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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 31 I Performance Evaluation of Coherent and Non-coherent Receivers for IR-UWB Systems using Multipath Channels for Industrial Environments 1 2 3 4 5 6 7 8 Introduction . . . . . . . . . . System Model . . . . . . . . . UWB Channel . . . . . . . . RAKE Receiver . . . . . . . . Conventional TR Receiver . . Conventional Energy Detector Performance Evaluation . . . Conclusions . . . . . . . . . . 1 3 5 9 15 19 23 25 . . . . . . . . xv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 . . . . . . . . 44 45 48 51 56 60 63 70 xvi CONTENTS Bibliography 73 II Recursive and Doublet-Based Transmitted Reference Schemes for Ultra Wideband Communications 77 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 81 82 92 100 106 110 115 117 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 124 126 127 133 137 147 149 IV Robust Weighted Non-Coherent Energy Detection Receiver for Impulse Radio UWB PPM Signals 151 1 2 3 4 5 6 Introduction . . . . . . . . . . System Model . . . . . . . . Weighted ED (WED) . . . . Weight Estimation for WED Performance Evaluation . . . Conclusions . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 155 156 159 162 165 167 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 173 176 183 186 187 192 197 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. 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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. 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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) 92 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. 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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) 132 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. 134 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 138 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. 140 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. 142 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. 144 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. 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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. 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