Institutionen för systemteknik

Institutionen för systemteknik
Institutionen för systemteknik
Department of Electrical Engineering
Examensarbete
ADS and Matlab to Optimize Predistortion of Amplifiers
Examensarbete utfört i Signalbehandling
av
Jessica Trinh
LiTH-ISY-EX--15/4880--SE
Linköping 2015
TEKNISKA HÖGSKOLAN
LINKÖPINGS UNIVERSITET
Department of Electrical Engineering
Linköping University
S-581 83 Linköping, Sweden
Linköpings tekniska högskola
Institutionen för systemteknik
581 83 Linköping
ADS and Matlab to Optimize Predistortion of Amplifiers
Examensarbete utfört i Signalbehandling
vid Linköpings tekniska högskola
av
Jessica Trinh
LiTH-ISY-EX--15/4880--SE
Handledare: Daniel Axehill
Examinator: Fredrik Gunnarsson
Linköping 10 juni 2015
Presentationsdatum
Institution och avdelning
Institutionen för systemteknik
2015-06-10
Publiceringsdatum (elektronisk version)
Department of Electrical Engineering
2015-06-11
Språk
Typ av publikation
ISBN (licentiatavhandling)
Svenska
X Annat (ange nedan)
Licentiatavhandling
X Examensarbete
C-uppsats
D-uppsats
Rapport
Annat (ange nedan)
ISRN LiTH-ISY-EX--15/4880--SE
English
Antal sidor
76
Serietitel (licentiatavhandling)
Serienummer/ISSN (licentiatavhandling)
URL för elektronisk version
http://www.ep.liu.se
Publikationens titel
ADS and Matlab to Optimize Predistortion of Amplifiers
Författare
Jessica Trinh
Sammanfattning
This master’s thesis deals with integrating simulations using Agilents Electronic Design Automation tool ADS with
customized Matlab scripts, for solving complex analog and digital radio architectures. In particular, it addresses
predistortion, realized in the digital domain, of power amplifiers, modeled in the analog domain. The former is implemented
in Matlab while the latter is implemented in ADS. Two versions of integrating the two systems have been tested: 1) Iterative
approach on sample basis and 2) Scheduled batch solution by matrix inversion. The concept has been tested on two different
PA configurations: 1) a standard class-AB PA and 2) a Doherty PA architecture. Evaluation has also been done on ADS
ability to correctly simulate memory effects in PAs and on the actual DPD-algorithms ability to compensate for these
memory effects.
An integrated simulation environment for ADS and Matlab was successfully established within the work of this thesis.
Matlab scripts, used in predistortion algorithms in the digital domain, could interact directly with component-based PA
models, in an enclosed simulation system.
The simulation results show that sample basis method is the most accurate, fast and reliable method to linearize a PA. The
PA1 proved to be easier than the DPA to linearize, except for when being close to saturation where better IMD-suppression
was achieved with the DPA.
ADS is clearly able to simulate memory effects in the analog domain. At low gain-levels the applied compensating memoryalgorithms showed a great improvement to the linearization of the output signal of the PA. At higher gain-levels though, the
compensation for memory effects lost their efficiency because the non-linearity of the PA became too significant.
Nyckelord
Predistortion, Digital predistortion, DPD, ADS, ACLR, WCDMA, IMD, Memory effect
Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Abstract
This master’s thesis deals with integrating simulations using Agilents
Electronic Design Automation tool ADS with customized Matlab scripts,
for solving complex analog and digital radio architectures. In particular, it
addresses predistortion, realized in the digital domain, of power
amplifiers, modeled in the analog domain. The former is implemented in
Matlab while the latter is implemented in ADS. Two versions of
integrating the two systems have been tested: 1) Iterative approach on
sample basis and 2) Scheduled batch solution by matrix inversion. The
concept has been tested on two different PA configurations: 1) a standard
class-AB PA and 2) a Doherty PA architecture. Evaluation has also been
done on ADS ability to correctly simulate memory effects in PAs and on
the actual DPD-algorithms ability to compensate for these memory
effects.
An integrated simulation environment for ADS and Matlab was
successfully established within the work of this thesis. Matlab scripts,
used in predistortion algorithms in the digital domain, could interact
directly with component-based PA models, in an enclosed simulation
system.
The simulation results show that sample basis method is the most
accurate, fast and reliable method to linearize a PA. The PA1 proved to be
easier than the DPA to linearize, except for when being close to saturation
where better IMD-suppression was achieved with the DPA.
ADS is clearly able to simulate memory effects in the analog domain. At
low gain-levels the applied compensating memory-algorithms showed a
great improvement to the linearization of the output signal of the PA. At
higher gain-levels though, the compensation for memory effects lost their
efficiency because the non-linearity of the PA became too significant.
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Preface
This thesis work is carried out at the Digital Radio group at Ericsson in
Kista. I would like to thank my supervisor Leonard Rexberg at Ericsson,
my advisor Daniel Axehill at LiTH and my examiner Fredrik Gunnarsson
for making this work possible.
Jessica Trinh
Linköping, May 2015
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Table of contents
Abstract ............................................................................................. 1
Preface .............................................................................................. 2
Table of contents ............................................................................... 3
Acronyms .......................................................................................... 5
1
Introduction ........................................................................... 6
1.1
1.2
1.3
2
Preliminaries ......................................................................... 9
2.1
2.1.1
2.1.2
2.1.3
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
2.5
3
Purpose..................................................................................... 7
Scope ........................................................................................ 7
Background .............................................................................. 7
The RF signal ........................................................................... 9
Modulation techniques ......................................................... 9
Multiplexing ....................................................................... 10
Complex baseband signal representation ........................... 11
Power Amplifiers ................................................................... 14
Nonlinear systems .............................................................. 15
PA memory effects ............................................................. 16
Polynomial modeling without memory effects .................. 16
Polynomial modeling with memory effects ....................... 17
Linearization techniques ........................................................ 17
Feedback ............................................................................ 18
Feedforward (FF) ............................................................... 18
Predistortion (PD) .............................................................. 19
Digital predistortion (DPD)................................................ 20
Behavioral modeling or Component-based modeling ........... 21
Advanced Design System (ADS)........................................... 21
Modelling of Power Amplifiers and Digital Predistortion 22
3.1
The Digital Predistortion algorithm ....................................... 22
3.1.1 Iterative solution on sample basis ...................................... 22
3.1.2 Iterative solution on matrix inversion basis ....................... 24
3.1.3 With memory effect ............................................................ 24
3.2
Component-based PA-modeling in ADS ............................... 25
3.2.1 The MRF5S21 PA (PA1) .................................................... 25
3.2.2 The Doherty PA (DPA) ....................................................... 26
3.3
System overview, Matlab-ADS integration ........................... 29
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
3.4
Matlab-ADS integration methods .......................................... 30
3.4.1 Approach 1: Iterative solution on sample basis ................. 30
3.4.2 Approach 2: Matrix inversion basis with post-distortion ... 33
3.5
Intermodulation distortion and the ACLR ............................. 36
3.6
ADS-simulators ..................................................................... 38
4
Simulation and evaluation ................................................. 39
4.1
4.2
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
5
ADS-Matlab integration in practice ....................................... 39
How the simulations were executed ...................................... 40
Simulation variables .............................................................. 43
PA gain ............................................................................... 43
Polynomial degree .............................................................. 43
Memory-depth .................................................................... 44
Simulation results .................................................................. 44
Non-linear and linearized signal ........................................ 45
ACLR1 and ACLR2 ........................................................... 46
Linearization relative to gain-levels ................................... 47
Polynomial degree (N-value) ............................................. 50
Memory effects .................................................................. 53
Sample and Matrix simulation ........................................... 62
Summary and conclusions ................................................ 64
Appendix 1.
Appendix 2.
Appendix 3.
Appendix 4.
Appendix 5.
Schematics of the PA1 and DPA..................................... 67
Schematics of the input and output matching networks . 69
Top level schematics ....................................................... 72
Schematics of modulators............................................... 75
The WCDMA test signal ................................................ 76
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Acronyms
3GPP
Third Generation Partnership Project
ACLR
ADS
ASK
BB
BPSK
CE
dB
dBc
DPA
DPD
DSP
DUT
EDA
FF
FSK
HB
IM
IMD
LDMOS
LMS
PA
PAR
PSD
PSK
QPSK
QAM
RF
RRC
UMTS
WCDMA
Adjacent Channel Power Leakage Ratio
Advanced Design System
Amplitude Shift Keying
Base Band
Binary Phase-Shift Keying
Circuit Envelope
Decibel
Decibel Below Carrier
Doherty Power Amplifier
Digital Predistortion/Predistorter
Digital Signal Processor
Device Under Test
Electronic Design Automation
Feedforward linearization
Frequency Shift Keying
Harmonic Balance
Inter Modulation
Inter Modulation Distortion
Laterally Diffused Metal Oxide Silicon
Least Mean Square
Power Amplifier
Peak-To-Average Ratio
Power Spectral Density
Phase Shift Keying
Quadrature Phase-Shift Keying
Quadrature Amplitude Modulation
Radio Frequency
Raised Root Cosine
Universal Mobile Telecommunication System
Wideband Code Division Multiple Access
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
1
Introduction
The use of radio communication services is augmenting continuously and
has created an increasing demand for channels with greater capacity and
higher data transmission rates. Since the available radio spectrum is
limited and the number of base stations is growing rapidly, two of the
most essential factors when designing modern wireless communication
systems are spectrum efficiency and power efficiency.
Power efficiency: In a mobile communication system, the power
amplifier (PA) is considered one of the most power consuming
components. Linear PAs are not desirable since they offer poor power
efficiency, which leads to heat dissipation in the base station and shorter
battery stand-by time in the mobile unit. To obtain higher power
efficiency, modern PAs are driven to operate in the non-linear region, as
near saturation as possible.
Spectrum efficiency: The Wideband Code Division Multiple Access
(WCDMA), which is used as a standard in today’s Third Generation (3G)
base stations, is a spectrum efficient modulation method using nonconstant envelope modulation schemes. This technique allows a large
number of channels to be transmitted on the same frequency by using
orthogonal spreading codes and by placing the channels very close to
each other as to minimize unused spectrum.
Combining these two competing factors is however a difficult task. The
fact that the WCDMA signal has a high peak-to-average power ratio
(PAR) implies a very high requirement on the linearity of the power
amplifier used. The large fluctuations in the signal envelopes lead to
intermodulation distortion (IMD) and hence spectral regrowth in
nonlinear amplifiers. In another word, in a system with WCDMA signals,
the nonlinearity of the PA degrades the system performance significantly
by introducing new, unwanted frequency components at its output,
causing expansion of the signal spectrum into the channels nearby.
In order to maintain both efficiency and linearity, one solution is to
linearize a power efficient PA by using an external circuitry. Thus, a lot of
research has been done on different linearization techniques. This thesis
focuses on digital predistortion (DPD), a cost-effective and reliable
linearization method that has been the subject to intensive researches
worldwide in recent years. Especially, the possibilities to integrate the
DPD technique into a simulation environment during the development of
PAs are investigated.
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
1.1
Purpose
The purpose of this master’s thesis is to create an integrated simulation
environment for ADS and Matlab, connecting the analog/RF and digital
domain, in a digital predistortion-PA system to be able to optimize the
parameters of the two subsystems as one entity.
The purpose is also to evaluate the reliability and robustness of
component-based modeling in ADS as an alternative to polynomial
modeling.
1.2
Scope
In this thesis a class AB PA model and a Doherty PA model will be
linearized by using a digital predistortion technique that is based on LMSalgorithm.
The goal is to create a simulation environment where we potentially can
switch between different DPD-algorithms and PA-designs easily, in order
to study the ability of model-based predistortion on component-based PA
modeling. Two different approaches will be tested and evaluated; the
sample and the matrix method.
Some of the questions to be answered are:
 How much can IMD be suppressed after linearization?
 Are there any differences between the sample or matrix approach?
 Can we model memory effects in ADS? If so, can memory effects
be counteracted?
 Do the Doherty PA and the class AB PA behave differently
according to the linearization algorithms?
1.3
Background
One way to attain both linearity and power efficiency when amplifying a
signal is to linearize a nonlinear but power efficient PA by using digital
predistortion technique. The idea is to insert a nonlinear element into the
signal path prior to the PA such that the combined transfer characteristic
of these two blocks is linear. A simplified block diagram of such a
combined system is shown in Figure 1.
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 1. Placing a DPD block (implemented in Matlab) with the
inverse characteristics of the amplifier response in front of the PA
block (implemented in ADS) results in distortion cancellation and
hence a linear output signal.
However, with the cascade of different options in designing these two
subsystems, that are normally developed separately in digital domain and
RF domain respectively, we are faced with the issue of optimizing the
integrated system for which the requirements are specified for, and not
each subsystem. As a consequence, designers of each subsystem have to
estimate a reasonable subsystem requirement to follow while designing in
each domain. This is not optimal, especially not in RF design.
It is therefore of great interest to create an environment that allows
simulation of both analog and DSP subsystems. The purpose is to make
them co-simulate throughout the design cycle, as to optimize subsystem
parameters and also to minimize the system integration problems in
hardware implementations later on.
Power amplifiers (PA) are often designed in the RF-domain using
computer aided design systems like ADS whereas linearization is best
performed in Matlab. As a consequence, the challenge lies within making
Matlab interact with ADS, either way as a stand-alone unit or as a
component directly inserted into the ADS circuit.
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
2
Preliminaries
In this chapter, the basic theory about the RF signal and complex
baseband signal presentation is explained. The three main linearization
techniques are described as well as the basics of power amplifiers and
nonlinear systems. In the end, Agilent’s design software ADS is
presented.
2.1
The RF signal
A signal is an entity capable of carrying some information. The basic
information carrying signal is the baseband signal. The baseband signal
carries analog information as voice, music or analog television signals or
digital pulse code modulated signals. The baseband signal is normally a
low frequency signal which is inconvenient to transmit on large distances.
To be able to transmit the baseband signal in a power- and bandwidth
efficient way it is modulated on a powerful high-frequency carrier signal.
The RF signal is then presented as a sampled envelope on the RF carrier
frequency. Modulation also allows us to move baseband signals to
different ranges of frequency which makes it possible to send signals in
any of a large number of frequency ranges without overlapping.
2.1.1
Modulation techniques
The three basic modulation methods are; amplitude, frequency and phase
modulation. Amplitude modulation (AM) samples the baseband signal on
the carrier by adjusting the amplitude of the carrier. Although the
amplitude modulation is commonly used it has some disadvantages, the
variation of the amplitude requires a linear amplifier to correctly
modulate the original signal on the carrier and it uses twice the bandwidth
of the original signal because of the double-sideband transmission.
Frequency modulation (FM) uses the continuous peak amplitude of the
carrier signal and instead varies its frequency according to the modulated
baseband signal. Frequency modulation, commonly used for radio
broadcasts and mobile cellular telephony, offers some advantages over the
AM. The FM signal can use more power efficient non-linear amplifiers
because of the constant peak amplitude and the received signal-to-noise
ratio does not degrade gradually as in AM but deteriorates suddenly,
which improves the signal-to-noise ratio of the recovered baseband
signal. A third advantage of FM is that when two interfering signals reach
a receiver, the stronger captures the receiver so that the weaker is not
heard. This phenomenon is important in mobile radio because we want to
hear the nearest and strongest transmitter without the interference from
more distant transmitters. (Pierce and Noll 1990)
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Phase modulation (PM) is used to change the phase of a signal among
different phase states to represent a pattern of bits. The simplest phase
modulation technique is the Binary Phase-Shift Keying (BPSK) where the
change of the phase by 180 degrees represents the digits 0 and 1. The
Quadrature Phase-Shift Keying QPSK has four different phase states,
which can also be called 4QAM because of its constant amplitude.
By combining AM and PM more phase states can be achieved to
represent more binary digits and thus to increase the possible data
transmission rate (Anderson 2003). Two examples are the 16QAM
(Quadrature Amplitude Modulation) and the 64QAM which have 16
respectively 64 phase states.
2.1.2
Multiplexing
Multiplexing is used for sending multiple signals in the same medium.
Frequency-Division Multiple Access (FDMA) uses frequency shifting of
individual single voice signals to produce a single signal of larger
bandwidth that combines the individual signals. Each individual voice
signal is carried over a single voice channel (Pierce and Noll 1990).
FDMA has enhanced the efficiency of long-distance telephone networks
and the early satellite communications.
Time-Division Multiple Access (TDMA) is a more economical and more
satisfactory multiplexing technique for short-distance transmissions over
wires and for all transmissions over optical fiber. The TDMA works with
the digital pulse code modulation signal and transmits several different
signals over a single channel by sending them at different times. The
individual signal is divided into small time slots which are sent as an
intermittent signal together with other signals on the same frequency. The
receiver then puts the time slots together and reconstructs the original
baseband signal. The TDMA is a so called packet-switched network
where the information is divided into smaller packets that are sent
individually with a flexible route instead of a circuit-switched network
like the FDMA where the path between the user and the destination node
is set up at the time the connection is established, and any needed
resources has to be reserved in the network until the connection is
terminated. The packet-switched networks are therefore more efficient
and flexible but also more complicated because data packets can take
different paths and can be received out of order (Groe and Larson 2000).
More about switching can be found in Signals, building blocks and
networks (Carne 1995) TDMA is used in the 2G GSM cellular system.
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Code-Division Multiple Access (CDMA) is a spread-spectrum
communication technique and a secondary modulation technique. The
signal is first modulated by traditional amplitude, frequency or phase
techniques. The individual message signals are then spread over a wide
frequency with the ability to hop in the frequency range by multiply the
message signal to a random carrier frequency. The spreading code are
fundamental in the spread-spectrum communication. The spreading code
enables synchronization of the transmitter and the receiver when the
signal hops between different frequencies (Groe and Larson 2000). The
advantage of the CDMA is that several transmitters can send information
simultaneously over a single communication channel by frequency
hopping and the use of spread codes. The fact that several signals are sent
at the same time on very close spectrums also makes the CDMA
technique sensitive to inter modulation distortion (IMD), this is explained
further in chapter 3.5. Wideband CDMA (WCDMA) is the CDMA
technique adapted for the UMTS mobile cellular network and currently
used for the 3G and 4G cellular system.
2.1.3
Complex baseband signal representation
The WCDMA signal that is fed into the DPD-PA-system is represented as
a complex baseband signal since it is more convenient to handle than the
traditional bandpass representation. When transmitting information, most
systems operate by modulating an information bearing waveform onto a
sinusoidal carrier. Hence, using complex baseband representation we can
easily characterize and analyze communication signals independently of
the carrier frequency.
As an example, a two-tone bandpass signal can be written as:
x c (t )  a  cos( c t )  b  cos( c  0 )(t )
(1)
By using complex notation, we can re-write this expression as:





x c (t )  Re a  e j c t  b  e j ( c  0 )t  Re a  b  e j ( c  0 )t  e j c t 


 Re I (t )  j  Q(t )   e j c t  I (t )  cos( c t )  Q(t )  sin( c t )
(2)
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
From (2) it is seen that a signal can be de-composed into a form
containing orthogonal components. We also see that the signal can be split
into a complex baseband signal (I + jQ) and a carrier component of
frequency c. As in ordinary AC calculations, where we do not concern
about the carrier frequency, we may omit this part and only deal with the
complex baseband. The difference to single-sinusoidal AC representation
will only be that now we have a time varying baseband component (Fitz
2007, p 4.4). The complex baseband signal may now be represented as:
x BB (t )  I t   j  Qt 
(3)
The treatment of nonlinearity of power amplifiers may be completely
referred to this complex baseband signal described in (3) although the
derivation may start at RF frequency. To see this we apply the
mathematical representation of a nonlinearity as a polynomial power
series. We postulate that the nonlinearity of a PA may be modeled in
terms of the input signal as:
x PA (t )   0  xc t    1  xc t    2  xc t    
2
N 1
3
(4)
  n  xc t 
n
n 0
From this we may insert the expression for xc(t) as in (2) to obtain the
following expression referred to as the complex baseband signal:
x PA (t ) 
   Rex
N 1
n 0
n
BB
(t )  e jwct

n
(5)
This can be further expanded to get rid of the “Re”-function and to further
later on also be able to drop the carrier frequency, as:
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
N 1
x PA (t )   n 
n 0
N 1
  n 
n 0

1
*
 x BB t   e j ct  x BB t   e  j ct
n
2

1 n  n
     x BB t   e j ct
2 n k 0  k 
  x

nk

n
*
BB

t   e  j t 
c
k

(6)

k
1 n  n
nk
*
    x BB t   x BB t   e jn  2k  ct  etc
n  
2 k 0  k 
n 0
So, we see from (6) that we obtain harmonic components at frequencies
(n-2k)c in addition to just at the carrier frequency c. However, we are
only interested in the components that are placed at exactly c, and
therefore we will omit the other terms in the expansion. That is, we will
only retain components where n-2 =1. Doing so, we arrive at the
following expansion:
N 1
  n 
x PA (t )  Only wc components, (n - 2k  1) 
N 1
  n 
n 0
N 1
  n 
n 0


1 k
k
1 n 1  2  k 
  x BB t   x BB * t   e j1 ct 
 
n 
2 k 0  k 
(7)
1 n 1  2  k 
2k
  x BB t    x BB t    e j1 ct  harmonics
 
2 n k 0  k 
We see from (7) that we will only retain “odd” power components of xBB.
That is, we may express the output signal from the non-linear PA as an
expansion in terms of the odd powers of xBB as:
N 1
xPA,BB (t )    n  xBB t    xBB t  
2n
(8)
n 0
However, it turns out that also the “even” components will contribute
although they on the paper just give harmonics that lie outside the carrier
frequency at higher harmonics, i.e. at 0 frequency and 2c. Therefore, we
will write the complex baseband representation of the signal that comes
out of the PA as:
N 1
xPA, BB (t )    n  xBB t    xBB t  
n
(9)
n 0
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Linköping University
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ADS and Matlab to Optimize Predistortion of Amplifiers
2.2
Power Amplifiers
A power amplifier (PA) is a circuit for converting dc-input power into a
significant amount of RF/microwave output power. A transmitter consists
of one or more PAs and usually auxiliary circuits like signal generators,
frequency converters, modulators, signal processors, linearizers and
power supplies.
The most challenging part of designing modern PAs is to create both a
high order of linearity as well as a power efficient unit. The old classical
RF signals like the FM, FSK and the GMSK which had a constant
envelope signal did not require linear amplification. Those signals were
best produced by a high-level amplitude modulation RF PA. The modern
RF signals which contains both amplitude and phase modulation such as
QAM, QPSK and CDMA does though request a high linearity RF PA
(Raab F, Asbeck P et al. 2002).
RF PA:s are commonly designed as classes A-F which differ in methods
of operation, efficiency and power-output capability. The following table
gives the main characteristics of the different classes.
Class
Linearity
Other characteristics
A
High
High gain, operation close to transistor
maximum frequency, often low output
power. Constant power consumption.
B
High
Power consumption proportional to input
signal, thus significantly more power
efficient than the class A,
C
Low
Very power efficient and commonly used
for high-level amplitude modulation
D
non-linear
Switch-mode amplifier. Normally not used
for frequencies over 300 Mhz.
E
non-linear
Switch-mode amplifier.
F
non-linear
Switch-mode amplifier.
Table 1. PA classes. (Raab F, Asbeck P et al. 2002)
To amplify a multicarrier signal with a non-constant envelope as the
CDMA signal a class A or B amplifier must be used, or a mix of the two
types (class AB) (Pothecary 1999, p 97).
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The class C amplifier has poor linear characteristics and the switch-mode
amplifiers are not possible to use with bandwidth-efficient modulation
schemes as for example the QPSK.
2.2.1
Nonlinear systems
In a perfectly linear system, the output is a scalar function of its input, as:
Vout (t)=K1 Vin (t)
where Vout and Vin are the output respectively input voltage and K1 is a
gain constant (Pothecary 1999, p. 43).
However, when using a power efficient amplifier, it is not easy to amplify
an input signal to the required levels for reliable transmission. It normally
produces both amplitude and phase distortion, which get worse when
approaching saturation. Moreover, the amplitude variation of an input
signal also has a strong effect on the distortion of the output signal.
Therefore, a PA is more sensitive to nonlinearities when using digitally
modulated signals like WCDMA. More about how to model
nonlinearities in PAs is discussed in chapter 3.1.
A nonlinear PA causes two types of distortion products. First, those near
the fundamental signals will interfere with the input signal itself and are
called cross modulation. Second, the other type appears in form of new
unwanted frequency components introduced at the output of the PA called
intermodulation distortion (IMD). These cause spectral regrowth and
interfere with adjacent channels making the information detection task in
these channels difficult. The latter is significantly important in the
WCDMA context, where channels are placed very close to each other.
One of the most important nonlinearity measurements is the ACLR, see
chapter 3.5, for which specific requirements are set in the 3GPP
specification to restrict the power leakage into neighboring channels.
Figure 2a) and b) new frequency components are introduced at the
output of a nonlinear amplifier, causing spectral regrowth and IMD.
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2.2.2
PA memory effects
Any PA will show some dynamic deviations from its static characteristics.
Those deviations are known as “memory effects”. Memory effects are an
additional source of nonlinear behavior that is usually not accounted for
in PA models. The memory effects can be categorized as dynamic thermal
effects, unintentional bias modulation and trapping effects. Thermal
effects can possibly be addressed to a physical based model but the other
two are results of anomalous semiconductor and circuit effects and
especially trapping effects defy analytical and even behavioral modeling.
Unintentional bias modulation effects can be predicted in an extensive
circuit simulator as the ADS-system, see chapter 2.5. Trapping effects on
the contrary is hard to simulate and is best handled by choosing
components which show none or very little of this affliction. The reducing
of memory effects through the semiconductor process and circuit
development and is an important area for ongoing research. (Cripps 1999)
Because the memory effects are hard to include in the PA models
characteristics they and can cause big problems in the developing of
predistortion algorithms, see chapter 3.1.3. However, there are ways to
include some of the memory effects in the algorithms.
2.2.3
Polynomial modeling without memory effects
The nonlinear output of a memoryless amplifier modeled with a
polynomial power series can be written as:
y  a0  a1  x  a 2  x 2  ...  a n  x n
Where x and y denote the input respective output signal, and
complex coefficients.
a0 a n
- are
However, such a simple polynomial model is insufficient to correctly
characterize a power amplifier used in applications like WCDMA, since
memory effects also must be taken into account. A system is said to suffer
from memory effects when its output signal does not depend only on the
instantaneous input values but also on previous ones. This is an undesired
phenomenon that exists in most PAs and that makes it more difficult to
model and to linearize the actual system.
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2.2.4
Polynomial modeling with memory effects
A polynomial power series with memory is best represented by a Volterra
series because it provides a general way to model a non-linear system
with memory. The Volterra series are however very complex and need
much computational power to be calculated as the number of parameters
to be estimated increases exponentially with the degree of nonlinearity
and with the memory length of the system. More about Volterra series and
non-linear systems can be found in Digital Pre-Distortion of Power
Amplifiers (Spångberg 2002, p 14-15).
A simpler version of the general Volterra series is the modified Volterra
series which separates the static memoryless behavior of the PA from the
purely dynamic behavior with memory effects. The two models are then
mixed and calculated in a classical power series, also called memory
polynomials.
A nonlinear system with memory-depth of two can then be represented as
follows:
y  (a 0  a1  x  a 2  x 2  ...  a n  x n )  (b0  b1  x k  b2  x k  ...  bn  x k ) 
2
n
...  (c0  c1  x k  m  c 2  x k  m  ...  c n  x k  m )
2
n
a a b b
c c
where 0 - n , 0 - n , and 0 - n are complex coefficients and x-i denote
previous samples of the input signal, k is the sample delay, n is the
polynomial order and m is the number of previous samples included.
2.3
Linearization techniques
PA linearization is used to correct the nonlinearities of the PA and make
the response more linear. This is done by comparing the output of the PA
to the input and generate appropriate corrections. There are two main
linearization techniques; input correction and output correction. Input
correction is applied on the input signal of the PA to make the response
linear. This technique does not increase the peak power and makes the
input signal subjected to the non-linearity of the PA. The output
correction is applied on the output signal and has to generate significant
amount of power to perform its function. It will then physically increase
the peak power of the linearized PA. When the PA saturates close to peak
power additional power is added to the signal to keep a linear response.
(Cripps 1999, p 399)
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Three main types of linearization techniques are commonly used on PAs
in wireless communication systems and is here briefly explained;
Feedback, Feedforward and Predistortion.
2.3.1
Feedback
The feedback technique, which corrects the input signal, has been long
used to eliminate unpredictable behavior of electronic devices. In a basic
direct feedback amplifier the feedback signal is subtracted from the
output source signal. The feedback signal is then scaled by a feedback
factor and then reintroduced on the input source signal generating a
different input signal which after amplifying should become more linear
than the original output signal. This is called a closed feedback-loop.
However basic direct feedback has a diminishing value as the signal
frequency enters the GHz region due to oscillations at a nearby frequency
and is not used on microwave amplifiers.
Instead of using the feedback technique on the high-frequency carrier it
can be used on the modulated baseband envelope. The Envelope feedback
technique was well used on the early mobile communication systems but
since the feedback signal only contains amplitude information it can just
correct AM distortion and not phase distortion (Pothecary 1999, p 119).
The Cartesian loop feedback technique can correct for both amplitude and
phase distortion and has been widely used in solid state radio transmitters
but is not suited for high-frequency microwave amplifiers.
2.3.2
Feedforward (FF)
Feedforward is an output correction linearization technique. The basic
feedforward correction loop subtracts a sample of the input signal and
delays it. The subtracted input signal is then combined with a subtracted
output sample of the main amplifier. This results in an RF error signal at
the output of the combiner. The error signal is then amplified back to the
original level by an additional amplifier and combined with the main
amplifier output signal. If the output signal of the main amplifier has no
gain or phase distortion the combined error signal will be of zero output
and the additional amplifier will remain inactive. But when an error signal
occurs the additional amplifier will produce an RF signal that
theoretically fills the gap between the main amplifiers distortion
properties and the requested linear output result. The combined output RF
signal of the two amplifiers will be linearized and the enclosed system
will have a capacity that exceeds the main amplifier because of the “help”
from the additional amplifier. This is the basic principle behind the
Doherty PA described in chapter 3.2.2.
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Feedforward is an instant correction technique that operates on the fully
formatted RF signal and the correction process is only limited by the
phase and amplitude tracking capability of the various components of the
system. Great accuracy in gain and phase tracking throughout the system
is inevitable to achieve a high precision in the operation, which must be
maintained by the system and its single components over time, frequency
and temperature. Nevertheless this technique has been well used and has
been a key element in the mobile communications infrastructure. (Cripps
1999, p410)
2.3.3
Predistortion (PD)
Predistortion is an input correction technique. The fundamental idea of
predistortion is to introduce a nonlinearity, based on the known amplifier
distortion, to the input signal which after it has been amplified provides a
linear gain. Predistortion can correct for both amplitude and phase
distortion. Both fixed and adaptive predistortion schemes can be applied
where the latter is able to compensate for amplifier characteristics over
time, for example, temperature. Predistortion normally provides good
improvement in linearity near saturation of the PA and is very power
efficient because it does not significantly reduce the efficiency of the
amplifier (Pothecary 1999). Predistortion can be applied both in an analog
or digital environment.
Analog predistortion has a long history but hasn't really reached
mainstream use but it is still in use for high power applications in the
upper GHz frequency bands. Predistortion linearizers has been used in
microwave links and satellite applications because of their relative
simplicity, their wide band capacity and their ability to be added to
existing amplifiers as stand-alone units (Katz 1999).
Analog predistortion though has some negative sides, it will always create
some additional high order distortion to the output signal that was not
there in the beginning but is caused by the process (Cripps 1999, p401).
The latest development of analog predistortion is to apply a second
degree predistortion on baseband level. This has shown good results but
due to the recent rapid development of digital predistortion (DPD) analog
predistortion will probably remain as a limited linearization technique for
some specific purposes but not for the big mainstream applications.
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2.3.4
Digital predistortion (DPD)
The working principle of the DPD technique can be understood when
looking at Figure 3 below. In order to counteract the nonlinearity of the
PA, a DPD preceding the PA is inserted into the signal path. The DPD
function operates on the baseband input signal in such a way that its
output is distorted in an inverse manner to the distortion generated by the
PA. In another word, the DPD response compensates for the nonlinearity
of the PA. Thus, when these two inverse nonlinearities are combined, it
results in distortion cancellation and a desired linear response.
Figure 3. The basic concept of the DPD-technique
Figure 4. The DPD transfer function is the inverse of the PA
transfer function.
Mathematically, this can be described as followed:
xˆ  PA y 
y  DPD x 
If xˆ  x  PADPD x   x
 DPD x   PA 1  x 
where x and y denote the input and output signal of the DPD-block. PA()
and DPD() denote the transfer functions of the PA respectively DPDblock. To get the final result: xˆ  x , DPD() must be the inverse of PA().
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Hence, if the PA transfer function is F(x) then the DPD transfer function
will be F-1(x). The problem here is that F(x) is often unknown and very
difficult to determine. However, by using LMS adaptation technique it is
possible to calculate F-1(x) directly without knowing F(x). More about
this is explained in chapter 3.1.
2.4
Behavioral modeling or Component-based modeling
There are several ways to model the nonlinearity of a system. Behavioral
modeling, also called polynomial modeling, is one of the most common
ways. Given the input and output signal, this method allows regenerated
spectral components to be calculated analytically based on polynomial
coefficients. This is called “black box” simulation because the simulation
method is not depending on how the system actually works, it just finds
the best representation of the output signal as a function of the input
signal. Polynomial modeling is usually easy to implement on nonlinear
memoryless systems but becomes very complex when introducing
memory effects. Further reading about polynomial modelling with
memory effects can be found in Modelling Power Amplifiers using
Memory Polynomials (Kokkeler 2005) and Dynamic deviation reductionbased Volterra behavioural modelling of RF power amplifiers (Zhu,
Pedro and Brazil 2006).
Component-based modeling is a simulation of a complete system on
component level. As contrary to the “black box” behavioral modeling this
means we need to have the exact knowledge of every individual
component and how they are connected in the enclosed system to be able
to get an accurate result. This demands a powerful and complex
simulation engine as well as detailed input of the simulated system. On
the other side the results should give a very detailed picture of the system
characteristics including memory effects. More about component-based
modeling in ADS is described in chapter 3.2.
2.5
Advanced Design System (ADS)
Advanced Design System (ADS) is an Electronic Design Automation
(EDA) tool from Agilent Technologies. It is a software tool that offers a
platform to design and simulate electronic circuits by using predefined
components available in its component libraries. One of the biggest
advantages when working in ADS is the possibility for RF designers to
work with circuits of all levels, from top system level down to transistor
level in the same simulation environment.
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ADS is divided into two separate domains: The Digital domain and the
RF/Analog domain. The RF-domain constitutes the main part of ADS and
offers techniques such as Harmonic Balance and Circuit Envelope and
SPICE-like time-domain simulation. These techniques will be discussed
briefly in chapter 3.6. It is in this domain that most of wireless design
work is carried out.
The Digital domain works with data that is sampled at discrete time
points suitable for digital signal processing. This domain has traditionally
been uninteresting for most RF-designers but with rapidly increasing
advances in today’s digital signal processors (DSP), its role in wireless
design has become more and more important. In the next section, a
description of the different simulation techniques that are available in
ADS is given.
The version ADS 2004A and ADS 2009A was used in conjunction with
Matlab 6.5 and Matlab 7.0 throughout this work. Also see chapter 4.4.
3
Modelling of Power Amplifiers and Digital
Predistortion
In this chapter the system environment as well as some basic theories of
the algorithms used is described. The two power amplifiers are explained
and the integration of ADS and Matlab.
3.1
The Digital Predistortion algorithm
This chapter presents the LMS algorithm on which the DPD technique in
this report is based. The computation of coefficients in a polynomial
expansion of the non-linearity can be done either by iterative adaptation
on sample basis or on matrix inversion based on the whole signal vector.
Both approaches will be tested to find the most efficient way to combine
Matlab algorithms with ADS. A more detailed description of the LMS
algorithm can be found in: ADS and Matlab to optimize predistortion of
amplifiers (Elgeryd 2003)
3.1.1
Iterative solution on sample basis
Adaptation of polynomial coefficients: In the LMS adaptation technique,
a so-called indirect learning scheme is applied. It makes it possible to use
the estimate of the polynomial coefficients α directly in the predistorter.
The incoming data is predistorted according to the polynomial with the
coefficients, which are updated for each sample.
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In order to update the DPD coefficient α, a small fraction of the PA output
is fed back, demodulated to baseband and compared to the original input
signal, see chapter 3.3, sample by sample. It is understood that the
reference signal has to be delayed in order to be time-aligned with the
feedback signal.
Let the input signal to the PA be x and α be the coefficient of the DPD:
 L1 (t1 ) L2 (t1 ) L3 (t1 ) L4 (t1 )
 L (t ) L (t ) L (t ) L (t )
2 2
3 2
4 2
 1 2
 L1 (t 3 ) L2 (t 3 ) L3 (t 3 ) L4 (t 3 )

 L1 (t 4 ) L2 (t 4 ) L3 (t 4 ) L4 (t 4 )
Where
L  [y
y. y
2
y. y
3
  1   x(t1 ) 
    x(t )
 2   2 
  3   x(t 3 ) 

   
  4   x(t 4 )
4
y. y ]
In matrix notation, this can be written as: L    x
Then α can be calculated by multiplying both left hand and right hand
side of the equation by LH, which denotes the conjugate transpose of the
Hermitian matrix L.
LH  L    LH  x
By matrix inversion, the sought coefficient vector can then be solved by:
  ( LH  L) 1  ( LH  x)
H
* T
* T
Note that a matrix L is called Hermitian if L  [ L ] , where [ L ]
denotes the transpose of the complex conjugate of L.
H
1
LH  x  W
Updating : Let ( L  L)  M and
such that   ( M )  W
The final matrix M and W are actually set up by the summations of all
sub-matrices that are built up by each sample. For each new sample, M
and W can therefore be updated by adding the new sub-matrix to the
existing matrix as follows:
M k 1  M k  LH k  Lk
Wk 1  Wk  LH k  x
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1
Finally we have:  k 1  ( M k 1   )  Wk 1 where  is set to a small
number (e.g. 0.00001) just to avoid division by zero. While the matrix α
is continuously built up for each signal sample, we take its instantaneous
value after each sample to use as DPD coefficients. Then by applying
these coefficients after each sample we may actually improve the DPD on
a sample basis. In general, the method converges within 4000 iterations
based on 4000 samples.
3.1.2
Iterative solution on matrix inversion basis
The iterative solution on matrix inversion basis is a more efficient method
based on the same ground as the sample-by-sample method. It compares
the input and output signal to determine the polynomial coefficients using
matrix inversion. Here, alpha is updated for the whole matrix instead of
after each sample. Given the relationship below:
 L1 (t1 ) L2 (t1 ) L3 (t1 ) L4 (t1 )
 L (t ) L (t ) L (t ) L (t )
2 2
3 2
4 2
 1 2
 L1 (t 3 ) L2 (t 3 ) L3 (t 3 ) l 4 (t 3 )

 L1 (t 4 ) L2 (t 4 ) L3 (t 4 ) L4 (t 4 )
  1   x(t1 ) 
    x(t )
 2   2 
  3   x(t 3 ) 

   
  4   x(t 4 )
Then:
L   x
 L\x
Note that the backslash operator is the Matlab notation for solving LMSproblems. Using this operator, the problem of possible singular matrix is
eliminated.
3.1.3
With memory effect
Memory effect can be taken into account both on sample and matrix basis
by expanding the L-polynomial such that it also includes one or several
previous input samples, as earlier described in chapter 2.2.4. For example,
with one previous sample included the L-polynomial becomes:
4
2
3
4
2
3
L   y y. y
y. y
y. y
y n 1 y n 1 . y n 1
y n 1 . y n 1
y n 1 . y n 1 


Here, we have a fourth order polynomial consisting of two tables: one for
the instantaneous input sample and one for the sample right before that.
The previous samples can be delayed by an arbitrary number of samples
compared to the instantaneous one.
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Parameters that can be varied are the polynomial order, the number of
tables (how many previous samples to include) and the sample delay.
3.2
Component-based PA-modeling in ADS
As previously described in chapter 2.4 behavioral modeling are
commonly used in high-level system designs thanks to their ability to
reduce the system simulation time. Nevertheless, one should retain that
this method is used at the expense of the result accuracy. In order to
compute an accurate DPD transfer characteristic, which is actually the
inverse transfer characteristic of the PA, we need to model the PA as
realistically as possible.
In this master’s thesis, we will consider and evaluate the reliability and
robustness of component-based modeling in ADS as an alternative to
polynomial modeling. Two RF PAs are completely modeled in ADS with
input matching network, output matching network and bias network and
tested in this study: a highly linear MRF5S21 PA and a power efficient
Doherty PA. These amplifier models are designed by Freescale and are
described below.
3.2.1
The MRF5S21 PA (PA1)
An MRF5S21 PA that has been designed in ADS using a LDMOS 130W
transistor from Freescale (former Motorola) is biased to 28V. It has a 19
dB gain and 50 dBm saturated power. Figure 5 shows the PA in its
simulation environment.
Figure 5. The MRF5S21 PA top level.
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The PA simulation environment, which is created in the RF-domain of
ADS consists of the PA block, a load of 50 Ohm, several variable
definitions and a Circuit Envelope simulator. The Envelope simulator is
the only simulator in the RF-domain that is suitable for digital modulated
signals as concluded in chapter 3.6. The ports are used to receive and to
output signals. In the simulation results this PA is referred to as PA1.
Pushing into the device under test (DUT) we can see the sublevel that
actually constitutes the PA as it is defined in ADS with input and output
matching networks, see Figure 6. The LDMOS 130W transistor used here
is designed especially for WCDMA base station applications at
frequencies between 2140 and 2170 MHz. Note that the same DUT is also
employed in the Doherty PA.
Figure 6. Schematics of the MRF5S21 PA at transistor level.
Pushing further down into the sublevels, we have the matching networks
consisting of microstrip lines, inductors and capacitors. See Appendix 2.
3.2.2
The Doherty PA (DPA)
The DPA tested here consists of a main amplifier, an auxiliary amplifier
with the same LDMOS 130W transistor as for the single PA design. It
also consists of a quarter-wave transmission line that combines the
outputs of the two amplifiers, see Figure 7 below. Both the main amplifier
and the auxiliary amplifier use the same DUT with the schematics already
shown in Figure 6. Yet, they are biased differently so that the auxiliary
amplifier turns on only when the main amplifier saturates. The auxiliary
PA are sometimes called peak PA. The system benefits then from a loadpulling effect and can achieve a maximum power efficiency of 78 %.
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The Doherty PA offers a higher efficiency than traditional power
amplifiers but it also suffers from reduced linearity. Thus, combining DPA
with DPD technique can result in both high power efficiency and
linearity. In the simulation results the Doherty PA is referred to as DPA.
Figure 7. Block diagram of a DPA.
Figure 8. Output power of the two PAs.
This DPA has a 15 dB gain and 51 dBm saturated output power, its
simulation environment is shown in Figure 9 and Figure 10 below:
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Figure 9. The DPA top level.
Figure 10. A Doherty structure with main PA, peak PA and /4transmission line.
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3.3
System overview, Matlab-ADS integration
With the understanding of how the PA and the DPD work independently
as systems, a simulation environment which combines these two
subsystems can be created. The goal is to linearize RF-PAs modelled in
ADS by using DPD-algorithms developed in Matlab.
In the following chapters the integration and the interface between the
digital domain that is simulated in Matlab and the RF/analog domain that
is simulated in ADS are explained. The main structure of the simulation
system is shown in Figure 11. Note that the DPD block and the DPDalgorithm blocks are implemented in Matlab while the rest is modeled in
ADS.
Figure 11. The flow-chart of the linearizer-PA system
The WCDMA signal enters the digital predistorter (DPD) in the form of
complex base band and is represented by the two real valued signals I and
Q. The DPD predistorts the input signal by multiplying it with the values
of alpha, attained from the DPD-algorithm. In this particular case,
polynomial DPD functions are used, as described in chapter 3.1. A further
explanation of the complex baseband representation is given in detail in
chapter 2.1.3.
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Having passed the DPD, the predistorted signal is then applied to an RF
carrier (2.14 GHz) through a QAM-modulator incorporating a Local
Oscillator (LO). Thereafter, the signal is passed to the PA where it is
amplified and distorted by the nonlinearities of the PA. In the feedback
path, a small fraction of the PA output is down-converted back to base
band by a demodulator before entering the DPD-algorithm where it is
compared to the reference signal. By using the LMS algorithm, the
inverse characteristic of the PA is then calculated and the polynomial
coefficients can be updated and passed to the DPD. These coefficients,
which are used to predistort the baseband input signal in the DPD as
described above, are updated by the LMS algorithm for each firing as the
iteration continues. The final result is an output signal with less distortion.
3.4
Matlab-ADS integration methods
An interface between Matlab and ADS must be created so that signals and
variables can be passed between the two software tools. The two possible
solutions are presented below.
3.4.1
Approach 1: Iterative solution on sample basis
In this method, polynomial coefficients are calculated and updated for
each data point using the LMS-algorithm described in chapter 3.1. Two
Matlab-components are inserted directly into the ADS environment.
During the simulation ADS calls on Matlab each time a Matlabcomponent is evoked. Produced data is saved in a special catalog in ADS
called “Data”, see Figure 13, which is accessible even by Matlab. The
DPD-algorithm couples the input signal and the output signal from the
feedback path to determine alpha as described previously. Alpha is saved
in the “Data” catalog and then fetched in the next firing by the adaptation
block called DPD, which is placed before the PA. Figure 12 illustrates the
idea.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 12. Block diagram: sample-by-sample iteration. The DPD
and DPD-algorithm blocks can be incorporated in an ADS
schematic by special Matlab-components which are available in the
component library of ADS. These are called on by ADS in each
firing.
Figure 13. Alpha is saved in the “Data” catalog in ADS, accessible
by both softwares.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Implementation:
In this approach, Matlab is directly integrated in the ADS simulation,
which eliminates the trouble of shifting between Matlab and ADS. Here,
simulation for the whole combined system can be carried out in one
single step. Though, this is a time-consuming method due to the process
of ADS calling on Matlab in each firing. To get a better speed, the faster
Matlab component MatlabliblinkCx can be used on one condition: the
Matlab scripts in use have to be pre-compiled and placed in a special
library. Pre-compiling must be redone as soon as there is any change in
the Matlab code. For this purpose, a Matlab script which takes care of the
pre-compiling task was developed. In fact, this script is one essential part
in the integration of Matlab and ADS, since it functions like a bridge
between these two software tools.
Figure 14. Top level in Approach 1. See Appendix 3 for detailed
charts of the different set ups.
Picture note: With two Matlab components, “MatlabLibLinkCx”,
integrated in the ADS test bed, the whole simulation takes place in ADS.
When the whole signal of 16000 samples has passed, the final output
signal is then read into Matlab for further analyse.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Working principle:
1)
2)
3)
4)
Place the two Matlab files (DPD and DPD-alg.) in the “Data”
library in ADS. Pre-compile them by running the script mcc.
Simulate in ADS.
Signal processing in Matlab for plotting and ACRL
calculation.
If changes are needed in the Matlab-files: click ”Stop and
release simulation”, recompile the files and simulate again.
Produced data such as simulations outputs are saved in the ADS-format
“.tim”, which is not compatible with Matlab. Hence, before the signal can
be read back into Matlab for further processing, the signal format has to
be converted. Even for this purpose, Matlab scripts were developed.
3.4.2
Approach 2: Matrix inversion basis with post-distortion
The vector processing technique handles data in large matrices instead of
processing single data points and is therefore an efficient method for
numerical calculations. By using this iterative solution on matrix
inversion basis, we can take full advantage of the capabilities possessed
by the signal processor.
A drawback is that this method only works under the condition that the
circuit does not contain any feedback path, since the result computation
does not take place until the whole matrix has passed through the circuit.
In our case, since the DPD-algorithm must adapt to the PA characteristic,
which varies due to changes in temperature, voltage and time etc, a
feedback path to make the algorithm adaptive is necessary.
However, one solution that allows both adaptation and matrix processing
is to apply post-distortion and to execute the amplification part and the
DSP part separately. The whole signal is first passed through the PA
which is modeled in ADS, and then the signal is processed in Matlab for
linearization using the matrix inversion technique. To get a good result, at
least two iterations are required.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Implementation:
The simulation consists of three steps as described below:
Step 1 (ADS): Let the input signal (x) pass through the PA to get the
amplified but distorted output (y). Save then y in a large matrix where it is
accessible to Matlab. This is done totally in the RF-domain of ADS.
Figure 15. Step 1: amplification in ADS.
Step 2 (Matlab): Both the input and output signals are read into Matlab as
two vectors. Now, efficient computations can be applied to calculate the
polynomial coefficients using the matrix inversion LMS-algorithm. The
input signal is then multiplied by these coefficients to make a new,
distorted input signal (New-x), which will be fed to the PA.
Figure 16. Step 2 and 3: signal processing in Matlab followed by
amplification in ADS.
Step 3 (ADS): The new, distorted signal passes through the PA for a linear
amplification. The output should now be linearized but if not, more
iteration can be carried on by repeating Step 2 and Step 3. Finally, the
output can be read into Matlab again for further signal processing, for
example computing the ACLR and plotting the DSP.
In practice, these steps are followed:
1)
2)
3)
4)
5)
First ADS simulation with x-org as input signal.
Signal processing in Matlab. Run read(1).
Second ADS simulation with newIQ as input signal.
Matlab: Run read(2).
Repeat step 3 and 4 for additional iterations.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Here, x-org is the original input signal to the PA, while newIQ is the
predistorted input signal that we get after linearization in Matlab. The
commands read(1 ) and read(2) starts the signal processing with x-org
and newIQ respectively as input signal in the DPD-algorithms.
ADS-implementation:
The solution in ADS consists of several levels. In the top level, a design
kit with parameters for the modelled PA, some variables and the
DataFlow controller are defined as showed in the picture below. The
modelled PA is included in the schematics as a sublevel which in turn has
sublevels for Input matching networks etc. In the PA top level, the
controller is used.
Figure 17. Top level in Approach 2, using DataFlow as simulation
controller. The chart shows ADS-simulation without Matlab. See
also Appendix 3.
The I and Q parts of a WCDMA signal are stored as .txt files which are
compatible with Matlab. These are read by the ReadFile components, and
then converted to a complex signal, amplified digitally, converted back to
timed signals, passed through a QAM-modulator before passing through
the PA. The amplified and distorted signal is then passed through a QAMdemodulator, several signal conversions and finally put out as .txt files by
the Printer components to be used in Matlab. The output from the
NumericSink component is useful for analyzing directly in ADS.
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ADS and Matlab to Optimize Predistortion of Amplifiers
The advantages with this simulation setup are the faster simulation speed
since ADS does not have to call on Matlab while executing and the
possibility to easily switch among different DPD-algorithms without
interfering with the simulation in ADS. Two iterations are enough to get a
good result.
Scheduled iteration
The many steps in Approach 2 can be avoided by using a feature called
“simulation sequencer” that is available in ADS. This feature allows users
to schedule the simulation of different blocks. In fact, it simulates several
blocks automatically one after the other in the order specified by the user,
using data produced by the previous block. By inserting Matlabcomponents in ADS, we can make a block that takes care of Step 2 above.
Placing these three steps as three blocks in a top level schematic using the
“sequencer controller”, the whole simulation can be started by just one
click.
Figure 18. Block diagram of scheduled simulation.
This could be a flexible method but unfortunately it cannot be done in
ADS today. The “sequencer” feature works well but it does not support
co-simulation of RF and DSP blocks. Since Step 2 is done in the DSPdomain and the rest is in RF, we will have to wait until Agilent
Technology has found a way to support co-simulation with this feature.
3.5
Intermodulation distortion and the ACLR
Intermodulation distortion (IMD) is unwanted frequency components
introduced at the output of the PA that does not belong to the actual
signal. These cause spectral regrowth and interfere with adjacent channels
making the information detection task in these channels difficult, see
chapter 2.2.1. Further reading about intermodulation distortion can be
found in Digital Pre-Distortion of Power Amplifiers (Spångberg 2002).
IMD is normally measured by using the ACLR requirements.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Adjacent Channel Power Leakage Ratio (ACLR) is one of the most
important linearity requirements in today’s communication systems. In
the past, it was called ACPR (Adjacent Channel Power Ratio) and was
defined as the power in an adjacent channel relative to the power in the
main channel. However, this definition was considered insufficient and
has been modified to also take into account the sensitivity for power
leakage of the receiving filter in a neighboring receiver. This sensitivity is
defined by the roll-off factor in the root raised-cosine filter (RRC) used in
receivers (Pothecary 1999, p 71ff).
According to the 3GPP specifications, the ACLR value of 3G base
stations must be higher than 45 dBc at 5 MHz frequency offset and 50
dBc at 10 MHz offset (3GPP TS 25.104, p 6.6.2.2.1). Considering the
contribution of other components in the TX-chain to the distortion (for
example the demodulator), the PA itself must be designed to meet even
higher requirements.
To evaluate the level of nonlinearity, ACLR calculations are made using a
RRC filter with a roll-off factor of 0.22 throughout this thesis. To simplify
the results a mean value for ACLR1 up (+5 MHz) and ACLR1 low
(-5 MHz) has been used in the charts to represent the ACLR1 value, the
same has been done for ACLR2.
Figure 19. The ACLR1 and ACLR2
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ADS and Matlab to Optimize Predistortion of Amplifiers
3.6
ADS-simulators
In the RF/analog domain, three different simulators are available in ADS:
SPICE, Harmonic Balance and Circuit Envelope. The working principles
of these simulators are presented below. The Ptolemy Data Flow
controller is used as a bridge between the digital and RF domain and
enables simulations of the whole system.
SPICE-like time domain simulation
Working in time-domain, this simulator solves nonlinear differential
equations by integration. It can simulate systems that contain both
baseband and RF-circuits. Nevertheless, to avoid the effect of aliasing, the
chosen time step has to be small enough to maintain the signal waveform.
This imposes a big problem for wireless applications since the difference
between the frequency of the RF-carrier and the BB-signal is very large.
Therefor the simulated time steps has to be very vast to get an accurate
and result the SPICE simulation will be very time consuming (Yap 1997).
Harmonic Balance (HB)
Harmonic Balance (HB) is on the other hand a nonlinear frequencydomain simulator which does not suffer from a large difference in
frequency like the SPICE-simulator. It computes the steady-state response
of a circuit by calculating the Fourier coefficients of the output solution.
HB is considered an efficient and accurate method except for one
drawback: it works only when the signal can be represented by a small
number of sinusoidal components (Kundert 1997). Thus, it is not
adequate to represent the continuous spectrum of non-periodic signals, as
the WCDMA signal, and can therefore not be represented accurately by
HB.
Circuit Envelope (CE)
Circuit Envelope simulation does not suffer from a large frequency
difference like SPICE and it can also deal with non-sinusoidal signals.
Working in both time and frequency domain, it combines SPICE and HB
by performing a HB simulation at each time step. In Circuit Envelope, the
RF-carriers are separated from the signal and only the modulation
envelope is sampled. The sampling requirement is thus reduced to
represent only the low-frequency baseband-signal instead of the highfrequency RF carrier. The modulation information is represented as a
baseband time-varying complex envelope riding on the RF carriers (Yap
1997). The result is a time-varying HB analysis that can be applied to
circuits with time-varying complex modulated signal, and even though
Circuit Envelope employs HB as part of the solution process, the matrix
size remain reasonable for simulation on even personal computers.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Ptolemy Data Flow in ADS
In the baseband processing models, the Ptolemy Data Flow controller is
used. The Ptolemy engine in ADS is mainly a framework for
synchronizing simulations with each other. The Ptolemy Data Flow
controller consists of two domains; the Synchronous Data Flow domain
(SDF) used for purely numeric simulations and the Timed Synchronous
Data Flow domain (TSDF) used for RF/analog simulations. ADS Ptolemy
thus acts like a bridge between the digital design or signal processing
simulation environment (SDF) and the RF/analog simulation domain
(TSDF) and is able to simulate both environments in an enclosed system.
The Ptolemy controller also allows other external simulation technologies
to run concurrently with native simulation domains like for example
Matlab, which will also be used in this thesis.
Simulation model chosen
Having studied the different simulators, it is concluded that the only
simulator that is suitable for simulation of circuits with time-varying
complex modulation in the RF domain is Circuit Envelope. This simulator
is chosen to enable the co-simulation with the digital domain where
Ptolemy Data Flow is used.
4
Simulation and evaluation
This chapter focuses on the simulation environment and the schematics in
practice. The used simulation variables are described as well as the
simulation results.
4.1
ADS-Matlab integration in practice
Matlab blocks are imported in the ADS simulation environment through
the ADS Ptolemy engine. In the latest version of ADS (2004A), a new
feature named ‘MatlabLiblink’ was introduced to shorten the simulation
time of circuits with inclusion of Matlab components. This feature can
operate in three different modes: Script Mode, Compile and Auto.
Script mode
The Script mode is very slow and time-consuming. It works in the same
way as the traditional Matlab-component, and interprets the Matlab script
step-by-step.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Auto mode
The Auto mode works with already compiled Matlab files, which are
placed in a special library. Organizing the Matlab-files in this way makes
it significantly easier for Ptolemy to parse them. Hence, the simulation
speed is increased to be 20 times faster compared to the Script mode. One
inconvenience is the requirement of recompiling the Matlab-files
whenever a change is made to the code.
Pre-compiling is also required when using the faster component
MatlabLiblinkCx. For pre-compiling, ADS (version 2004A) only works
with Compiler 3.0 provided in Matlab 6.5 Release 13. The latest version
of Compiler in Release 14 cannot be used since there are some changes in
Matlab that are not updated in the software of ADS.
Compile mode
In the Compile mode, there is no need to pre-compile the scripts since
ADS would call on the Matlab compiler itself and therefore simulations
with Matlab files would be greatly simplified. However, this last feature
does not yet work in ADS 2004A. Due to different reasons, the
communication between ADS and the Matlab compiler somehow cannot
be established. Thus, the Auto mode is a natural choice.
4.2
How the simulations were executed
Regardless simulation approach, these first steps are required to create a
test bed in ADS:
Step 1:
Choose ADS-mode: RF/analog or DSP, here both.
Step 2:
Create the top level schematic using DF-simulator
(DataFlow). See Figure 20.
Step 3:
Add Design Kit on the top level. Note that it should
only be placed here. (Here, FSL_TECH_INCLUDE is
used).
Step 4:
Include PA-schematics in sublevels, using Circuit
Envelope on the PA top level. See Figure 21.
Step 5:
Specify the simulation time and other variables, for
example sampling frequency etc. The simulation time
should be long enough to give an accurate spectrum.
The DefaultNumericStop specifies the number of values
of a certain variable to be saved. The sampling
frequency is set to 61.44 MHz.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 20. Test bed in ADS with top level DF-simulator
Figure 21. ADS schematics, Approach 1: Iterative solution on
sample basis.
Figure 22 and Figure 23 shows enlargements of the digital respectively
the analog domain. In digital domain MatlabLibLink is used to call on
pre-compiled Matlab scripts placed in a special library which contain the
DPD-algorithm. At the end of the chain the new alpha-value is extracted.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 22. Enlargement of the digital domain with DPD and
extraction of alpha-value. The two MatlabLiblinkCx components
runs the files “DPD” respectively “DPD-alg”
From the digital domain the signal is transferred to the analogue domain
in ADS through the Ptolemy engine. The simulation is synchronized by
time-steps. One part of the amplified output signal is redirected to a
demodulator and feed back to the digital domain in Figure 22.
Figure 23. Enlargement of the analog domain with PA and
modulators and demodulators
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ADS and Matlab to Optimize Predistortion of Amplifiers
4.3
Simulation variables
As described in the scope of this thesis each PA is simulated on both
sample and matrix inversion basis for comparison between the different
methods. In addition to those four main cases several other variables have
been tested in each case throughout the simulations to get an authentic
result. These variables are the gain, the polynomial degree of the signal
representation and the memory-depth. These factors are explained below.
4.3.1
PA gain
The linearity of the power amplifier is dependent of the gain as the
nonlinearity of the PA increases near saturation. To test the DPDalgorithms ability to linearize the output signal the PA must be driven
close to and above saturation. Different gains are therefore fed into the PA
in the simulations to analyze its behavior. For PA1 the following gainlevels has been simulated; 20, 24, 26 and 28. For DPA the following gainlevels have been simulated; 20, 25, 30, 34. The relation between gainlevels and output effects are shown in Table 2.
PA
20
Mean
power
22,8 W
Maximum
output power
123 W
24
33,5 W
182 W
26
39,1 W
215 W
28
43 W
223 W
20
14,6 W
80 W
25
22,9 W
125 W
30
32,2 W
170 W
34
40,1 W
215 W
Gain-level
PA1 (sample)
DPA (sample)
Table 2, Relation between gain-level and output effect
4.3.2
Polynomial degree
The polynomial degree is important to get a correct representation of the
baseband signal in the digital domain. With higher degree a better
representation of the signal was performed. But with higher degree
polynomials the amount of data to be calculated also increases. Therefore
it is of interest to analyze if there is an optimal polynomial degree for
simulation to which further increasing of the polynomial degree shows
little improvement to the resolution of the signal. In the simulations
performed, the polynomial degree has been varied between from 4 to
about 12-15.
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ADS and Matlab to Optimize Predistortion of Amplifiers
4.3.3
Memory-depth
One of the purposes of this thesis is to analyze if ADS can simulate
memory effects. As described in chapter 2.2.4, a formula to compensate
for memory effects has been implemented in the Matlab scripts. In
addition to calculation of the current signal the formula also takes into
account the last one or two signals passing the DPD-loop. If the output
signal becomes more linear after compensating for the possible memory
effects, it will be taken as proof that memory effects exists in the
simulation. If the output signal show no visible difference, with or
without compensation for memory effects or gets even more distorted,
memory effects does probably not exists in the simulations. Memorydepths used in the simulations are: M1, M2 and M3, where M1 is without
any compensation= no memory, M2 compensates for the last signal and
M3 compensates for the last two signals.
4.4
Simulation results
In the following chapters the simulation results will be displayed and
analyzed. We will focus on how the results differ in linearization effect
depending on PA output effect, the polynomial degree, the matrix or
sample method and of memory-depth. In chapter 5 the results will be
summarized and conclusions will be drawn.
In year 2005 the main simulations were made in ADS2004A for the
sample and matrix method. But the simulations with the matrix method
were not convincing and did not show the expected results. For example
the PAs did not seem to saturate at any gain-level, as must be the case. In
spite of much troubleshooting nothing wrong with the simulations could
be determined. In the year 2010 the matrix method was again simulated
with the newest version of ADS at the time, ADS 2009A. This time the
results were more plausible and matched the results from the sample
method. The following simulation results are therefor from 2005 for the
sample method and from 2010 for the matrix method.
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Non-linear and linearized signal
As the PA gain increases the non-linear behavior is augmented and
linearization of the input signal becomes necessary. Figure 24 shows the
concept of linearization, the non-linearized signal suffers from substantial
inter modulation distortion (IMD) that may distort the adjacent channels.
After linearization the IMD in the example has been suppressed about -10
to -15 dB and with compensation for memory effects some -10 dB further.
dB
4.4.1
Figure 24. An example of the concept of linearization.
Figure 25 shows the difference between a non-linearized and a linearized
signal for amplifier PA1 and DPA. In both cases the IM-level is
suppressed about -10 to -20 dB compared to the non-linear signal. Both
examples also show that the effect of linearization decreases as the gain
increases, this will be discussed further in chapter 4.4.3.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Nonlinearized signal compared to linearized signal
(ACLR1, PA1 and DPA without memory effect)
70
65
60
dBc
-dB
55
Sample PA1 Non-linear
50
Sample DPA Non-linear
45
Sample PA1 M1
Sample DPA M1
40
35
30
25
DPA20/PA1 20
DPA25/PA1 24
DPA30/PA1 26
DPA34/PA1 28
Figure 25. Non-linearized compared to linearized signal for PA1
and DPA sample without memory effect.
4.4.2
ACLR1 and ACLR2
The simulations show that the ACLR2 level very much follows the
ACLR1 level. In Figure 26 the ACLR2 noise levels are about 5 dB lower
than the ACLR1 for all gain levels. This meets the specification for the
3GPP standard very well because the minimum suppression of noise level
for ACLR1 is 45 dBc and 50 dBc for ACLR2, which also means a 5 dB
difference between the levels.
The simulations also show that the PA1 exceeds the 3GPP specifications
for gain levels 20, 24 and 26 but not for 28 which becomes too distorted
and thus non-linear.
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dBc
ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 26. ACLR1 compared to ACLR2, PA1 sample.
Linearization relative to gain-levels
Does the linearization effect drop when gain-levels rise? This is the
expected behavior because a more non-linear signal from the PA is more
difficult for the predistorter to linearize. In the following charts this
behavior is analyzed.
Linearization relative to effect
(PA1 sample without memory effect)
250
70
60
200
50
150
40
30
100
-dB
dBc
(W)
effect
output
PAPA
effect
output
4.4.3
PA1 Effects
ACLR1
20
50
10
0
0
PA1 20
PA1 24
PA1 26
PA1 28
Gain
Figure 27. ACLR-value relative to output effect, PA1 sample.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 27 shows an increasing non-linear behavior of the signal as the
output effect of the PA increases. This is a likely result because a higher
gain brings the PA closer to saturation where the non-linearities of the PA
become too significant for the predistorter to handle.
Linearization relative to effect (DPA sample with memory
effect)
250
80
70
200
50
150
40
100
30
DPA Effects
-dB
dBc
(W)
effect
output
PAPA
effect
output
60
M1
M2
M3
20
50
10
0
0
DPA 20
DPA25
DPA30
DPA34
Gain
Figure 28. ACLR-value relative to output effect with memory effect,
DPA sample.
The DPA show a similar result as the PA1. In Figure 28 the memory
effects are included and they follow the same dropping trend when the
gain increases. The linearity of the DPA does not drop as fast the PA1 at
high gains.
The matrix solutions show almost the same result, see Figure 29 and
Figure 30. The linear behavior is dropping with higher gain-levels. The
PA1 seems to drop more rapidly than the DPA at higher gain-levels, as
was the result with the sample method. An explanation is that the
auxiliary PA increases the linearity of the DPA near saturation.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Linearization relative to effect
(PA1 matrix with memory effect), sim 2010
200
70
180
65
160
60
55
120
50
100
Effekter
-dB
dBc
effect
output
(W)
effect
output
PA PA
140
M1
45
M2
80
40
60
35
40
30
20
0
25
PA1 20
PA1 24
PA1 28
Gain
Figure 29. ACLR-value relative to output effect with memory effect,
PA1 matrix.
140
75
120
70
65
100
60
80
55
60
DPD Effects
-dB
dBc
effect(W)
output
PAoutput
effect
PA
Linearization relative to effect
(DPA matrix with memory effect), sim 2010
M1
M2
50
40
45
20
40
0
35
DPA20
DPA25
DPA30
Gain
Figure 30. ACLR-value relative to output effect with memory effect,
DPA matrix.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Polynomial degree (N-value)
It is of interest to study how the polynomial degree of the DPD-algorithm
affects the linearization of the output signal. A higher N-value should give
a more linear result because of better resolution of the signal frequency
spectrum. The drawback is that a high N-value will need a higher
processing capacity of the DPD to calculate the compensated signal. To
optimize linearization compared to processing capacity we would like to
find the ideal polynomial degree and to see if the results settle at any
point.
Linearization effect PA1 sample (ACLR1 without memory)
65
60
55
PA1 20
dBc
-dB
4.4.4
50
PA1 24
PA1 26
45
40
35
4
5
6
7
8
9
10
11
12
N
Figure 31. ACLR-value as function of polynomial degree, PA1
sample.
The highly linear amplifier PA1 shows a typical and expected response to
the polynomial degree. A clear improvement in linearization from low Nvalues until the effect settles after a certain point of about N=7-8. The
effect levels out at higher polynomial degree. The different gain-levels
also shows an expected result with a more non-linear behavior at higher
output effects that to a certain level can be compensated with a higher
polynomial degree. This result indicates that a more non-linear signal can
be compensated for with a powerful DPD.
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Linearization effect DPA sample (ACLR1 without memory)
70
65
60
DPA 20
dBc
-dB
55
DPA25
DPA30
50
DPA34
45
40
35
44
55
66
77
88
99
10
1
11
1
12
1
13
1
14
1
15
1
N
Figure 32. ACLR-value as function of polynomial degree, DPA
sample.
The power efficient DPA does not show the same characteristics as the
PA1. At the gain-level 20 the signal peaks and thereafter declines but with
higher gain the linearization effect never really settles and levels out. The
Doherty PA uses the feedforward technique which in itself compensates
for non-linear behavior with its auxiliary PA. The first simulated gainlevel of 20 does probably not activate the auxiliary PA, as the other levels
must do, and therefore have the characteristics of a normal PA. Except for
gain 20, the DPA is not as linear as the PA1 and does not reach over 60
dBc for ACLR1.
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ADS and Matlab to Optimize Predistortion of Amplifiers
Linearization effect PA1 matrix (without memory), sim 2010
65
60
55
PA1 20
dBc
-dB
50
PA1 24
45
PA1 28
40
35
30
3
4
5
6
7
8
9
10
11
12
N
Figure 33. ACLR-value as function of polynomial degree, PA1
matrix.
The matrix method for PA1 shows a graph with more deviation but with a
similar trend line as the sample method. After about N=6 the polynomial
degree does not seem to improve the linearity of the signal substantially,
at least not for gain 20.
Linearization effect DPA matrix (without memory), sim 2010
70
65
60
dBc
-dB
55
DPA20
DPA25
DPA30
50
45
40
35
4
5
6
7
8
9
N
Figure 34. ACLR-value as function of polynomial degree, DPA
matrix.
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The DPA matrix simulations show a similar outcome as the sample
method. Gain 20 has a decreasing behavior after N=5 and with higher
gain the trend is increasing over the chart but from a lower starting point.
As for the sample method the IM-level does not reach over 60 dBc for
ACLR1.
Memory effects
In the following results the effect of the memory algorithm described in
chapter 2.2.4 is analyzed. The memory algorithm is applied in the Matlab
script to simulate the DPD in the digital domain.
The M1 results are the predistorted signal without compensation for
memory effects. The M2 signal includes compensation for the last
processed signal and the M3 signal includes compensation for the last two
signals.
If ADS includes memory effects in the simulations the compensated
signals should show a more linear result than the non-compensated signal.
Memory effect PA1 20 sample (ACLR1)
67
65
63
M1
dBc
-dB
4.4.5
61
M2
M3
59
57
55
4
5
6
7
8
9
10
11
12
N
Figure 35. PA1 sample, gain 20 with memory effect
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From Figure 35 we can see that applying the memory algorithm to the
signal results in a more linear output. The non-compensated signal (M1)
has an ACLR1-value of about 62 dBc while the M2 signal has an average
of about 63 dBc. The M3 signal is even better for some N-values.
From this result we can conclude that ADS actually simulates memory
effects. If ADS did not simulate memory effects, the M2 and M3 signal
would almost certainly not have shown any improvements or the results
would have been more distorted than the M1 signal.
Memory effect PA1 24 sample (ACLR1)
64
62
dBc
-dB
60
M1
58
M2
M3
56
54
52
50
4
5
6
7
8
9
10
11
12
N
Figure 36. PA1 sample, gain 24 with memory effect
With gain-level 24 the compensation for memory effects has less effect
than gain 20. At higher gain-levels the signal get more distorted and
harder to linearize, thus the memory algorithm also gets less effective.
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Memory effect PA1 26 sample (ACLR1)
60
58
56
54
dBc
-dB
52
M1
50
M2
M3
48
46
44
42
40
4
5
6
7
8
9
10
11
12
N
Figure 37. PA1 sample, gain 26 with memory effect
At gain 26 the compensation for memory effects shows no improvements,
instead we get the opposite result. The signal is too distorted and the
memory algorithm can't tribute to the result. In this case the output signal
for M2 and M3 is actually worse than the non-compensated M1-signal.
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Memory effect DPA 20 sample (ACLR1)
75
73
71
69
dBc
-dB
67
M1
65
M2
M3
63
61
59
57
55
4
5
6
7
8
9
101
N
Figure 38. DPA sample, gain 20 with memory effect
For the DPA amplifier at gain-level 20 the compensation for memory
effect shows a huge improvement in linearization. Figure 38 shows that
the M2 signal has about 4 dBc less distortion than M1 and the M3 signal
has up to 8 dBc less distortion than the non-compensated signal.
According to the results the DPA amplifier suffers from far more memory
effects than the PA1 amplifier. On the other hand the DPA amplifier
reaches a 65 dBc IM-level before compensation for memory effects while
the PA1 amplifier only reaches about 62 dBc IM-level at the M1 signal.
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Memory effect DPA 25 sample (ACLR1)
65
60
55
dBc
-dB
M1
M2
M3
50
45
40
4
5
6
7
8
9
10
11
12
13
14
15
N
Figure 39. DPA sample, gain 25 with memory effect
Memory effect DPA 30 sample (ACLR1)
54
52
dBc
-dB
50
M1
48
M2
M3
46
44
42
40
4
5
6
7
8
9
10
11
12
13
14
15
16
N
Figure 40. DPA sample, gain 30 with memory effect
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Figure 39 and Figure 40 show a similar result for the DPA amplifier as for
the PA1 on higher gain-levels. When distortion increases and the PA
saturates the linearization algorithm loses its effect and cannot
compensate for memory effects. At gain-level 25 the compensation for
memory effect shows no improvement and at level 30 the result is slightly
worse than the non-compensated signal.
Memory effects in matrix method
The compensation for memory effects in the matrix method does not
show the same clear improvement as in the sample method. For PA1, as
shown in Figure 41 and Figure 42 below, a slight improvement for gain
20 can possibly be observed with memory effects which correlate with the
result of the sample method. For gain 24 a slight improvement can maybe
also be seen but due to the big deviations of the memory-less signal it is
hard to say if that really is the case.
Memory effect PA1 20 matrix (ACLR1), sim 2010
70
65
60
dBc
-dB
M1
M2
55
50
45
3
4
5
6
7
8
9
10
11
12
13
14
N
Figure 41. PA1 matrix, gain 20 with memory effect
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Memory effect PA1 24 matrix (ACLR1), sim 2010
70
65
-dB
dBc
60
M1
M2
55
50
45
3
4
5
6
7
8
9
10
11
12
13
14
N
Figure 42. PA1 matrix, gain 24 with memory effect
The memory-algorithm applied to the DPA at gain 20 shows the same big
improvement as for the sample method, see Figure 43. While the M1
curve is dropping with higher N-values the M2 curve levels out on about
74 dBc. This behavior is further analyzed in chapter 4.4.4.
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Memory effect DPA 20 matrix (ACLR1), sim 2010
75
70
dBc
-dB
65
M1
M2
60
55
50
44
5
5
66
77
88
99
10
1
11
1
12
1
13
1
N
Figure 43. DPA matrix, gain 20 with memory effect
With higher gain-levels the compensation for memory effect loses its
effect and does not contribute to the linearization. The same results were
observed in the DPA sample simulations. Figure 44 and Figure 45 show
no improvement compared to the memory-less signal. The output signal
of the PA is significantly more non-linear at higher gains, as can be seen
in the charts, thus the memory-algorithm is not effective.
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Memory effect DPA 25 matrix (ACLR1), sim 2010
65
60
dBc
-dB
55
M1
50
M2
45
40
35
4
4
55
66
77
88
9
9
10
1
11
1
121
N
Figure 44. DPA matrix, gain 25 with memory effect
Memory effect DPA 30 matrix (ACLR1), sim 2010
65
60
dBc
-dB
55
M1
50
M2
45
40
35
4
5
6
N
Figure 45. DPA matrix, gain 30 with memory effect
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Sample and Matrix simulation
From the results we can conclude that there are no big differences
between the sample and matrix method in linearizing a signal. In Figure
46 both the non-linear and the linearized appearance for PA1 is almost
identical between the sample and matrix result.
From the charts in chapter 4.4.4 and 4.4.5 we can see that the sample
results are generally smoother than the matrix diagram plots. This is a
plausible result because the sample method builds up the matrix sampleby-sample thus constantly tuning the linearization algorithm while the
matrix method estimates a convenient average alpha-value to update the
whole matrix using the LMS-algorithm. The sample method therefore
provides a more accurate result than the matrix method but to the cost of
more comprehensive calculations.
The average simulation time in ADS for the sample method was
approximately 20 minutes/simulation. For the matrix method it was about
10 minutes/iteration, with three iterations the overall simulation time was
about 30 minutes.
dBc
4.4.6
Figure 46. Comparison between non-linear and linearized signal
PA1 for different gain-levels, without memory
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ADS and Matlab to Optimize Predistortion of Amplifiers
Figure 47. Comparison between non-linear and linearized signal
DPA for different gain-levels, without memory
As for the PA1, the result for DPA shows the same characteristics
regardless of if the sample or matrix method was used.
The overall efficiency of the linearization technique is obvious when
looking at Figure 46 and Figure 47 above. For gain-levels 20-24, for PA1,
respectively 20-25, for DPA, the linearized signal shows a significant
suppression of the IM-level by -20 to -25 dB for ACLR1, which very well
exceeds the 3GPP standards. And as shown in chapter 4.4.5 that reduction
can be further enhanced by compensation for memory effects.
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5
Summary and conclusions
The simulation results show that digital predistortion is a very powerful
and efficient way of linearizing the output signal and suppress IMD of a
power amplifier. At the best, IMD was suppressed up to -24 dB for PA1 at
gain 24 and -24 dB for DPA at gain 20. With compensation for memory
effect IMD was suppressed up to -26 dB for PA1 and -33 dB for DPA.
An integrated simulation environment for ADS and Matlab was
successfully created within the work of this thesis. Matlab scripts could
easily be used for predistortion algorithms in the digital domain together
with analog simulations of component-based PA models by using the
ADS Ptolemy engine with MatlabLiblink. The total simulation time was
approximately 20 minutes for the sample method and 30 minutes for the
matrix inversion method.
The sample method proved to be the most accurate linearization
algorithm. This method provided the expected results without much
deviation. The matrix method did not show the same good results as the
sample method as it suffered from substantial deviation in the results. The
lack of a feedback path caused longer overall simulation time than the
sample method because at least three iterations hade to be executed.
In most cases it was also possible to find an optimal polynomial degree of
the linearization-algorithm. As expected, the linearization effect did level
out at a certain polynomial degree, making further polynomial modeling
of the signal irrelevant and time-consuming.
At low gain-levels it was apparent that ADS was able to simulate memory
effects in the analog domain. The applied memory-algorithms to the
linearization-algorithm showed a great improvement to the linearization
of the output signal of the PA. These results would have been unlikely if
memory effects did not exist in the simulations. At higher gain-levels
though, the compensation for memory effects lost their efficiency which
also was expected because the big non-linearitys of a saturated PA makes
the memory effects a small part of the linearization problem.
The PA1 proved to be the easiest power amplifier to linearize but
saturated very sharply when exposed to high gain-levels. The Doherty PA
could hang on a little longer at high gain-levels due to its auxiliary PA.
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References
Literature
Anderson Harry, Fixed broadband wireless system design, Wiley,
Chichester, U.K, 2003
Carne Bryan E, Telecommunications Primer: Signals, building blocks
and networks, IEEE press, New York, U.S.A, 1995
Cripps Steve C, RF Power Amplifiers for Wireless Communications,
Artech House, Boston, Massachusetts, U.S.A, 1999.
Fitz Michael P, Fundamentals of Communications Systems, McGraw-Hill
Companies, U.S.A, 2007
Groe John and Larson Lawrence, CDMA -Mobile Radio Design, Artech
House, Boston, Massachusetts, U.S.A, 2000.
Pierce John and Noll Michael, Signals -the science
telecommunications, Scientific American Library, U.S.A, 1990
of
Pothecary Nick, Feedforward Linear Power Amplifiers, Artech House,
Boston, Massachusetts, U.S.A, 1999.
Articles/Master Thesis/Papers
Elgeryd T, Master Thesis: ADS and Matlab to Optimize Predistortion of
Amplifiers, KTH, Stockholm, Sweden, 2003.
Katz Allen, SSPA Linearization, Linearizer Technology Inc, Microwave
Journal, U.S.A, 1999
Kokkeler A.B.J, Modeling Power Amplifiers using Memory Polynomials,
University of Twente, Enschede, Netherlands, 2005
Kundert Ken, Simulation Methods for RF Integrated Circuits, Cadence
Design Systems, San Jose, California, U.S.A, 1997
Raab F, Asbeck P et al. Power Amplifiers and Transmitters for RF and
Microwave, Green Mountain Radio Research Company, Vermont, U.S.A,
2002
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Linköping University
Master’s thesis
ADS and Matlab to Optimize Predistortion of Amplifiers
Spångberg D, Master Thesis: Digital Pre-Distortion of Power Amplifiers,
Uppsala University, Uppsala, Sweden, 2002
Yap How-Siang, Designing to Digital Wireless Specifications Using
Circuit Envelope Simulation, HP Eesof Division, Hewlett-Packard, Asia
Pacific Microwave Conference 1997
Zhu A, Pedro J. C. and Brazil T. J, Dynamic deviation reduction-based
Volterra behavioral modeling of RF power amplifiers, IEEE Transactions
on Microwave theory and techniques, Vol 54, No 12, 2006
Technical Specifications
3GPP TS 25.104 v9.2.0, 3rd Generation Partnership Project; Technical
Specification Group Radio Access Network (Release 9), 2009-12
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Appendix 1.
Schematics of the PA1 and DPA
The PA1
PA1- and DPA-DUT
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The Doherty PA (DPA)
Doherty structure
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Appendix 2.
Schematics of the input and output
matching networks
Designing the input and output matching networks is an important part of
the PA design. The goal is to find the matching networks that maximize
the power delivered to a 50-Ohm load, which means a minimized
reflection coefficient. By using the Smith chart and S-parameter
simulations a matched amplifier can be found. The figures below give an
idea of how a matching network can look like.
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PA input-matching network
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PA output-matching network
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Appendix 3.
Top level schematics
Sample PA1 top level
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Sample DPA top level
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Matrix PA1 top level
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Appendix 4.
Schematics of modulators
QAM-modulator
QAM-demodulator
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Appendix 5.
The WCDMA test signal
There exist several different test models of WCDMA signals for different
test purposes. The Test Model 1 (TM1) is employed in this thesis since
according to the 3GPP specifications it should be used for ACLR
measurements, which are central in this study. The WCDMA signal used
here has a bandwidth of 5 MHz and a peak-to-average-ratio (PAR) of 7
dB. Its sampling frequency is chosen to be 61.44 MHz, which is equal to
16 times a chip rate of 3.84 MHz.
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