TITLE OF THESIS A DSP Controlled Adaptive Feedforward Amplifier

A DSP CONTROLLED ADAPTIVE FEEDFORWARD AMPLIFIER

LINEARIZER

by

Stephen James Grant

B.A.Sc., University of British Columbia, 1993

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in the School

of

Engineering Science

? Stephen J. Grant 1996

SIMON FRASER UNIVERSITY

July 1996

All rights reserved. This work may not be

reproduced in whole or in part, by photocopy

or other means, without permission of the author.

APPROVAL

NAME:Stephen James Grant

DEGREE:Master of Applied Science

TITLE OF THESIS: A DSP Controlled Adaptive Feedforward Amplifier

Linearizer

Examining Committee:

Chair: Dr. John Jones

______________________________

Dr. James Cavers

Senior Supervisor

______________________________

Dr. Paul Goud

Senior Supervisor

______________________________

Dr. Paul Ho

Supervisor

______________________________

Dr. Shawn Stapleton

Examiner

Date Approved: ____________________

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ABSTRACT

Currently, the only available wideband (multiple MHz), accurate, amplifier linearization method is feedforward. Feedforward, though, requires automatic adaptation of key parameters for reliable distortion cancellation as operational and environmental conditions vary. In this thesis, previous analysis on adaptive feedforward linearization is extended to include an alternative placement of the adaptive signal cancellation coefficient. In contrast to previous analysis, this placement results in a non-quadratic error surface. Consequently, two available criteria for the optimization of the signal cancellation coefficient result in different optimal values. This result can have practical implementation consequences under certain operating conditions. A new analysis is presented that shows that various inaccuracies in the implementation of baseband correlation, such as frequency and phase offsets, filter mismatches, and incomplete image suppression, do not affect the final converged coefficient values. With a novel and appropriate use of DSP, a feedforward linearizer has been implemented with adaptation driven by easily computed gradient signals. This overcomes the difficulties, such as DC offsets at the output of analog mixers and masking of weak signals by stronger ones, that slow and/or cause incorrect convergence of many previously reported implementations. The result is 40 dB reduction of intermodulation spectra over a bandwidth of 7 MHz. Coefficient convergence occurs within 50 msec of start-up, and following a 6 dB change in input power, reconvergence occurs in 3 msec with no loss in distortion suppression.

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ACKNOWLEDGEMENTS

Nothing is ever done alone; thus, I would like to thank certain people who helped me along the way with this project. Thanks to my Senior Supervisors, Jim Cavers and Paul Goud, who, I feel, were responsible for advancing my knowledge and confidence in the area of wireless communications to a new and hopefully much higher level than before. Deserving of thanks as well, is my wife, Irma, for her constant support the whole way through the project, from start to finish.

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TABLE OF CONTENTS APPROVAL (ii)

ABSTRACT (iii)

ACKNOWLEDGEMENTS (iv)

LIST OF TABLES (vii)

LIST OF FIGURES (viii)

1. INTRODUCTION (1)

1.1 Characterization of Amplifier Nonlinearities (1)

1.2 Overview of Linearization Strategies (4)

1.3 Development of Feedforward Linearization (6)

1.4 Project Goals (12)

2. PRINCIPLES OF ADAPTATION (14)

2.1 Comparison of Optimization Criteria for Signal Cancellation Coefficient (23)

2.2 Adaptation of Signal Cancellation Coefficient (27)

2.3 Adaptation of Error Cancellation Coefficient (30)

2.4 Effect of Delay Mismatches (34)

2.5 Effect of Downconversion Errors (35)

2.6 Effect of Vector Modulator Errors (39)

3. IMPLEMENTATION (42)

3.1 Baseband Correlation in DSP (44)

3.2 Hardware Design (50)

3.2.1 Vector Modulator Design (57)

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3.3 Software Design (59)

3.3.1 Filter Design (63)

3.3.2 TMS320C30 Assembly Code Design (68)

4. RESULTS (72)

5. CONCLUSIONS (81)

REFERENCES (84)

APPENDIX A: Assembly Code and Linker Command File for Adaptation of α (xx)

APPENDIX B: Assembly Code and Linker Command File for Adaptation of β (xx)

vi

LIST OF TABLES

Table 1. Relative difference in γo as a function of backoff for a 1% relative error in α (21)

vii

LIST OF FIGURES

Figure 1.Measured characteristics of a typical class AB power amplifier (3)

Figure 2.Simulated input and output power spectra for class AB amplifier with a π/4-DQPSK input signal (4)

Figure 3.RF circuit configuration of a typical feedforward amplifier (7)

Figure 590bec77f46527d3240ce0efplex baseband model of adaptive feedforward linearizer (14)

Figure 5.Power of v e(t) as a function of α for a π/4-DQPSK input signal and

1 dB backoff (24)

Figure 6.Contours and negative gradient of P e(α) surface for a π/4-DQPSK input signal and 1 dB backoff (26)

Figure 7.Contours of P e(α) surface and σ

2 for a π/4-DQPSK input signal and

em

1 dB backoff (29)

Figure 590bec77f46527d3240ce0efplex baseband equivalent of adaptation loop for α (37)

Figure 590bec77f46527d3240ce0efplex baseband equivalent of vector modulator (40)

Figure 10.Analog circuit for bandpass computation of gradient signal for adaptation of α (43)

Figure 11.Block diagram of feedforward circuit showing downconversion of signals necessary for baseband correlation (45)

Figure 12.Two-step downconversion process for selection of subbands (47)

Figure 13.Conceptual diagram showing spectrum of downconverted signal subband (47)

Figure 14.DSP algorithm for adaptation of α (50)

Figure 15.Schematic diagram of signal cancellation circuit (52)

Figure 16.Schematic diagram of error cancellation circuit (53)

Figure 17.Schematic diagram of vector modulator (58)

Figure 18.Measured (a) attenuation for φ = 45° and (b) phase for r = 0.7 V provided by vector modulator (59)

Figure 19.Simplified DSP algorithm for adaptation of α (63)

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ix Figure 590bec77f46527d3240ce0efplex bandpass filter ()~

h n used for ()~v n m and ()~v n e

in adaptation of α..................................................................................................................64Figure 21.(a) Reference signal and (b) error signal for α = αopt both filtered using ()~h n . (65)

Figure 590bec77f46527d3240ce0efplex bandpass filters (a) ()~h n e used for ()~v n e and (b) ()

~

h n o used for ()~v n o in adaptation of β.................................................................................67Figure 23.(a) Error signal for α = αopt filtered using ()~

h n e and (b) linearizer output signal for β = 0 (no distortion cancellation) filtered using ()~h n o (68)

Figure 24.Convergence of (a) α and (b) β for narrowband π/4-DQPSK input

signal (PA output power ≈ +35 dB m ) (73)

Figure 25.Histogram of instantaneous power of error signal normalized to unity

average power for π/4-DQPSK input signal (PA output

power ≈ +32 dB m ) (75)

Figure 26.Spectra of π/4-DQPSK input signal and error signal with reference

signal completely canceled (76)

Figure 27.Spectrum of linearizer output signal before and after distortion

cancellation (77)

Figure 28.Spectra of linearizer output signal after distortion cancellation and

linearizer input signal (77)

Figure 29.Spectrum of narrowband π/4-DQPSK input signal at 815 MHz plus

tone at 812.5 MHz (78)

Figure 30.Spectrum of amplifier output signal for narrowband π/4-DQPSK input

signal at 815 MHz plus tone at 812.5 MHz (79)

Figure 31.Spectrum of linearizer output signal before and after distortion

cancellation for narrowband π/4-DQPSK input signal at 815 MHz plus

tone at 812.5 MHz (80)

1. INTRODUCTION

All wireless radio transmitters contain RF amplifiers which are nonlinear to some degree. The primary consequence of amplifier nonlinearities is the generation of intermodulation distortion (IMD) if the signal to be amplified has a non-constant envelope, such as for linear or multicarrier modulation formats. Not only does IMD corrupt the amplified signal itself, but more seriously it causes adjacent channel interference due to spectral regrowth. In interference limited systems such as cellular radio, strict limits are usually placed upon allowable intermodulation power in adjacent channels; consequently, some form of amplifier linearization is usually required. Several linearization techniques employed to combat IMD are feedback, predistortion, and feedforward. Adaptive feedforward is the scheme studied in this thesis.

1.1 Characterization of Amplifier Nonlinearities

Nonlinear RF amplifiers are characterized by measurement of their AM/AM (amplitude dependent gain) and AM/PM (amplitude dependent phase shift) characteristics. These measurements may be performed using a network analyzer in power sweep mode. Specifically, the gain and phase of the amplifier are measured at a single frequency as the input power level is varied. Not only are RF amplifiers nonlinear, but they also possess memory: the output signal depends on the current value of the input signal as well as previous values spanning the memory of the amplifier. If the reciprocal of the bandwidth of the input signal is much larger than the memory of the amplifier, as is the case for most RF amplifiers driven with narrowband signals, the amplifier can be modeled as memoryless

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for that particular input signal. Thus, for complex baseband analytical and simulation purposes, the AM/AM and AM/PM measurements can be summarized in a single frequency-independent memoryless function, namely complex voltage gain

()

=φ(1)

G x g x e j x

()()

The magnitude and phase of G(x) are simply the measured gain and phase of the amplifier as functions of x—the instantaneous power in the input signal. For wideband signals, the memory of the amplifier becomes a significant fraction of the reciprocal of the bandwidth of the input signal; thus, it must be considered for accurate analytical and simulation studies. In this case, a single frequency-independent function is not sufficient to model the amplifier nonlinearity, and more powerful modeling techniques must be used such as a Volterra series approach. For the analysis presented in this thesis, though, the power amplifier is assumed to be memoryless.

Figure 1 shows the characteristics of a typical class AB RF power amplifier measured at a single frequency within the passband of the amplifier [1]. Note that the gain and input power are normalized such that saturation occurs at unity output power for unity input power. Consequently, normalized input power also represents input backoff from saturation. For example, 6 dB backoff corresponds to an input power of 0.25.

2

3

Evident in Figure 1 is a strong amplitude dependence of the amplifier gain and phase. Because the transistors in the amplifier are biased in class AB rather than class A,they cut off at low signal voltages. This causes the gain to fall off at low input power.The gain also rolls off at high input power due to saturation of the transistors. The variation in phase with input power is due to voltage-dependent device capacitances.

Figure 2 shows simulated power spectra of a narrowband π/4-DQPSK signal before and after amplification with the amplifier whose nonlinear characteristics are shown in Figure 1. For simulation purposes, G (x ) is represented by polynomials fitted to the measured gain and phase curves over the range of input powers extending from 0 to 1(saturation); G (x ) is then extrapolated further into saturation. If v m (t ) is the complex envelope of the amplifier input signal, then the complex envelope of the distorted amplifier output signal is given by v a (t ) = v m (t )G [|v m (t )|2]. 35% rolloff root raised cosine filtering is used for the simulation which results in a peak-to-average power ratio of approximately 2.5 dB; input backoff is 3 dB. Note that frequency has been normalized by the symbol rate. As can be seen, the amplifier nonlinearity causes significant spectral regrowth.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Input Power 0.00.20.40.6

0.81.01.2

1.41.6

1.8

2.0G a i n

510

1520

2530

3540P h a s e (d e g r e e s )

Phase

Gain

0.0

0.20.40.60.8 1.0 1.2

Input Power

0.00.2

0.4

0.6

0.8

1.0

1.2

O u t p u t P o w e

r

Figure 1.Measured characteristics of a typical class AB power amplifier

4Regulatory bodies usually specify power spectral density (PSD) masks which define maximum allowable adjacent channel interference (ACI) levels. TETRA [2], for example, uses a π/4-DQPSK modulation format with 35% root raised cosine filtering at a symbol rate of 18 kHz; the channel spacing is 25 kHz. Adjacent channel protection is specified as 60 dB at 25 kHz, and 70 dB at 50 and 75 kHz. The corresponding spectrum mask is shown in Figure 2. Clearly, TETRA limits are exceeded; consequently, some form of linearization for this amplifier is required in order to conform to this standard.

1.2 Overview of Linearization Strategies

Perhaps the simplest method of achieving linear RF amplification without the use of additional hardware is output backoff of an existing class A amplifier such that it

-4.0-3.0-2.0-1.00.0 1.0 2.0 3.0 4.0

Frequency

-100

-90

-80

-70

-60-50-40-30-20-10

P o w e r S p e c t r a l D e n s i t y (d B )Input TETRA

Distorted Output Mask

Figure 2.Simulated input and output power spectra for class AB amplifier with a π/4-DQPSK input

signal

operates completely in its linear region. Typically though, the backoff required to achieve linear operation is high (25 to 30 dB), and the resulting power efficiency is very low (1 to 2%). Also, for a fixed output power requirement, the cost of building an amplifier with output power rating 25 to 30 dB higher than necessary can be high. Moreover, the heat dissipation from the higher power amplifier may become a problem.

Several other techniques to achieve linear RF amplification have been developed. The most popular are feedback, predistortion, and feedforward, all of which make use of additional hardware. Making a choice of which linearization strategy to employ for a particular application involves tradeoffs of complexity, degree of IMD suppression, and bandwidth. The most prominent feedback scheme, namely Cartesian coordinate modulation feedback [3], has relatively low complexity, offers reasonable IMD suppression, but stability considerations typically limit the bandwidth to a few hundred kHz. Digital implementations of predistortion [4,5] have higher complexity than feedback, offer better IMD suppression, but again, possible bandwidths are low (up to a few tens of kHz) due to limited DSP computation rates. Reported implementations of analog predistortion [6], although potentially wideband, have modest complexity, but suffer from limited IMD suppression. In contrast to the above linearization techniques, feedforward [7,8,9] is currently the only linearization strategy that simultaneously offers wide bandwidth and good IMD suppression; the cost is relatively high complexity. Automatic adaptation of key parameters, though, as discussed in the next section, is essential for reliable distortion cancellation as operating conditions vary.

Wide bandwidth capability makes feedforward an attractive scheme for several applications. At cellular base stations, rather than using one amplifier per channel

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followed by lossy high power combiners, it is more efficient to combine channels at low power and use a single wideband linearized amplifier for the resultant signal. Another potential use of feedforward is for emerging PCS applications, including wideband CDMA, in which the bandwidth requirements place feedback and predistortion out of the league of viable linearization schemes.

1.3 Development of Feedforward Linearization

In 1927, H.S. Black of Bell Telephone Laboratories invented the concept of negative feedback as a method of linearizing amplifiers for the Bell Telephone system [10]. Lesser known is that four years earlier, in the search for a linearization method, he invented the concept of feedforward. His idea for feedforward was simple: reduce the amplifier output to the same level as the input and subtract one from the other to leave only the distortion generated by the amplifier. Amplify the distortion with a separate amplifier and then subtract it from the original amplifier output to leave only a linearly amplified version of the input signal. Black’s idea for negative feedback was spawned from his simple feedforward concept: feed an attenuated version of the amplifier output signal back to the input in anti-phase and combine it with the input signal. Use the same amplifier (rather than a separate amplifier as in feedforward) to amplify the difference signal thus producing a linearly amplified version of the input signal. The advantage of the feedback solution, due to the fact that it operated closed-loop, was that it was automatic and required no manual adjustment as operating conditions changed. Its disadvantage, of course, was its potential for instability.

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7The basic operating principles of a feedforward amplifier as shown in Figure 3 are now described. The feedforward configuration consists of two circuits, the signal cancellation circuit and the error cancellation circuit. The purpose of the signal cancellation circuit is to suppress the reference signal from the main amplifier (or PA)output signal leaving only amplifier distortion, both linear and nonlinear, in the error signal. Linear distortion, in contrast to nonlinear distortion described already, is due simply to deviations of the amplifier’s frequency response from flat gain and linear phase

[11]. Note that the feedforward technique can also compensate for memory effects, since distortion due to memory in the main amplifier is also included in the error signal and thus ultimately canceled in the linearizer output. The fact that the PA output can be decomposed into two components—a linear term and a distortion term—is discussed in

Section 2.

Signal Cancellation Circuit Error Cancellation Circuit

and Phase Amplifier

Variable Attenuation Main Delay Line Sampling Output Figure 3.RF circuit configuration of a typical feedforward amplifier

In order to suppress the reference signal, the values of the sampling coupler and fixed attenuation are chosen to match the gain of the main amplifier so that the PA output signal is reduced to approximately the same level as the reference signal. The variable phase shifter ahead of the PA is then adjusted to place the PA output in anti-phase with the reference. The variable attenuation serves the fine tuning function of precisely matching the level of the PA output and the reference. The delay line in the reference branch, necessary for wide bandwidth operation, compensates for the group delay of the main amplifier by time aligning the PA output and reference signals before combining.

The purpose of the error cancellation circuit is to suppress the distortion component of the PA output signal leaving only the linearly amplified component in the linearizer output signal. In order to suppress the error signal, the gain of the error amplifier is chosen to match the sum of the values of the sampling coupler, fixed attenuator, and output coupler so that the error signal is increased to approximately the same level as the distortion component of the PA output signal. The variable phase shifter ahead of the error amplifier is then adjusted to place the error in anti-phase with the PA output. The variable attenuation, again, serves the fine tuning function of precisely matching the level of the error signal and the distortion component of the PA output. The delay line serves the same purpose as in the signal cancellation circuit. The error amplifier must be chosen such that it linearly amplifies the error signal while still providing the required output power, otherwise uncorrectable IMD shows up in the linearizer output. This usually dictates the use of a linear class A amplifier with sufficient backoff. Note that any bandwidth limit, manifested as incomplete distortion suppression, is imposed either by

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imperfect delay matching or by linear distortion in the error amplifier, the variable attenuators/phase shifters, or the couplers and combiners.

The crux of the proper operation of the feedforward circuit is the proper adjustment of the attenuation and phase in the signal and error cancellation circuits such that good IMD suppression is maintained over time. Variations of component characteristics with temperature and time as well as changes in operating conditions such as input power level and supply voltage all necessitate readjustment. For these reasons Black, himself, essentially abandoned feedforward in favour of feedback. He found, using vacuum tube amplifiers, that “every hour on the hour—24 hours a day—somebody had to adjust the filament current to its correct value. In doing this, they were permitting plus or minus 1/2- to 1-dB variation in amplifier gain, whereas, for my purpose, the gain had to be absolutely perfect. In addition, every six hours it became necessary to adjust the B battery voltage, because the amplifier gain would be out of hand. There were other complications too, but these were enough!” [10]. Even with modern solid state amplifiers, changes with temperature and time are still significant enough, with respect to the accuracy requirements of the feedforward circuit, to necessitate adaptation.

After its invention in 1923, feedforward was essentially ignored until Seidel, also at Bell Laboratories, investigated the use of feedforward for microwave frequency TWT amplifiers in the late sixties and early seventies [7]. Seidel constructed a feedforward amplifier which achieved distortion suppression of 38 dB over a 20 MHz band. The setup employed an automatic control scheme for the variable attenuation and phase in the error cancellation circuit. The control scheme was based on driving a mechanical attenuator/phase shifter with an error signal derived by comparing the amplitude and phase

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at two different points in the error cancellation circuit of a pilot tone inserted after the main amplifier. No control scheme was utilized for the variable attenuation and phase in the signal cancellation circuit. In this way he was able to maintain time independent distortion suppression over a period of several months.

Several patents concerned with adaptive feedforward systems then started to appear in the mid-eighties, and many more appeared in the early nineties. These patents deal with two general methods of adaptation both with or without the use of pilot tones, namely adaptation based on power minimization [12,13] and adaptation based on gradient signals [14,15]. The control scheme for the former attempts to adjust the attenuation and phase in the signal cancellation circuit in such a way to minimize the measured power of the error signal in the frequency band occupied by the reference signal. Minimum power in the error signal is equivalent to suppression of the reference signal. The attenuation and phase in the error cancellation circuit are adjusted in such a way to minimize the measured power of the linearizer output signal in a frequency band occupied only by distortion. Minimum power in the output signal is equivalent to suppression of distortion. Once the optimal parameters are found, deliberate misadjustment is required over time to assess whether or not the respective powers are indeed still minimized. This deliberate perturbation periodically reduces IMD suppression—an undesirable side effect.

Adaptation using gradient signals is based on continually computing estimates of the gradient of a 3-dimensional power surface which depends on two parameters—the variable attenuation and phase in either the signal or error cancellation circuits. The gradient signal is then used to adapt the parameters in each circuit always in a direction towards the global minimum of the surface. The surface for the signal cancellation circuit

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is the power in the error signal; the power is minimized when the reference signal is completely suppressed, leaving only the amplifier distortion in the error signal. The surface for the error cancellation circuit is the power in the linearizer output signal; the power is minimized when the distortion is completely suppressed from the PA output signal. The advantage of adaptation based on gradient signals over that based on power minimization, is that since the gradient signals are continually computed, the control scheme constantly searches for the optimum operating point. No algorithm for deliberate misadjustment is required.

Adaptation using either of the above methods plus pilot tones is based on inserting a pilot both at the input to the feedforward linearizer as artificial signal and at the output of the main amplifier as artificial distortion. The control scheme for the signal cancellation circuit either attempts to null the first pilot tone in the error signal if using the power minimization approach, or uses it to derive a gradient signal if using the gradient approach. The same is true for the second pilot tone, except the observation point is the linearizer output. When both pilots are canceled, so is the amplifier distortion. As is the case for other components in a communication system, it is desirable to avoid pilot tones, if possible, and use traffic signals only.

Other than in the patent literature, very little has been published on implementations or analysis of adaptive feedforward linearizers since Seidel’s work. Two publications of note on adaptive feedforward linearization, though, are by Cavers [16] and Narahashi and Nojima [17]. Cavers’work is the first published analysis of adaptation behaviour of a feedforward linearizer and is intended as a benchmark and analytical framework for others developing such linearizers.

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Narahashi and Nojima report an implementation of an adaptive feedforward linearizer for multicarrier signals with adaptation based on a power minimization technique using pilot tones. A pilot tone is inserted at the output of the main amplifier and its level is measured in the linearizer output signal by means of a narrowband energy detector. A microprocessor is used to adjust the attenuation and phase in the error cancellation circuit using a perturbation technique. Adaptation in the signal cancellation circuit is performed using the same method, except that one of the carriers is used as the pilot signal, rather than an explicit pilot tone. With this setup, it is reported that 30 dB distortion improvement is obtained in a stable manner for a 100 W, 1.5 GHz, GaAs-FET power amplifier.

1.4 Project Goals

Based on an increasing need for a wide bandwidth, adaptive linearization technique and a lack of published work on adaptive feedforward, it was decided to implement, in contrast to [17], a gradient driven adaptive feedforward linearizer without the use of pilot tones. Gradient adaptation was selected because of the advantages it offers over the power minimization technique as discussed above. Based on available equipment, a 5 Watt, 815 MHz, class AB amplifier was chosen as the main amplifier.

A number of patents, e.g. [14], propose a gradient adaptation technique that relies on analog bandpass correlation requiring the mixing of two modulated RF signals. This method, elaborated on later, suffers from accuracy problems such as mixer DC offsets and the generation of additional IMD—both highly undesirable effects. To overcome these problems, the current work demonstrates a novel and appropriate use of DSP to perform

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