is modeled as
s(t)
=
=
u(t) ∗ h(t),
f −1
∞ NX
X
p
Ep
g(t − iTs − jTf − di TBP P M ),
(2)
i=−∞ j=0
PL−1
where g(t) is the aggregate channel response, i.e., g(t) = l=0 αl p(t − τl ). Additive white Gaussian noise (AWGN), denoted as n(t), with mean zero and doublesided PSD No /2 is also added to the signal, the received signal is then given
by
r(t)
=
=
s(t) + n(t),
∞ NX
f −1
X
p
Ep
g(t − iTs − jTf − di TBP P M ) + n(t).
(3)
i=−∞ j=0
3
Weighted ED (WED)
The signal received at the antenna is passed through a bandlimiting filter f (t) to
remove out-of-band noise and the output signal is written as
r̃(t) = s̃(t) + ñ(t).
(4)
In the conventional ED, the output of the filter is passed through a square-law
device and an integrator with an integration interval TI (≤ TBP P M ). The basic
concept of the WED is to improve the energy integration capability by dividing
the frame interval into several sub-intervals (or energy bins), i.e., each half of the
frame interval is divided into M equal length non-overlapping sub-intervals, such
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
157
that the duration of each sub-interval is Tb = Tf /(2M ). The energies of each
sub-interval are integrated and combined using optimal weighting coefficients, as
depicted in Fig.1. The WED decides whether the current bit is −1 (hypothesis
H0 ) or 1 (hypothesis H1 ) in favor of the pulse position which carries greater
weighted energy.
For the WED, without loss of generality, detection of the ith symbol is considered. The energy estimates of the sub-intervals of the j th frame of the ith symbol
are obtained by sampling the outputs of the integrator after each sub-interval Tb ,
i.e.,
Z iTs +jTf +(m+1)Tb
yi0,j,m =
[r̃(t)]2 dt,
(5)
iTs +jTf +(m+1)Tb
yi1,j,m
=
Z
iTs +jTf +TBP P M +(m+1)Tb
[r̃(t)]2 dt,
(6)
iTs +jTf +TBP P M +(m+1)Tb
where m = {0, 1, · · · , M − 1}. The energy estimates are represented using vector
notation yil,j = [yil,j,0 , yil,j,1 , · · · , yil,j,M−1 ]T , where l ∈ {0, 1}. Based on the
sampling theorem, the energy estimates for each frame, which are obtained from
the integration over each sub-interval Tb , can be seen as sums of 2W Tb virtual
samples (see [4]). Under hypothesis H0 , the sampled energy estimates are given
by
yi0,j,m
∼
=
2W T
2
1 Xb
s̃i0,j,m (tn ) + ñi0,j,m (tn ) ,
2W t =1
(7)
n
yi1,j,m
∼
=
2W T
2
1 Xb
ñi1,j,m (tn ) ,
2W t =1
(8)
n
where tn is the virtual sample index. Similarly, under hypothesis H1 , the sampled
energy estimates are given by
yi0,j,m
∼
=
2W T
2
1 Xb
ñi0,j,m (tn ) ,
2W t =1
(9)
n
yi1,j,m
∼
=
2W T
2
1 Xb
s̃i1,j,m (tn ) + ñi1,j,m (tn ) .
2W t =1
(10)
n
The random variables ni0,j,m (tn ) and ni1,j,m (tn ) are uncorrelated and Gaussian
with mean zero and variance No W , and the noise and the signal are independent [4]. Each yi0,j,m and yi1,j,m follows non-central (NC) and central (C) chisquare probability density function (PDF), respectively, under hypothesis H0 ,
158
Part IV
and vice versa for hypothesis H1 . Both distributions have 2W Tb degrees of freedom. The conditional joint PDF for the j th frame of the ith symbol, denoted as
fH0 (yi0,j , yi1,j ) and fH1 (yi0,j , yi1,j ) under hypothesis H0 and H1 , respectively,
can be written as
fH0 (yi0,j , yi1,j ) =
M−1
Y
fN C (yi0,j,m )|H0
m=0
fH1 (yi0,j , yi1,j ) =
M−1
Y
M−1
Y
fC (yi1,j,m )|H0 ,
(11)
fN C (yi1,j,m )|H1 .
(12)
m=0
fC (yi0,j,m )|H1
m=0
M−1
Y
m=0
The decision strategy to minimize the error probability computes the likelihood
ratio, i.e.,
R=
fH0 (yi0,j , yi1,j )
.
fH1 (yi0,j , yi1,j )
(13)
By inserting the PDFs and performing some straightforward approximations according to [4], the decision statistics for the two positions of the WED are determined as
ZWED,i0
=
Nf −1
X
wT yi0,j ,
(14)
X
wT yi1,j ,
(15)
j=0
ZWED,i1
=
Nf −1
j=0
where the weighting coefficients w = [w0 , w1 , · · · , wM−1 ]T are given by
wm
≈
Z
(m+1)Tb
[g(t)]2 dt.
(16)
mTb
The decision statistic in the WED receiver is formed as
ZWED,i = ZWED,i0 − ZWED,i1 ,
(17)
and the decision is made in favor of the pulse position which carries greater
energy, i.e.,
b̂i = sgn(ZWED,i ).
(18)
The performance of this detector is close to that of an optimal detector based on
the log-likelihood ratio [4].
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
159
4
Weight Estimation for WED
In practice, the weighting coefficients are estimated using sub-optimal methods.
A description of the commonly used methods and the proposed method for estimation of the weighting coefficients, is given in the following subsections.
4.1
Data-aided (DA) WED
In the DA WED [4], estimation of the suboptimal weights is performed by sending
P (known) training symbols to the receiver. Assuming a pattern of all zeros and
a single frame per symbol, the signal component is present in the first half of each
symbol, while the second half contains only the noise. The weighting coefficients
can be estimated as
ŵ = E yi0 − yi1 ,
(19)
where E{·} is the ensemble average of P known symbol statistics. In practice,
the weighting coefficients are estimated by replacing the ensemble average with
the arithmetic mean of P independent vectors as
P
1 X
ŵ =
yi0 − yi1 ,
P i=1
(20)
where i is the symbol index.
4.2
Non-data-aided (NDA) WED
To estimate the weighting coefficients of the WED receiver without using training symbols, an eigenvector-based NDA scheme for IR-UWB PPM system is
used in [5]. According to [5], the optimal weight vector of the NDA weighted
non-coherent receiver is the maximum eigenvector of the IR-UWB signal energy
sample autocorrelation matrix. In practice, it recursively estimates the autocorrelation matrix from the recently received I symbol statistics as
R̂(i) =
1
Nf I
i
X
Nf −1
X
i′ =i−I+1 j=0
yi′ 0,j − yi′ 1,j
yi′ 0,j − yi′ 1,j
T
,
(21)
Nf −1
T
η X
R̂(i) ≈ (1 − η)R̂(i − 1) +
yi0,j − yi1,j yi0,j − yi1,j , (22)
Nf j=0
where i is the time index for the current symbol. The weight parameter η ∈ [0, 1]
controls the method’s ability to track channel variations and to suppress weight
160
Part IV
fluctuations. It is suggested that η = 1I , where I is the approximative number
of recently received symbols used in the averaging. Based on the estimated
autocorrelation matrix, a sub-optimal weight vector is obtained by singular value
decomposition (SVD) of the matrix R̂(i). The implementation complexity of this
scheme is proportional to O(M 3 ), as the process is repeated for every symbol by
updating the autocorrelation matrix and computing its SVD.
4.3
Proposed Robust WED
The proposed scheme is based on the key observation that a suboptimal weight
vector can be directly estimated from the received data symbol by exploiting the
symmetric structure of the IR-UWB BPPM signaling scheme. To be precise, the
absolute value of the difference of two energy sample vectors of each frame is
constant regardless of which hypothesis is true and it is therefore selected as the
approximate weight vector, i.e., for the j th frame of the ith symbol
(23)
yi0,j |H0 − yi1,j |H0 = yi1 |H0 − yi0,j |H0 ,
or alternatively,
yi0,j |H1 − yi1,j |H1 = yi1,j |H1 − yi0,j |H1 ,
(24)
where |·| stands for the element-wise absolute value. This implies that an adaptive
method for time-varying channels can be developed in which the approximate
weight vector estimated from recently received symbol can be used to update
the weighting coefficients. The proposed method is composed of two processing
stages given in the following subsections.
Stage 1 - Direct Update : The first stage of the proposed method estimates
the weight update vector, denoted as ∆ŵ1 (i), based on the currently observed
data symbol as
Nf −1
1 X ∆ŵ1 (i) =
yi0,j − yi1,j ,
Nf j=0
(25)
where i is the symbol sample index and the arithmetic mean of Nf frames is
computed. The adaptive method performs exponentially weighted averaging over
previous observations to reduce weight fluctuations due to the received stochastic
data and, in addition, it is able to track the channel variations by assigning higher
weights to the recent observations. The weight vector, denoted as ŵ(i), is updated
according to
ŵ(i) ← (1 − β)ŵ(i − 1) + β∆ŵ1 (i),
(26)
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
161
where the exponential weight parameter β ∈ [0, 1] controls the method’s ability
to track channel variations and to suppress weight fluctuations. It is suggested
that β = N1 , where N is the approximative number of previous symbols used
in the average. The updated weight vector ŵ(i) is used by the robust WED in
making the symbol decision. It is worth mentioning that this first stage of the
proposed method can independently provide a suboptimal estimate of the weight
vector.
Stage 2 - Decision Directed Update : In the second stage, denoting the
current symbol decision as b̂i ∈ {−1, 1}, a second weight update vector ∆ŵ2 (i)
is computed as
∆ŵ2 (i) =
Nf −1
b̂i X
yi1,j − yi0,j .
Nf j=0
(27)
Finally, the proposed algorithm performs exponentially weighted averaging of the
output vectors from stage 1, to update the weight vector ŵ(i), according to
ŵ(i) ← (1 − ρ)ŵ(i) + ρ∆ŵ2 (i),
(28)
where the weight parameter ρ ∈ [0, 1] is an exponential weight suggested as
ρ = L1 , where L amounts to the approximative number of symbols used in the
second stage’s average. The second stage can afford a higher exponential weight,
i.e., ρ ≥ β, as the weight update vector is estimated assuming correct previous
decision. The error propagation due to erroneous previous decisions is mitigated
in the proposed DD approach as the first stage continuously provides the the
most recent approximate CSI. The computing steps of the method are provided
in Table 1.
A few remarks about β and ρ are in order. First, a small value of exponential weight (i.e., β → 0 or ρ → 0) discounts the previous observations very slowly
making the current observation less significant and, thus, minimizes weight fluctuations but rapid channel variations cannot be tracked. In contrast, a large
value of exponential weight (i.e., β → 1 or ρ → 1) assigns more weight to the
current observation, thus, any change to the channel is rapidly tracked but the
weight fluctuations are now determined by the variability of the recently received
stochastic data. Hence, the values of β and ρ are proportional to the channel
variation rate and they comprise the normally occurring design trade-off between
performance (channel tracking ability) and robustness (mitigation of weight variability due to noise). In practice, the values of exponential weights β and ρ are
suggested to be set adaptively according to an estimate of the channel variation
rate to achieve robustness in a dynamic channel environment.
162
Part IV
Table 1: Proposed Robust WED weight estimation method
For i = 0, initialization :
ŵ(i) = ∆ŵ1 (i), β = 0.03, ρ = 0.05, Nf = 1
For every i ≥ 1, iterate the steps 1 ∼ 8 :
(1) Estimate yi0,j and yi1,j
PNf −1
(2) ∆ŵ1 (i) = N1f j=0
|yi0,j − yi1,j |
(3) ŵ(i) ← (1 − β)ŵ(i − 1) + β∆ŵ1 (i)
PNf −1
T
T
(4) ZWED,i = j=0
ŵ(i) yi0,j − ŵ(i) yi1,j
(5) b̂i = sgn(ZWED,i )
PNf −1
yi1,j − yi0,j
(6) ∆ŵ2 (i) = Nb̂if j=0
(7) ŵ(i) ← (1 − ρ)ŵ(i) + ρ∆ŵ2 (i)
(8) i = i + 1
5
Performance Evaluation
In the performance evaluation, an IR-UWB system is simulated using the multipath channels proposed by IEEE 802.15.4a [6]. The second derivative of a
Gaussian pulse with parameters Nf = 1, Tp = 0.5 ns, TBP P M = 200 ns and
Tf = 400 ns is used for BPPM modulation. For the ED, TI = 100 ns; while for
the WEDs, K = 20, Tb = 5 ns and the weight parameters are set to be β = 0.03,
ρ = 0.05 and η = 0.4. The channel coherence time is Tco = 0.04 ms, and the
energy of multipath channels impulse responses is normalized to unity.
The BER performance of the conventional ED, the NDA WED, the DA WED,
and the proposed robust WED with one and two stage implementation using
CM1, CM2, CM3 and CM4 channels is shown in Figs. 2, 3, 4 and 5, respectively.
The BER curves show that, as the SNR increases, performance of the two stage
robust WED approaches to that of the NDA WED which is using singular value
decomposition of the decision statistic autocorrelation matrix. In addition, the
performance of the DA WED is only about 0.5 to 1 dB better than the proposed
one stage and two stage robust WED.
To show the influence of channel coherence time, the convergence of the mean
error of the proposed two stage robust WED is shown in Fig. 6. The figure
shows the initial convergence of the mean error and illustrates the robustness
of the proposed scheme as the mean error slightly increases with the channel
variation and it reconverges within 10 to 20 symbols.
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
163
0
10
−1
BER
10
−2
10
Conventional ED
One stage Robust WED
Two stage Robust WED
NDA WED
DA WED
−3
10
−4
10
0
2
4
6
8
Eb /No [dB]
10
12
14
Figure 2: BER curves of the proposed one and two stage robust WED, the
conventional ED, the NDA WED and the DA WED, using CM1 channel.
0
10
−1
BER
10
−2
10
Conventional ED
One stage Robust WED
Two stage Robust WED
NDA WED
DA WED
−3
10
−4
10
0
2
4
6
8
Eb /No [dB]
10
12
14
Figure 3: BER curves of the proposed one and two stage robust WED, the
conventional ED, the NDA WED and the DA WED, using CM2 channel.
164
Part IV
0
10
−1
BER
10
−2
10
Conventional ED
One stage Robust WED
Two stage Robust WED
NDA WED
DA WED
−3
10
−4
10
0
2
4
6
8
Eb /No [dB]
10
12
14
Figure 4: BER curves of the proposed one and two stage robust WED, the
conventional ED, the NDA WED and the DA WED, using CM3 channel.
0
10
−1
BER
10
−2
10
Conventional ED
One stage Robust WED
Two stage Robust WED
NDA WED
DA WED
−3
10
−4
10
0
2
4
6
8
Eb /No [dB]
10
12
14
Figure 5: BER curves of the proposed one and two stage robust WED, the
conventional ED, the NDA WED and the DA WED, using CM4 channel.
Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB
PPM Signals
165
−3
3.5
x 10
3
2.5
Mean error
2
Channel variation
and reconvergence
Initial convergence
1.5
1
0.5
0
Channel 2
Channel 1
0
20
40
60
80
100
120
140
160
180
200
Symbol index
Figure 6: Mean error of the proposed two stage robust WED with the channel
coherence time Tco = 0.04 ms, corresponding to a block length of 100 symbols.
6
Conclusions
An energy detection based robust weight estimation scheme is proposed for the
BPPM IR-UWB signals. The proposed method is a low-complexity suboptimal
weight estimation scheme which effectively reaps the advantages of rich UWB
multipath diversity without explicit CSI. The robust WED constitutes two processing stages, which enable the receiver to track the channel variations with little
system overhead. Simulation results verify that the performance of the robust
WED weight estimation method is close to that of the eigenvector based NDA
scheme and the training symbol based DA scheme.
Bibliography
[1] Z. Tian and B.M. Sadler, ”Weighted energy detection of ultra-wideband signals,” Proc. IEEE 6th Workshop on Signal Processing Advances in Wireless
Communications, 2005, pp. 1068–1072.
[2] J. Wu, Q. Liang, and H. Xiang, ”Adaptive Weighted Noncoherent Receiver
for UWB-PPM Signal in Multipath Channels,” Proc. ICWMMN Conference,
2006.
[3] J. Wu, H. Xiang, and Z. Tian, ”Weighted Noncoherent Receivers for UWB
PPM Signals,” IEEE Commun. Lett, vol. 10, no. 9, 2006, pp. 655–657.
[4] A.A. D’Amico, U. Mengali, and E. Arias-de-Reyna, ”Energy-Detection UWB
Receivers with Multiple Energy Measurements,” IEEE Transactions on Wireless Communications, 2007, vol. 6, no. 7, pp. 2652–2659.
[5] S. Bin, Y. Rumin, C. Taiping, and K. Kyungsup, ”Non-data-aided Weighted
Non-coherent Receiver for IR-UWB PPM Signals,” ETRI Journal, vol. 32,
no. 3, Jun. 2010, pp. 460–463.
[6] A. F. Molisch et al., “IEEE 802.15.4a channel model - final report,” Tech.
Rep. Document IEEE 802.15-04-0662-02-004a, 2005
167
Part V
Weighted Code-Multiplexed
Transmitted-Reference and
BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB
Systems
This Part is based on the following publication:
Muhammad Gufran Khan, Benny Sällberg, Jörgen Nordberg, and Ingvar Claesson, “Energy Efficient Binary PPM/Code-Multiplexed Transmitted-Reference
Multi-user UWB System, in Proceedings of IEEE International Conference on
UWB, ICUWB 2011, pp. 615–619, Bologona, Italy.
Weighted Code-Multiplexed Transmitted-Reference and
BPPM/Code-Multiplexed Transmitted-Reference
Multi-user UWB Systems
November 22, 2011
Abstract
Code-multiplexed transmitted-reference (CM-TR) UWB system is interesting for non-coherent reception, but it is not energy efficient as one
half of the energy is used to transmit reference pulses and, even at low-tomedium data rates, it suffers from strong multi-user interference (MUI) and
inter-frame interference (IFI). To this end, first, an energy detection based
robust weighted code-multiplexed TR (WCM-TR) receiver is presented and
a non-data-aided (NDA) and adaptive weight estimation scheme proposed
for weighted energy detector (ED) is extended to the WCM-TR detector.
Secondly, a combined binary pulse position modulation (BPPM)/CM-TR
UWB system is presented. Keeping the information rate constant, the
combined BPPM/CM-TR UWB system utilizes 3 dB less energy per bit
and bit-error-rate (BER) of the BPPM/CM-TR is better than the CM-TR
system in the high signal-to-noise ratio (SNR) region under MUI. Finally,
a dual-mode BPPM/CM-TR UWB system is proposed to cope with the
problems raised by the BPPM/CM-TR in the low SNR conditions and in
the absence of MUI.
1
Introduction
For sensor networks incorporating IR-UWB technology at the physical layer,
non-coherent detection schemes such as energy detection (ED) and transmitted
reference (TR) are well-suited. At the expense of performance degradation, the
conventional ED scheme uses OOK or PPM modulations and performs low complexity detection using only a square-law device, an integrator and a sampler [1].
In time-domain TR system, a reference signal and a time-delayed modulated signal are transmitted together [2, 3], whereas the receiver has to align and correlate
172
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
173
these signals. However, the seemingly simple time-domain TR receiver requires
long analog delay lines, which are not trivial to implement. A frequency-domain
implementation of a TR system, called frequency-shifted reference (FSR) system, is proposed in [4]. In an FSR system, the reference and the data-modulated
pulses become orthogonal to each other over a symbol period Ts by introducing a
slight frequency shift of 1/Ts between the two overlapping pulses [4, 5]. However,
the detection of FSR UWB signals requires generation of a carrier signal at the
receiver and its performance also degrades as the data rate increases [6, 7].
Motivated by the observation that the reference and the data-modulated
pulses can also be separated in the code-domain, code multiplexed TR (CM-TR)
UWB systems are proposed in [5–8]. In the CM-TR UWB system, orthogonal
code sequences (OCSs) taken from the rows of an Hadamard matrix are used
to provide orthogonalization between reference and data-modulated pulses [5].
The detector of the CM-TR system has a low implementation complexity as it
neither needs analog delay lines nor a carrier generator. In addition, the BER
performance of the CM-TR is also better than the FSR and the TR systems [5].
In this part of the thesis, first, an energy detection based weighted CM-TR
(WCM-TR) receiver is developed and, additionally, BPPM is used in conjunction
with the CM-TR modulation to improve the system performance in the presence
of both IFI and MUI. The rest of Part V is outlined as follows. The signal model
and detection method of the CM-TR UWB system is presented in Section 2 and
Section 3 presents the WCM-TR receiver. Section 4 describes the motivation,
signal model and detection method of the BPPM/CM-TR UWB system and a
dual-mode solution of the BPPM/CM-TR is discussed in Section 5. In Section
6, performance of the proposed systems is compared with the CM-TR system
and simulation results are presented. Finally, conclusions are summarized in
Section 7.
2
CM-TR UWB System
The CM-TR UWB system proposed by Amico et. al. [9] is used as a reference,
hence, it is described in the following subsections.
2.1
Signal Model
In a multi-user CM-TR UWB system, assuming Nu users transmitting at the
same rate, the modulated signal generated by the k th user is modeled as
u(k) (t)
=
f −1 ∞ NX
X
p
(G)
(k) (k)
Ep
cj p(t − iTs − jTf ) + bi cj p(t − iTs − jTf ) ,
i=−∞ j=0
(1)
174
Part V
RT
where p(t) is a normalized UWB pulse of duration Tp , i.e., 0 p [p(t)]2 dt = 1. Ep
and Tf are energy per pulse and frame duration, respectively. Each information
(k)
symbol consisting of a single bit bi ∈ {−1, 1} contains Nf frames with a symbol duration Ts = Nf Tf , and energy per symbol is Es is equal to energy per
(G)
(k)
bit Eb . In addition, cj ∈ {−1, 1} and cj ∈ {−1, 1} are the two orthogonal
code sequences (OCSs) of the period Nf . The orthogonal code sequence (OCS)
(G) (G)
(G)
c(G) = [c0 , c1 , · · · , cNf −1 ]T , where G stands for global OCS, is common to all
(k)
(k)
(k)
users; while c(k) = [c0 , c1 , · · · , cNf −1 ]T is specific to the k th user. The OCSs
are taken from the rows of a Hadamard matrix of size Nf × Nf and they satisfy
the orthogonality condition [9], i.e.,
Nf −1
X
(G) (k)
cj cj
= 0,
1 ≤ k ≤ Nu .
j=0
(2)
The k th user signal is assumed to be transmitted over a tapped-delay line
PL−1 (k)
(k)
multipath channel with the impulse response h(k) (t) =
l=0 αl δ(t − τl ),
(k)
(k)
where L is the number of MPCs received at the antenna, while αl and τl are
th
the weight and delay associated with the l multipath component, and δ(·) is the
Dirac delta function. The signal s(k) (t) associated with the k th user, obtained
at the output of the multipath channel, is the convolution of u(k) (t) and h(k) (t),
i.e.,
s
(k)
(t)
∞ NX
f −1 X
p
(G)
Ep
cj g (k) (t − iTs − jTf )
=
i=−∞ j=0
(k) (k)
+bi cj g (k) (t
− iTs − jTf ) ,
(3)
P
(k)
where g (k) (t) is the aggregate channel, i.e., g (k) (t) = L−1
l=0 αl p(t − τl ). The
(k)
(k)
duration of g (k) (t) is defined as Tg = Tp + Tmds , where Tmds stands for the
th
maximum delay spread of the k channel. IFI between two adjacent frames
(k)
occurs due to delay spread effect of the UWB multipath channel, i.e., if Tf ≤ Td .
The signal at the receiving antenna is also corrupted by AWGN noise n(t) with
two-sided PSD No /2.
2.2
CM-TR Detection
Since multiple users are assumed simultaneously active, the signal at the receiving
antenna is corrupted by AWGN noise as well as MUI. First of all, the received
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
175
r(t)
BPF
f (t)
r̃(t)
(·)2
t+T
R I
Nf −1
P
(·)dt
j=0
t
(kd )
b̂i
(k )
yi,jd
(kd )
cj
Timing
Figure 1: Architecture of the CM-TR receiver.
signal r(t) is passed through a bandlimiting filter f (t) which removes out-of-band
noise and the filtered signal is modeled as
r̃(t) =
s̃R (t) + ñ(t),
(4)
where ñ(t) is the band-limited noise. The signal component s̃R (t) in the received
signal contains the superposition of Nu user signal components, i.e.,
s̃R (t) =
Nu
X
s̃(k) (t),
(5)
k=1
where the band-limited k th user signal component s̃(k) (t) is given by
f −1 ∞ NX
X
p
(G)
s̃(k) (t) =
Ep
cj g̃ (k) (t − τ̃ (k) − iTs − jTf )
i=−∞ j=0
(k) (k)
+bi cj g̃ (k) (t
− τ̃
(k)
− iTs − jTf ) ,
(6)
where g̃ (k) (t) = g (k) (t)∗f (t). τ̃ (k) is the time asynchronism parameter to represent
that the users are asynchronous and its value is assumed to be a random variable
uniformly distributed over the interval [0, Ts ].
Without loss of generality, it is henceforth assumed that the user kd is the
desired user out of Nu users, and the detection of the ith symbol is considered.
The asynchronism parameter related to the desired user kd is assumed to be zero,
since perfect synchronization is assumed for this user. The received signal in Eq.
(4) can be rewritten as
(k )
d
r̃(t) = s̃(kd ) (t) + s̃MUI
(t) + ñ(t),
(kd )
s̃MUI
(t)
where
kd , i.e.,
(7)
is the MUI signal of Nu − 1 users interfering with the desired user
(kd )
s̃MUI
(t)
=
Nu
X
k=1,k6=kd
s̃(k) (t).
(8)
176
Part V
In the CM-TR receiver, the output of the filter is passed through a square-law
device and an integrator, see Fig. 1. The sampled energy estimates are obtained
for Nf frames of the ith symbol as
Z iTs +jTf +TI
(k )
yi,jd =
[r̃(t)]2 dt,
(9)
iTs +jTf
where j = {0, 1, · · · , Nf − 1} and TI is the length of integration interval. The
(k )
(k )
decision statistic Zi d is determined using the user specific OCS cj d as
(kd )
Zi
=
Nf −1
X
(kd ) (kd )
yi,j .
cj
(10)
j=0
A threshold circuit is used to make the decision whether the current symbol is
−1 or 1 as
(kd )
b̂i
3
(kd )
= sign[Zi
].
(11)
Weighted CM-TR UWB System
The following subsections describe the motivation of robust WCM-TR receiver
and the adaptive weight estimation scheme.
3.1
Motivation
Like conventional non-coherent systems, the performance of multi-user CM-TR
UWB system is greatly affected by the integration interval and the low SNR
of the decision statistic. Thus, it is essential to develop techniques to enhance
the performance of the CM-TR receiver. For non-coherent receivers, weighted
processing using either a single integrator with a high-speed analog-to-digital
converter (ADC) or multiple integrators using many low-speed ADCs have been
proposed in [10–13]. Likewise, at the expense of an increase in complexity, the
weighted processing technique can be used for improving the detection performance of the CM-TR UWB signals.
In order to perform weighted detection, an estimate of the power delay profile (i.e., weighting coefficients) of the channel is required. A data-aided (DA)
weight estimation method based on a preamble of known training symbols is presented in [13]. In a multi-user scenario, this method is used in [14] to develop a
receiver structure which is robust to MUI. In practical channel conditions, however, performance of the preamble-based DA method may degrade if the channel
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
177
coherence time is less than the period between training data re-transmission.
Moreover, the DA method has an overhead due to transmission of training symbols for channel estimation. Additionally, [15] has proposed an eigenvector based
non-data-aided (NDA) scheme. However, the NDA has considerably higher implementation complexity as it needs to perform singular value decomposition
(SVD) of the estimated data autocorrelation matrix.
In a recent work, a robust weight estimation scheme for weighted energy
detector (WED) using BPPM IR-UWB signals is proposed by Khan et.al. in [16]
and is also given in Part IV. The method proposed in [16] is a low-complexity
suboptimal weight estimation scheme which requires no a priori knowledge of the
channel and the noise. Motivated by the important observation that the CMTR system may also be considered a “generalized” PPM system [8], the weight
estimation scheme presented in [16] is extended to the multi-user CM-TR system
and an adaptive weighted detection scheme called robust WCM-TR is developed.
3.2
WCM-TR Receiver
In the WCM-TR receiver, the integration interval is divided into several subintervals or bins, i.e., each frame duration is divided into M equal length nonoverlapping sub-intervals, such that the duration of each sub-interval or bin is
Tb = Tf /M . After squaring the output of the filter, the receiver performs bin rate
sampling at the output of the integrator. The estimated bin energies are multiplied with the corresponding elements of the code sequence in the multiplier. For
each frame, the outputs of the multiplier are combined using optimal weighting
coefficients and, finally, the summation of the weighted values is performed over
Nf frames of each symbol, see Fig. 2.
Considering the detection of the ith symbol of the desired user kd , the bin
energies of the j th frame are obtained by sampling the outputs of the integrator
after each bin, i.e.,
Z iTs +jTf +(m+1)Tb
(kd )
yi,j,m
=
[r̃(t)]2 dt,
(12)
iTs +jTf +mTb
where m = {0, 1, · · · , M − 1} and j = {0, 1, · · · , Nf − 1}. The bin energies of the
(k )
(kd ) (kd )
(kd )
j th frame are denoted in vector form as yi,jd = [yi,j,0
, yi,j,1 , · · · , yi,j,M−1
]T .
Unlike the WED, the bin energies of the j th frame are multiplied with the
corresponding element of the code sequence of user kd to obtain
(k )
(kd ) (kd )
yi,j,m ,
d
zi,j,m
= cj
(k )
(13)
(k )
(k )
(k )
d
d
d
which can be denoted in a vector form as zi,jd = [zi,j,0
, zi,j,1
, · · · , zi,j,M−1
]T . The
decision statistic for the WCM-TR is obtained by summation of the corresponding
178
Part V
weighted bin vectors of the Nf frames as
(kd )
Zi
=
Nf −1
X
(k )
wT zi,jd ,
(14)
j=0
where the vector w = [w0 , w1 , · · · , wM−1 ]T denotes the weighting coefficients.
(k )
(k )
Similar to the CM-TR receiver, the decision is made as b̂i d = sign[Zi d ].
In the absence of MUI, the optimal decision rule for the WCM-TR receiver
can be derived based on the maximum likelihood criterion. Assuming that the
(k )
user kd is the desired user out of Nu users. In the CM-TR system, cj d is 1
for Nf /2 frame indices and −1 for remaining Nf /2 frame indices. Following [8],
(k )
let S and S̄ represent the sets of Nf /2 frame indices for which cj d = 1 and
(kd )
cj
= −1, respectively; i.e.,
S
S̄
(k )
= {j ∈ F {0, 1, . . . , Nf − 1}cj d = 1},
(k )
= {j ∈ F {0, 1, . . . , Nf − 1}cj d = −1},
where F is the set of Nf frame indices. In this generalized PPM system, under
hypothesis H1 , the pulses are transmitted in Nf /2 frames indexed by S and no
pulses are transmitted in remaining Nf /2 frames indexed by S̄, and vice versa.
Based on the sampling theorem, the bin energy estimates for each frame,
which are obtained from the integration over each bin duration Tb , can be seen
as sums of 2W Tb virtual samples (see [13]). This implies that, under hypothesis
H0 , the sampled energy estimates of the j th frame of the ith symbol are given by
(k )
d
yi,j,m
∼
=
2W T
1 Xb
[ñi,j,m (tn )]2 , if j ∈ S|H0 ,
2W t =1
(15)
n
(k )
d
yi,j,m
∼
=
2W T
1 Xb (kd )
[g̃
(tn ) + ñi,j,m (tn )]2 , if j ∈ S̄|H0 .
2W t =1 i,j,m
(16)
n
Similarly, under hypothesis H1 , the sampled energy estimates are
(kd )
yi,j,m
∼
=
2W T
1 Xb (kd )
[g̃
(tn ) + ñi,j,m (tn )]2 , if j ∈ S|H1 ,
2W t =1 i,j,m
(17)
n
(kd )
yi,j,m
∼
=
2W T
1 Xb
[ñi,j,m (tn )]2 , if j ∈ S̄|H1 .
2W t =1
(18)
n
Following [13], the random variables ni,j,m (tn ) are uncorrelated and Gaussian
with mean zero and variance No W , and the noise and the signal are independent.
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
179
Under hypothesis H0 , each yi,j∈S,m follows central (C) chi-square probability
density function (PDF), and each yi,j∈S̄,m follows non-central (NC) chi-square
PDF with non-centrality parameter λm = No1/2 wm [13,14], where wm is given by
wm ≈
Z
(m+1)Tb
[g̃ (kd ) (t)]2 dt,
(19)
mTb
and m = {0, 1, · · · , M − 1}. Both distributions have 2W Tb degrees of freedom.
The decision strategy to minimize the error probability computes the likelihood
ratio, i.e.,
fH0 (yi,j∈S , yi,j∈S̄ )
R=
,
(20)
fH1 (yi,j∈S , yi,j∈S̄ )
where fH0 (yi,j∈S , yi,j∈S̄ ) and fH1 (yi,j∈S , yi,j∈S̄ ) represent the joint PDF of the
independent components under hypothesis H0 and H1 , respectively. By inserting the PDFs and performing some straightforward approximations, the loglikelihood ratio provides the optimal decision statistic for the WCM-TR [13, 14],
i.e.,
√
√
wm yi,j,m !
wm yi,j,m !
M−1
I
Iα
X M−1
X
X
X
α
No /2
No /2
p
p
−
ln
, (21)
Zi =
ln
α
α
(yi,j,m )
(y
)
i,j,m
m=0
j∈S m=0
j∈S̄
where α = W Tb − 1 and Iα (·) denotes the α-th order modified Bessel function of
the first kind. According to [13], the approximations are used to reduce Eq. (21)
to a more practical decision statistic, i.e.,
Zi
X M−1
X
=
j∈S m=0
X
=
j∈S
wm yi,j,m −
wT yi,j −
X
X M−1
X
wm yi,j,m ,
j∈S̄ m=0
wT yi,j ,
(22)
j∈S̄
(kd )
since S and S̄ represent the sets of Nf /2 frame indices for which cj
(k )
cj d
= 1 and
= −1, respectively, Eq. (22) may be reformulated as
X
X
(k )
(k )
Zi =
wT cj d yi,j +
wT cj d yi,j ,
j∈S
=
X
T
w zi,j +
j∈S
=
Nf −1
X
j=0
X
j∈S̄
wT zi,j ,
j∈S̄
wT zi,j ,
(23)
180
Part V
Adaptive
Weight
Estimation
(k )
r(t)
BPF
f (t)
r̃(t)
wm
d
zi,j,m
t+T
R I
(·)2
Nf −1 M
P P
(·)dt
t
b̂i
j=0 m=1
(k )
d
yi,j,m
(kd )
cj
Timing
Figure 2: Architecture of the WCM-TR receiver, which employs bin rate sampling.
where the vector w = [w0 , w1 , · · · , wM−1 ]T denotes the weighting coefficients
given in Eq. (19). The performance of this detector is close to that of an optimal
detector in Eq. (21), based on the log-likelihood ratio [13].
3.3
Weight Estimation for WCM-TR
In the following, subsections weight estimation methods extended to the WCMTR receiver are discussed.
Data-aided (DA) WCM-TR
In the DA scheme, estimation of the suboptimal weights is performed by sending
P (known) training symbols to the receiver. For the WCM-TR receiver, assuming
a pattern of all zeros, i.e., hypothesis H0 is true, the signal component is present
in half of the frames of each symbol, which are represented by the set S; while the
remaining half frames, which are represented by the set S̄, contain only the noise.
Under this condition, the weighting coefficients for WCM-TR can be estimated
by taking the arithmetic mean of P independent values as
P −1
1 X
ŵ =
P i=0
(
)
X (k ) 1 X (kd )
d
zi,j |H0 +
zi,j |H0
.
Nf /2
j∈S
(24)
j∈S̄
Since S ∪ S̄ = F , Eq. (24) can be reformulated as
P −1
1 X
ŵ =
P i=0
(
)
Nf −1
X (k )
1
d
z
|H0 .
Nf /2 j=0 i,j
(25)
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
181
Non-data-aided (NDA) WCM-TR
According to an eigenvector-based NDA scheme [15], the energy sample autocorrelation matrix is recursively estimated from the recently received symbol
statistics. The NDA method can be extended to the WCM-TR UWB system
using the arithmetic averaging to estimate the autocorrelation matrix from the
recently received I symbol statistics as
R̂(i) =
R̂(i) ≈
1
I
i
X
i′ =i−I+1
(
Nf −1
Nf −1
T )
1 X (kd ) X (kd ) z′
z′
,
Nf /2 j=0 i ,j j=0 i ,j Nf −1
Nf −1
T
η X (kd ) X (kd ) (1 − η)R̂(i − 1) +
z
z
,
Nf /2 j=0 i,j j=0 i,j where i is the current symbol index. The weight parameter η ∈ [0, 1] controls the
method’s ability to track channel variations and to suppress weight fluctuations
and its value is selected as η = 1I . Based on the estimated autocorrelation matrix,
a sub-optimal weight vector is obtained by SVD of the matrix.
Proposed Robust WCM-TR
Like the robust WED in [16], the proposed robust weight estimation method
for the WCM-TR is also based on the key observation that a suboptimal weight
vector can be directly estimated from the received data symbol due to symmetry
of the received signal of the CM-TR modulation. The element-wise absolute
(kd )
value of the element-wise sum of the estimated bin energy vectors zi,j∈S
and
(k )
(k )
(k )
d
zi,j∈
, which correspond to the frames for which cj d = 1 and cj d = −1,
S̄
respectively, provide an approximate weight vector. In addition, under the same
channel and noise conditions, the approximate weight vector is equal regardless
of which hypothesis is true, i.e.,
(kd )
(kd )
(kd )
(kd )
z
,
|
+
z
|
=
z
|
+
z
|
(26)
i,j∈S H0
i,j∈S H1
i,j∈S̄ H0 i,j∈S̄ H1 where | · | stands for the element-wise absolute value of the vector. As S and S̄
represent the sets of Nf /2 frame indices each, equality in Eq. (26) is also valid
for the summation over all Nf /2 frame indices of sets S and S̄, i.e., Eq. (26) is
extended to
X (k ) X (k )
X (k ) X (kd )
d
d
d
=
(27)
z
|
+
z
|
z
|
+
z
|
i,j H0
i,j H0 i,j H1
i,j H1 .
j∈S
j∈S̄
j∈S
j∈S̄
182
Part V
Since S ∪ S̄ = F , Eq. (27) can be reformulated as
Nf −1
Nf −1
X (kd ) X
(kd )
z
|
=
z
|
i,j H0 i,j H1 .
j=0
(28)
j=0
This implies that, regardless of which hypothesis is true, a sub-optimal weight
vector can be estimated for WCM-TR receiver from the bin energy vectors of the
frames of the recently received symbol. Following the same approach as presented
in [16] for robust WED, the two stage implementation of the adaptive algorithm
for the WCM-TR receiver is given in the following subsections.
Stage 1 - Direct Update : The weight update vector, denoted as ∆ŵ1 (i),
is computed based on the Nf bin vectors of the current data symbol as
∆ŵ1 (i) =
Nf −1
1 X (kd ) z
,
Nf /2 j=0 i,j (29)
which is equivalent to taking an arithmetic mean over Nf /2 approximate weight
vectors. The weight vector, denoted as ŵ(i), is updated according to
ŵ(i) ← (1 − β)ŵ(i − 1) + β∆ŵ1 (i),
(30)
where i is the time index for the current symbol. The exponential weight parameter β ∈ [0, 1] controls the method’s ability to track channel variations and to
suppress weight fluctuations. It is suggested that β = N1 , where N is the approximative number of previous symbols used in the average. The estimated weight
vector ŵ(i) is used by the WCM-TR in making the symbol decision.
Stage 2 - Decision Directed Update : In the second stage, denoting the
(k )
current symbol decision as b̂i d ∈ {−1, 1}, the weight update vector ∆ŵ2 (i) is
computed based on Nf bin energy vectors and assumed correct decision of the
current data symbol as
∆ŵ2 (i) =
Nf −1
(k )
b̂i d X (kd ) z
,
Nf /2 j=0 i,j
(31)
which is equivalent to taking an arithmetic mean over Nf /2 approximate weight
vectors based on the current symbol decision. Finally, the proposed algorithm
performs exponentially weighted averaging of the output vectors from stage 1, to
update the weight vector ŵ(i), according to
ŵ(i) ← (1 − ρ)ŵ(i) + ρ∆ŵ2 (i),
(32)
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
183
Table 1: Robust WCM-TR weight estimation method
For i = 0, initialization :
ŵ(i) = ∆ŵ1 (i), β = 0.03, ρ = 0.05
For every i ≥ 1, iterate the steps 1 ∼ 8 :
(k )
(1) Estimate zi,jd PNf −1 (kd ) 1 (2) ∆ŵ1 (i) = Nf /2 j=0 zi,j (3) ŵ(i) ← (1 − β)ŵ(i − 1) + β∆ŵ1 (i)
PNf −1
(k )
(k )
(4) Zi d = j=0
ŵ(i)T zi,jd
(k )
(k ) (5) b̂i d = sign Zi d
(k ) P
Nf −1 (kd )
b̂ d
z
(6) ∆ŵ2 (i) = Nif /2
j=0
i,j
(7) ŵ(i) ← (1 − ρ)ŵ(i) + ρ∆ŵ2 (i)
(8) i = i + 1
where the parameter ρ ∈ [0, 1] is an exponential weight suggested as ρ = L1 ,
where L amounts to the approximative number of symbols used in the average.
The computing steps are also summarized in Table 1.
4
BPPM/CM-TR UWB System
The following subsections present the motivation, signal model and detection
strategy of the combined BPPM/CM-TR UWB system.
4.1
Motivation
The main drawback of the multi-user CM-TR UWB system is degradation in the
performance caused by strong IFI and MUI. In [9], low data rate application,
and hence limited amount of IFI, is considered for the CM-TR UWB system.
For medium data rates (i.e., around 2 − 4 Mbps) and even at low data rates, e.g.,
over UWB channels in residential environments [17], BER of the CM-TR UWB
system worsens due to significant amount IFI present in the received signal. In
order to increase the data rate and/or mitigate IFI due to large delay spread
of the UWB channels, higher order modulations, e.g., M −ary PPM, have been
proposed [18–20].
As mentioned previously, the CM-TR system is essentially a generalized PPM
system and the receiver structure of the CM-TR UWB system is also based on
184
Part V
the conventional ED for PPM and OOK signals. Thus, PPM modulation is
well-suited to be combined with the CM-TR modulation as the combined signal
format can be detected without altering the receiver structure. In line with this,
BPPM is used in conjunction with the CM-TR modulation to improve the system
performance in the presence of both IFI and MUI. The combined BPPM/CMTR is more energy efficient as the energy required to transmit a single bit of
the BPPM/CM-TR is half the energy required per bit of the CM-TR system.
In addition, the BPPM/CM-TR signaling is able to transmit two bits within
the duration of one bit. For low-to-medium data rate applications, as increasing
the data rate is of less importance, frame duration of the BPPM/CM-TR is
increased instead keeping the data rate constant. This leads to longer silent
periods between the pulses, which in turn decrease the IFI and the MUI due to
a smaller probability of collisions between multiple asynchronous users.
4.2
Signal Model
In the BPPM/CM-TR system, two bits are transmitted per symbol, and each
frame is designed to provide two orthogonal pulse positions due to the BPPM.
Each user uses the first bit of each symbol to determine one of the two pulse
positions in each frame. In addition, the second bit of each symbol is modulated
according to the CM-TR modulation. Due to the peak power constraint in UWB
systems, equal energy per pulse is assigned to both systems, which means that
the transmitter of the BPPM/CM-TR is energy efficient by a factor of 2. To keep
the data rate equal for both systems, the frame duration of the BPPM/CM-TR
system is increased to T̄f = 2Tf [19].
The modulated signal of k th user of the multi-user BPPM/CM-TR system is
modeled as
f −1 ∞ NX
X
p
(G)
(k)
(k)
ū (t) =
Ep
cj p(t − di,1 TBP P M − iT̄s − j T̄f )
i=−∞ j=0
(k) (k)
+bi,2 cj p(t
−
(k)
di,1 TBP P M
− iT̄s − j T̄f ) ,
(33)
where TBP P M = T̄f /2 is the BPPM shift. Each information symbol contains Nf
frames and transmits two bits within a symbol duration T̄s = Nf T̄f . The first
(k)
bit bi,1 ∈ {−1, 1} of the ith symbol determines the position of the pulse using
(k)
(k)
(k)
di,1 = (bi,1 + 1)/2 ∈ {0, 1}. The second bit bi,2 ∈ {−1, 1} of the ith symbol is
used to modulate the signal according to the CM-TR modulation.
A few remarks regarding the use of M −ary PPM (MPPM) follows. The
MPPM/CM-TR transmits (1 + log2 M ) bits by utilizing the energy required for
a single bit. However, the frame duration for MPPM is T̄f = Tf (1 + log2 M ),
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
185
r(t)
BPF
f (t)
r̃(t)
(·)2
t+T
R I
Nf −1
P
(·)dt
t
arg max
(k )
(k )
dˆi,1d ⇒ b̂i,1d
(k ) {Zil d }
b̂i,2d
l∈{0,1}
j=0
(k )
yil,jd
(k )
(k )
cj d
Timing
Figure 3: Architecture of the BPPM/CM-TR receiver.
i.e., there is a limited increase in the frame duration as it increases linearly with
log2 M instead of M [19]. Obviously, the higher values of M provide higher energy
efficiency but only a marginal amount of additional IFI and MUI mitigation. As
the value of M comprises a tradeoff between performance and energy efficiency,
2PPM or BPPM, is a judicious choice as its frame duration increases linearly
with M .
4.3
BPPM/CM-TR Receiver
It is assumed that the received BPPM/CM-TR signal is subjected to a similar
channel, MUI and noise conditions as the CM-TR signal, and the ith symbol
of the desired user kd is to be detected. The receiver structure uses the same
sampling rate as the CM-TR receiver, see Fig. 3. The energy of the two possible
pulse positions is computed by integrating the output of a square-law device and
the output of the integrator is sampled twice per frame to generate the sampled
signal for positions “0” and “1” of the ith symbol, respectively, as
(k )
yi0,jd
(k )
yi1,jd
=
Z
iT̄s +j T̄f +TI
[r̄(t)]2 dt,
(34)
iT̄s +j T̄f
=
Z
TBP P M +iT̄s +j T̄f +TI
[r̄(t)]2 dt,
(35)
TBP P M +iT̄s +j T̄f
(k)
where j = {0, 1, · · · , Nf − 1}. Further, the OCS cj of the desired user kd is
multiplied with the Nf output samples of the integrator corresponding to each
(k )
position, and two decision statistic values Zil d , where l ∈ {0, 1} is the index for
both BPPM positions, of the ith symbol are estimated as
(k )
Zil d
=
Nf −1
X
j=0
(kd ) (kd )
yil,j .
cj
(36)
186
Part V
(k )
Finally, the index l corresponding to the maximum absolute value of Zil d determines the position information of first bit, i.e.,
(k ) (k )
dˆi,1d = arg max {Zil d }.
(37)
l∈{0,1}
Thus, the decision for the first bit of the ith symbol is made as
(k )
(k )
b̂i,1d = (2dˆi,1d − 1),
(38)
and, for the second bit of the ith symbol, the decision is made based on the phase
(kd )
information of Zilmax
as
(k )
(k )
d
b̂i,2d = sign[Zilmax
],
(39)
where lmax is the argument l that maximizes Eq. (37).
5
Dual-Mode BPPM/CM-TR UWB System
Considering the decision strategy of the BPPM/CM-TR, it is evident that the
BPPM/CM-TR decision relies on the positions of the pulses, while the CM-TR
receiver has a 3 dB advantage as its decision is solely based on the phase information. Owing to the bipolar nature of the CM-TR, the BPPM/CM-TR advantage
can not be observed in the absence of MUI, i.e., in a single-user scenario. Though
IFI mitigation is achieved in a single-user scenario, it is not enough to beat the
CM-TR.
On the contrary, in a multi-user scenario, the CM-TR performance deteriorates significantly due to MUI, while the BPPM/CM-TR is expected to be more
resistant to MUI as the advantage of longer silent periods comes into play in
this case. Another aspect which needs to be considered here is the SNR of the
received signal. For very low SNRs, the BPPM/CM-TR is not expected to work
better than the CM-TR as the performance limiting factor in this regime is not
the MUI but the additive noise. The CM-TR and the proposed BPPM/CM-TR
are capable to cancel the MUI with the help of OCSs, however, they are not as
effective against the additive noise. Thus, in the low SNR regime, the proposed
BPPM/CM-TR is unable to beat the CM-TR due to its 3 dB advantage mentioned above. In short, in a single-user scenario and in the low SNR region, the
BPPM/CM-TR is not expected to perform better than the CM-TR system.
In order to cope with the problems raised by the BPPM/CM-TR, a dualmode BPPM/CM-TR UWB system may be used without altering the receiver
architecture. As the name suggests, the system operates in two modes depending
on the SNR and the number of users in the system. In the first mode, modulation
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
187
and detection is performed in the BPPM/CM-TR fashion, whereas the CMTR modulation and detection method is utilized in the second mode. Since
the BPPM/CM-TR is expected to have better performance than the CM-TR
in the high SNR region and in the presence of MUI, the proposed dual-mode
system will work in the first mode if SNR level is above a certain threshold.
Otherwise, i.e., if the SNR level is below the threshold or only a single-user is
transmitting, the system will switch to the second mode of operation. Indeed, the
switching between different modes requires estimation of the current SNR level
and knowledge of the number of active users in the network. For brevity, the
signal model and detection strategy of the proposed dual-mode BPPM/CM-TR
UWB system is not described here as it is based on the systems presented in the
previous sections.
6
Performance Evaluation
The expression for the BER of the CM-TR receiver has been derived in [9] in the
absence of IFI. In the presence of IFI, receiver performance of the CM-TR systems needs to be assessed empirically via computer simulation. To this end, the
multipath channel model proposed by IEEE 802.15.4a [17] is used to evaluate and
compare BER performance of the systems. The energy of the channel impulse
responses is normalized to unity. To achieve multi-user scenario in the simulations, the maximum number of users in the system are set to be Nu = 4. The
OCSs c(k) assigned to the users are taken from the rows of a 16 × 16 Hadamard
matrix and the OCS c(G) which is common to all the users coincides with the
first row of the matrix [9]. For Nu = 1 to 4, the optimal set of OCSs {2, 5, 9, 15},
which is obtained using the code sequence optimization criterion given in [9],
is used in all the evaluations, and the desired user is always assigned the first
element of this optimal set. It is assumed that the signals of all the users at the
receiver have equal power. The time asynchronism parameter τ̃ (k) is uniformly
distributed over the symbol duration of each system and it is assumed that a
perfect synchronization is achieved for the desired user.
6.1
CM/TR versus WCM-TR
The BER of the desired user is computed as a function of the Eb /No (as Es = Eb )
for both receivers. For both systems, the second derivative of a Gaussian pulse
with Tp = 2 ns is used and the number of frames is set be Nf = 16 per symbol.
The data rate Rb = 2 Mbps is achieved with the frame duration Tf = 125 ns.
For the CM-TR, TI = 30 ns; while for the WCM-TR, K = 15, Tb = 2 ns and the
weight parameters of the robust WCM-TR are β = 0.08, and ρ = 0.1 and for the
NDA WCM-TR η = 0.3.
188
Part V
0
10
−1
BER
10
−2
10
−3
10
CM-TR
One stage Robust WCM-TR
Two stage Robust WCM-TR
NDA WCM-TR
DA WCM-TR
−4
10
6
8
10
12
14
16
Eb /No [dB]
Figure 4: BER curves of the proposed WCM-TR, the conventional CM-TR, the
NDA WCM-TR and the DA WCM-TR using CM1 channel.
0
10
−1
BER
10
−2
10
−3
10
CM-TR
One stage Robust WCM-TR
Two stage Robust WCM-TR
NDA WCM-TR
DA WCM-TR
−4
10
6
8
10
12
14
16
Eb /No [dB]
Figure 5: BER curves of the proposed WCM-TR, the conventional CM-TR, the
NDA WCM-TR and the DA WCM-TR using CM2 channel.
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
189
0
10
−1
BER
10
−2
10
−3
10
CM-TR
One stage Robust WCM-TR
Two stage Robust WCM-TR
NDA WCM-TR
DA WCM-TR
−4
10
6
8
10
12
14
16
Eb /No [dB]
Figure 6: BER curves of the proposed WCM-TR, the conventional CM-TR, the
NDA WCM-TR and the DA WCM-TR using CM3 channel.
0
10
−1
BER
10
−2
10
−3
10
CM-TR
One stage Robust WCM-TR
Two stage Robust WCM-TR
NDA WCM-TR
DA WCM-TR
−4
10
6
8
10
12
14
16
Eb /No [dB]
Figure 7: BER curves of the proposed WCM-TR, the conventional CM-TR, the
NDA WCM-TR and the DA WCM-TR using CM4 channel.
190
Part V
The BER curves of the conventional CM-TR, the NDA WCM-TR, the DA
WCM-TR, and the proposed WCM-TR with one and two stage implementation
using the CM1, CM2, CM3 and CM4 channels are shown in Figs. 4, 5, 6 and7,
respectively. The DA WCM-TR has about 0.5dB better performance than the
proposed two stage WCM-TR, while performance of the two stage WCM-TR is
about 0.5 dB better than the NDA WCM-TR.
6.2
CM-TR versus BPPM/CM-TR
For both systems, the second derivative of a Gaussian pulse with Tp = 1 ns is
used and the number of frames is set to be Nf = 16 per symbol. For the CMTR system, the data rate Rb = 2 Mbps is achieved with the frame duration
Tf = 30 ns, and integration time TI = Tf . The BPPM/CM-TR system enables
the data rate Rb = 2 Mbps with the frame duration T̄f = 60 ns, the BPPM shift
is TBP P M = 30 ns and TI = TBP P M .
First of all, a BER versus Eb /No result is presented in Fig. 8, using the
CM4 channel, for a single-user (Nu = 1) and a multi-user (Nu = 4) scenario.
The curves show about 2 dB advantage in the single-user case and about 4 − 5
dB advantage for the multi-user setting. Obviously, as equal energy per bit is
used, the BPPM/CM-TR has no longer energy-efficiency advantage. Though it
is a fair comparison under the average power constraint, it assigns higher energy
per pulse for the BPPM/CM-TR system. On the other hand, the peak power
constraint in UWB systems demands equal energy per pulse for both systems. In
order to fulfill this requirement, energy per bit is decreased to half, which makes
the BPPM/CM-TR 3 dB energy efficient. In other words, energy per symbol is
equal for both systems if peak power constraint is satisfied, thus, BER versus
Es /No results are presented in the following evaluations.
In Figs. 9, 10 and 11, the performance of the CM-TR and the BPPM/CMTR system is shown using the CM4, CM7 and CM3 channel, respectively, for
a single-user (Nu = 1) and a multi-user (Nu = 4) scenario. In the single-user
case, Figs. 9, 10 and 11 show that the BER performance of the BPPM/CM-TR
is about 1.5 − 2 dB worse than the CM-TR system over all three channels. As
the biphase modulation has a 3 dB advantage over the orthogonal position modulation, it is intuitive that the single-user CM-TR system with biphase modulation
outperforms the single-user BPPM/CM-TR system having a combination of orthogonal position and biphase modulation. In contrast to the single-user case, the
results for the multi-user scenario show that the BPPM/CM-TR is significantly
more resistant to MUI as compared to the CM-TR system. In Figs. 9 and 10,
the multi-user BPPM/CM-TR outperforms the multi-user CM-TR for Es /No
higher than 16 dB and it improves as the SNR increases. From the comparison
of the single-user and the multi-user scenarios, it can be concluded that the MUI
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
191
0
10
CM-TR
BPPM/CM-TR
CM4
Rb = 2 Mbps
−1
10
BER
Nu = 4
−2
10
−3
10
Nu = 1
−4
10
8
12
16
Eb /No [dB]
20
24
Figure 8: BER versus Eb /No performance comparison of the single-user (Nu = 1)
and the multi-user (Nu = 4) CM-TR and BPPM/CM-TR systems for 2 Mbps
per user with CM4 channel.
0
10
CM-TR
BPPM/CM-TR
CM4
Rb = 2 Mbps
−1
10
BER
Nu = 4
−2
10
−3
10
Nu = 1
−4
10
8
12
16
Es /No [dB]
20
24
Figure 9: BER versus Es /No performance comparison of the single-user (Nu = 1)
and the multi-user (Nu = 4) CM-TR and BPPM/CM-TR systems for 2 Mbps
per user with CM4 channel.
192
Part V
significantly worsens the performance of the CM-TR system, whereas, for higher
SNRs, the BPPM/CM-TR is very effective in minimizing the MUI in the received
signal.
Figs. 12, 13 and 14 show the BER results for CM4, CM7 and CM3 channels,
respectively, using 4 users and the data rates of Rb = 1 Mbps and Rb = 2 Mbps.
The BER performance of the two system is compared for two different data
rates by varying the frame duration, which means the effect of IFI is assessed.
In the high SNR region (i.e., > 16 dB), these results depict the ability of the
BPPM/CM-TR to counter IFI as the data rate increases. However, compared to
Figs. 12 and 13, a large amount of IFI is present in Fig. 14 as the CM3 channel
has a relatively large delay spread and the BER saturates for very low SNRs.
For CM4 and CM7, it is observed that the BER performance of the BPPM/CMTR is better than the CM-TR system for Es /No values higher than 16 dB. In
Fig. 13, the BER results using the CM3 channel show that the BPPM/CM-TR
outperforms the CM-TR system for Es /No values of higher than 18 dB when
Rb = 1 Mbps. For Rb = 2 Mbps, the amount of IFI is so significant that the
performance of both systems is almost the same.
The evaluation results presented above show that the BPPM/CM-TR provides worse performance than the CM-TR for SNRs less than 16 dB, and improvements are only for SNR above 16 dB. Indeed, the BPPM/CM-TR uses 3
dB less energy per bit in its transmission, as equal energy per pulse is used due
to peak power constraint in UWB systems. However, if the same energy per bit
is used instead for both systems, the BER curve of the proposed BPPM/CM-TR
will be shifted −3 dB on the SNR-scale, and thereby always provide a better
result than its opponent CM-TR.
7
Conclusions
First, an energy detection based robust weight estimation scheme, originally proposed for BPPM IR-UWB signals, is extended to the multi-user CM-TR UWB
system and an adaptive robust WCM-TR receiver is developed. The proposed
method is a low-complexity suboptimal weight estimation scheme which requires
no a priori knowledge of the channel and the noise. The simulation results verify
that the performance of the robust WCM-TR scheme is close to that of an ideal
DA scheme with perfect CSI and always better than the NDA scheme.
Secondly, an energy efficient combined BPPM/CM-TR system is presented
for multiuser scenario. The BPPM/CM-TR enables energy efficient transmission as its transmitter requires 3 dB less energy per bit. The higher order PPM
modulations improve the energy efficiency at the cost of degradation in performance, while the BPPM/CM-TR provides the best tradeoff. In the high SNR
region, the multiuser BPPM/CM-TR UWB system improves the BER perfor-
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
193
0
10
CM-TR
BPPM/CM-TR
CM7
Rb = 2 Mbps
−1
10
BER
Nu = 4
−2
10
−3
10
Nu = 1
−4
10
8
12
16
Es /No [dB]
20
24
Figure 10: BER versus Es /No performance comparison of the single-user (Nu =
1) and the multi-user (Nu = 4) CM-TR and BPPM/CM-TR systems for 2 Mbps
per user with CM7 channel.
0
10
CM-TR
BPPM/CM-TR
CM3
Rb = 2 Mbps
−1
10
BER
Nu = 4
−2
10
−3
10
Nu = 1
−4
10
8
12
16
Es /No [dB]
20
24
Figure 11: BER versus Es /No performance comparison of the single-user (Nu =
1) and the multi-user (Nu = 4) CM-TR and BPPM/CM-TR systems for 2 Mbps
per user with CM3 channel.
194
Part V
0
10
CM-TR
BPPM/CM-TR
CM4
−1
BER
10
Nu = 4
Rb = 2 Mbps
−2
10
−3
10
Rb = 1 Mbps
−4
10
8
12
16
Es /No [dB]
20
24
Figure 12: BER versus Es /No performance comparison of the CM-TR and the
BPPM/CM-TR for 4 users using 1 Mbps and 2 Mbps per user with CM4 channel
channel.
mance by mitigating IFI and MUI. However, the simulation results reveal that
the BPPM/CM-TR is unable to beat the CM-TR system in a single-user scenario
and in the low SNR region. This issue may be resolved by employing a dual-mode
BPPM/CM-TR system, which normally operates in the BPPM/CM-TR mode
if the current SNR level is above a certain threshold and multiple-users are active, else it switches to the CM-TR mode. Hence, without increasing the receiver
complexity, the proposed dual-mode BPPM/CM-TR UWB system may be used
in multi-user wireless sensor network environments.
Weighted Code-Multiplexed Transmitted-Reference and BPPM/Code-Multiplexed
Transmitted-Reference Multi-user UWB Systems
195
0
10
CM-TR
BPPM/CM-TR
CM7
Nu = 4
−1
10
BER
Rb = 2 Mbps
−2
10
−3
10
Rb = 1 Mbps
−4
10
8
12
16
Es /No [dB]
20
24
Figure 13: BER versus Es /No performance comparison of the CM-TR and the
BPPM/CM-TR for 4 users using 1 Mbps and 2 Mbps per user with CM7 channel
channel.
0
10
CM-TR
BPPM/CM-TR
CM3
−1
BER
10
Nu = 4
Rb = 2 Mbps
−2
10
−3
10
Rb = 1 Mbps
−4
10
8
12
16
Es /No [dB]
20
24
Figure 14: BER versus Es /No performance comparison of the CM-TR and the
BPPM/CM-TR for 4 users using 1 Mbps and 2 Mbps per user with CM3 channel
channel.
Bibliography
[1] M. Weisenhorn, W. Hirt, “Robust noncoherent receiver exploiting UWB channel properties” In Proc. IEEE Conf. on UWB Systems and Tech., 2005, pp.
156–160.
[2] R. Hoctor, H. Tomlinson, “Delay-hopped transmitted-reference RF communications” In Proc. of IEEE UWBST Baltimore, MD, 2002, pp. 265–269.
[3] T. Q. S. Quek, M. Z. Win, “Analysis of UWB Transmitted-Reference Communication Systems in Dense Multipath Channels” IEEE Journal on Selec.
Areas in Comm., 2005, vol. 23, no. 9, pp. 1863–1874.
[4] D. Goeckel and Q. Zhang, “Slightly frequency-shifted reference ultrawideband
(UWB) radio,” IEEE Trans. Commun., vol. 55, no. 3, pp. 508–519, Mar. 2007.
[5] A.A. D’Amico and U. Mengali, “Code-multiplexed UWB transmittedreference radio,” IEEE Trans. on Comm., vol. 56, 2008, p. 2125–2132.
[6] J. Zhang, H.-Y. Hu, L.-K. Liu, and T.-F. Li, “Code-orthogonalized
transmitted-reference ultra-wideband (UWB) wireless communication systems,” in Proc. International Conf. Wireless Commun., Netw. Mobile Comput., Sep. 2007, pp. 528–532.
[7] H. Nie, Z. Chen, “Code-Shifted Reference Ultra-Wideband (UWB) Radio
Communication” 6th Annual Networks and Services Research Conf. (CNSR),
May 2008, pp. 385–389.
[8] S. Gezici, “Coded-Reference Ultra-Wideband Systems”, Proc. IEEE Inter.
Conf. on UWB, 2008, vol. 3. pp. 117–120.
[9] A. A. D’Amico, and U. Mengali, “Code-Multiplexed Transmitted-Reference
UWB Systems in a Multi-User Environment,” IEEE Trans. on Comm., March
2010, vol. 58, no. 3, pp. 966–974.
[10] Z. Tian and B.M. Sadler, ”Weighted energy detection of ultra-wideband
signals,” Proc. IEEE 6th Workshop on Signal Processing Advances in Wireless
Communications, 2005, pp. 1068–1072.
[11] J. Wu, H. Xiang, and Z. Tian, ”Weighted Noncoherent Receivers for UWB
PPM Signals,” IEEE Commun. Lett, vol. 10, no. 9, 2006, pp. 655–657.
197
198
BIBLIOGRAPHY
[12] J. Wu, Q. Liang, and H. Xiang, ”Adaptive Weighted Noncoherent Receiver
for UWB-PPM Signal in Multipath Channels,” Proc. ICWMMN Conference,
2006.
[13] A. A. D’Amico, U. Mengali, and E. Arias-de-Reyna, “Energy-Detection
UWB Receivers with Multiple Energy Measurements,” IEEE Transactions
on Wireless Comm., 2007, vol. 6, no. 7, pp. 2652–2659.
[14] M. Flury, R. Merz, J.-Y. Le Boudec, ”An Energy Detection Receiver Robust to Multi-User Interference for IEEE 802.15.4a Networks” Proc. IEEE
International Conference on UWB, 2008, vol. 1, pp. 149–152
[15] S. Bin, Y. Rumin, C. Taiping, and K. Kyungsup, ”Non-data-aided Weighted
Non-coherent Receiver for IR-UWB PPM Signals,” ETRI Journal, vol. 32, no.
3, Jun. 2010, pp. 460–463.
[16] M. G. Khan, B. Sällberg, J. Nordberg and I. Claesson, “Robust Weighted
Non-Coherent Receiver for Impulse Radio UWB PPM Signals”, accepted to
IEEE Communications Letters, March 2011.
[17] A. F. Molisch et al., “IEEE 802.15.4a channel model - final report,” Tech.
Rep. Document IEEE 802.15-04-0662-02-004a, 2005.
[18] F. Ramirez-Mireles, “Performance of ultrawideband SSMA using time hopping and M −ary PPM”, IEEE Journal Select. Areas in Comm., vol. 19, pp.
1186–1196, June 2001.
[19] S. Erkucuk, Dong In Kim, “Combined M −ary code shift/differential chaos
keying for low-rate UWB communications”, IEEE International Conf. on
UWB, ICU 2005., pp. 33–37, 2005.
[20] C. Carbonelli and U. Mengali, “M-PPM Noncoherent Receivers for UWB
Applications”, IEEE Trans. on Wireless Comm., vol. 5, no. 8, pp. 2285–2294,
August 2006.
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