Digital Predistortion of Power Amplifiers

ZBCSHN

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Modeling Memoryless Power Amplifiers . . . . . . . . . . . . . . . . . 5
2.2 Predistortion of Memoryless Power Amplifier . . . . . . . . . . . . . . 7
2.2.1 Data Predistortion for Memoryless Power Amplifiers . . . . . 7
2.2.2 Signal Predistortion for Memoryless Power Amplifiers . . . . . 8
2.3 Modeling Power Amplifiers with Memory Effects . . . . . . . . . . . . 10
2.4 Predistortion of Power Amplifiers with Memory Effects . . . . . . . . 14
Chapter 3 Digital Predistorter Design . . . . . . . . . . . . . . . . . . . . . 17
3.1 Hammerstein Predistorter Design . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Hammerstein Predistorter Training . . . . . . . . . . . . . . . 17
3.1.2 Hammerstein Predistorter Simulation . . . . . . . . . . . . . . 22
3.2 Memory Polynomial Predistorter Design . . . . . . . . . . . . . . . . 25
3.2.1 Memory Polynomial Predistorter Training . . . . . . . . . . . 25
3.2.2 Memory Polynomial Predistorter Simulation . . . . . . . . . . 26
3.2.3 Memory Polynomial Predistorter Discussion . . . . . . . . . . 33
3.3 A New Combined Predistorter Design . . . . . . . . . . . . . . . . . . 35
3.3.1 Combined Predistorter Model . . . . . . . . . . . . . . . . . . 36
3.3.2 Combined Predistorter Training . . . . . . . . . . . . . . . . . 37
3.3.3 Effects of Noise and Initial Estimates . . . . . . . . . . . . . . 40
v
3.3.4 Combined Predistorter Performance . . . . . . . . . . . . . . . 45
Chapter 4 Effects of Even-order Nonlinear Terms . . . . . . . . . . . . . . 47
4.1 Passband and Baseband Nonlinearities . . . . . . . . . . . . . . . . . 47
4.1.1 Memoryless Case . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.2 Quasi-memoryless Case . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Even-Order Terms in the Baseband Power Amplifier Model . . . . . . 50
4.3 Even-Order Terms in the Baseband Predistorter Model . . . . . . . . 53
4.4 Extensions to Power Amplifiers and Predistorters with Memory . . . 58
Chapter 5 Analog Imperfection Compensation . . . . . . . . . . . . . . . . 61
5.1 Two-Stage Upconversion Transmitter . . . . . . . . . . . . . . . . . . 61
5.1.1 System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1.3 Equalizer Design . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Direct Upconversion Transmitter . . . . . . . . . . . . . . . . . . . . . 71
5.2.1 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.3 Compensator Construction . . . . . . . . . . . . . . . . . . . . 79
5.2.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 6 Real-time Implementations . . . . . . . . . . . . . . . . . . . . . 87
6.1 Memory Polynomial Model . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Indirect Learning Architecture . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Predistorter Construction . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.4 DSP Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.4.1 Implementation Details . . . . . . . . . . . . . . . . . . . . . . 91
6.4.2 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Testbed Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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SUMMARY
Power amplifiers are essential components in communication systems and are inherently
nonlinear. The nonlinearity creates spectral growth (broadening) beyond the signal
bandwidth, which interferes with adjacent channels. It also causes distortions within the
signal bandwidth, which decreases the bit error rate at the receiver. Newer transmission
formats, such as wideband code division multiple access (WCDMA) or orthogonal frequency
division multiplexing (OFDM), are especially vulnerable to the nonlinear distortions due to
their high peak-to-average power ratios (PAPRs). If we simply back-o the input signal to
achieve the linearity required for the power amplifier, the power amplifier eciency will be
very low for high PAPR signals.
Another choice is to linearize a nonlinear power amplifier so that overall we have a
linear and reasonably ecient device. Digital predistortion is one of the most cost eective
ways among all linearization techniques. However, most of the existing designs treat the
power amplifier as a memoryless device. For wideband or high power applications, the
power amplifier exhibits memory eects, for which memoryless predistorters can achieve
only limited linearization performance.
In this dissertation, we propose novel predistorters and their parameter extraction algorithms.
We investigate a Hammerstein predistorter, a memory polynomial predistorter,
and a new combined model based predistorter. The Hammerstein predistorter is designed
specifically for power amplifiers that can be modeled as a Wiener system. The memory
polynomial predistorter can correct both the nonlinear distortions and the linear frequency
response that may exist in the power amplifier. It is a robust predistorter, which has demonstrated
good performance on several nonlinear system models. Real-time implementation
aspects of the memory polynomial predistorter are also investigated in the dissertation.
The new combined model includes the memory polynomial model and the Murray Hill
model, thus extending the predistorter’s ability to compensate for strong memory eects in the power amplifier. Performance of the new model is demonstrated through experimental
measurements.
The predistorter models considered in this dissertation include both even- and oddorder
nonlinear terms. In the literature, most of the power amplifier and predistorter
models consider only the odd-order terms. Here, we show that it is beneficial to include
even-order nonlinear terms in both the baseband power amplifier and predistorter models.
By including these even-order nonlinear terms, we have a richer basis set, which oers
appreciable improvement.
The ideal performance of digital predistortion certainly relies on robust predistorters
that can completely compensate for the nonlinearities of the power amplifier. In reality,
however, the performance can also be aected by the analog imperfections in the transmitter,
which are introduced by the analog components; mostly analog filters and quadrature
modulators. There are two common configurations for the upconversion chain in the transmitter:
two-stage upconversion and direct upconversion. For a two-stage upconversion
transmitter, we design a band-limited equalizer to compensate for the frequency response
of the surface acoustic wave (SAW) filter which is usually employed in the IF stage. For a
direct upconversion transmitter, we develop a model to describe the frequency-dependent
gain/phase imbalance and dc oset. We then develop two methods to construct compensators
for the imbalance and dc oset. These compensation techniques help to correct for
the analog imperfections, which in turn improve the overall predistortion performance.

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REFERENCES
[1] Bai, E. W., “An optimal two stage identification algorithm for Hammerstein-Wiener
nonlinear systems,” in Proc. American Contr. Conf., pp. 2756–2760, June 1998.
[2] Benedetto, S. and Biglieri, E., “Nonlinear equalization of digital satellite channels,”
IEEE J. Select. Areas Commun., vol. SAC-1, pp. 57–62, Jan. 1983.
[3] Benedetto, S. and Biglieri, E., Principles of Digital Transmission with Wireless
Applications. New York, NY: Kluwer Academic/Plenum, 1999.
[4] Benedetto, S., Biglieri, E., and Daffara, R., “Modeling and performance evaulation
of nonlinear satellite links – a Volterra series approach,” IEEE Trans. Aerosp.
Electron. Syst., vol. AES-15, pp. 494–507, July 1979.
[5] Brandwood, D. H., “A complex gradient operator and its application in adaptive
array theory,” IEE Proc. Part F and H, vol. 130, pp. 11–16, Feb. 1983.
[6] Cavers, J. K., “Amplifier linearization using a digital predistorter with fast adaptation
and low memory requirements,” IEEE Trans. Veh. Technol., vol. 39, pp. 374–382,
Nov. 1990.
[7] Cavers, J. K., “The eect of quadrature modulator and demodulator errors on
adaptive digital predistorters for amplifier linearization,” IEEE Trans. Veh. Technol.,
vol. 46, pp. 456–466, May 1997.
[8] Cavers, J. K., “New methods for adaptation of quadrature modulators and demodulators
in amplifier linearization circuits,” IEEE Trans. Veh. Technol., vol. 46, pp. 707–
716, Aug. 1997.
[9] Cavers, J. K. and Liao, M., “Adaptive compensation for imbalance and oset losses
in direct conversion transceivers,” IEEE Trans. Veh. Technol., vol. 42, pp. 581–588,
Nov. 1993.
[10] Chang, S. and Powers, E. J., “A simplified predistorter for compensatoin of nonlinear
distortion in OFDM systems,” in Proc. IEEE Global Telecommun. Conf., vol. 5,
pp. 3080–3084, Nov. 2001.

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CONCLUSIONS
This dissertation considered the design of digital predistortion systems to linearize power
amplifiers with memory eects. By adding a digital predistorter in the baseband, the power
amplifier is allowed to operate into its nonlinear region, thereby significantly increasing its
eciency. The eciency gain translates into electricity and cooling cost savings for service
providers and longer battery life for mobile terminal users. The challenge here is to address
the memory eects exhibited by the higher power amplifiers or the power amplifiers for
wideband signals. In addition, analog components in the transmitter have imperfections
that need to be compensated as well.

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7.1 Contributions
Primary contributions of this dissertation are summarized here:
• Designed novel predistorters and their parameter extraction algorithms, which include
the Hammerstein predistorter, the memory polynomial predistorter, and the combined
predistorter.
• Explained the benefits of including even-order terms in power amplifier modeling and
predistorter design.
• Designed compensation techniques for analog imperfections in the transmitter, which
include the linear frequency distortion and frequency-dependent gain/phase imbalance.
• Integrated a wideband predistortion testbed.
In addition, we implemented the memory polynomial predistorter training algorithm on
a Texas Instruments C6711 Starter Kit and evaluated the real-time performance of the
algorithm.

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7.2 Suggestions for Future Research
This dissertation can be extended in a number of directions, including:
• Designing a fast adaptive memory polynomial predistorter based on the orthogonal
polynomial theory.
• Performing tests on dierent types of power amplifiers and establishing connections
between the memory behavior of the power amplifier and the kernels of the Volterra
series.
• Combining predistortion with peak-to-average ratio reduction techniques to further
improve the eciency of the power amplifier.

gogodie

不错不错

arsin

thank you

tmchrry

谢谢，学习一下

wangjianping