數位衛星通訊系統上配備有非線性放大器(如，行波管放大器)為了得到較好的效率常操作於飽和區。此時行波管放大器會分別發生振幅與相位(調幅/調幅與調幅/調相)的非線性失真。在數位衛星通訊的傳送路徑上的干擾不僅有發射器放大器的非線性現象也有碼際干擾與可加性白色高斯雜訊。為了補償以上非線性現象，本篇論文中提出一種新的補償機制：包含預失真器與適應性三階沃特拉架構等化器利用反QR分解遞迴最小平方演算法，分別置於非線性通道的之後端與前端。
在此提出的三階沃特拉濾波等化器使用反QR分解遞迴最小平方演算法，在收斂率，穩態均方差與計算數值穩定等方面可達成優越的表現。此類等化器可利用平行處理陣列架構來實現，如心臟型陣列。在電腦模擬結果方面利用M位元相位調變機制作為實驗訊號，分別比較傳統的最小均方差，梯度適應性格狀預測器，具格狀前置濾波器適應性最小均方差演算法等之訊號星座分佈圖，均方差的學習曲線與誤碼率。

Digital satellite communication systems are equipped with nonlinear amplifiers such as travelling wave tube (TWT) amplifiers at or near saturation for better efficiency. The TWT exhibits nonlinear distortion in both amplitude and phase (AM/AM and AM/PM) conversion, respectively. That is, in the digital satellite communication the transmission is disturbed not only by the non-linearity of transmitter amplifier, but also by the inter-symbol interference (ISI) with additive white Gaussian noise. To compensate the non-linearity of the transmitter amplifier and ISI, in this thesis, a new nonlinear compensation scheme consists of the predistorter and adaptive third-order Volterra-based equalizer, with the inverse QRD-RLS (IQRD-RLS) algorithm, which are located before and after the nonlinear channel, is proposed respectively.
The third-order Volterra filter (TVF) equalizer based on the IQRD-RLS algorithm achieve superior performance, in terms of convergence rate, steady-state mean-squared error (MSE), and numerically stable. They are highly amenable to parallel implementation using array architectures, such as systolic arrays. The computer simulation results using the M-ary PSK modulation scheme are carried out the signal’s constellation diagrams, the learning curve of the MSE and the bit error rate (BER) are compared with conventional least mean square (LMS), gradient adaptive lattice (GAL) and adaptive LMS with lattice pre-filter algorithms.

Contents
Acknowledgement i
Abstract ii
Contents iii
List of Figures and Tables v
Chapter 1 Introduction 1
Chapter 2 The Adaptive Linear Filtering Algorithm
2.1 Introduction 3
2.2 The Adaptive LMS Filtering Algorithm 5
2.3 The Adaptive Lattice Algorithm with Pre-filter 7
2.3.1 The Gradient Adaptive Lattice Predictor 7
2.3.2 The Adaptive Lattice Algorithm with Pre-filter 10
2.4 The Recursive Least-Squares Filtering Algorithm 14
2.4.1 Method of Exponentially Weight Lest-Squares 14
2.4.2 The Recursive Least-Squares Algorithm 15
2.5 The Inverse QR-Decomposition-Based Recursive Least-Squares Algorithm
18
2.5.1 QR-Decomposition Based RLS Filtering 18
2.5.2 Inverse QR-Decomposition Based RLS Filtering 20
Chapter 3 The Adaptive Nonlinear Equalizer Filtering Algorithm for
Satellite Channel
3.1 Introduction 25
3.2 Signal Model of Adaptive Channel Equalizer 26
3.2.1 Volterra Series Expansion For Nonlinear Systems 26
3.2.2 Signal Model of Adaptive Channel Equalizer 30
3.3 Signal Model of Predistorter 32
3.4 The Adaptive LMS Third-Order Volterra Filter with Lattice Pre-filter 35
3.4.1 The Adaptive LMS Third-Order Volterra Filter 35
3.4.2 The Adaptive LMS Third-Order Volterra Filter with GAL Predictor 37
3.4.3 The Adaptive LMS Third-Order Volterra Filter with Lattice Pre-filter 41
3.5 The Adaptive Inverse QRD-RLS Third-Order Volterra Filter 43
3.6 Computer Simulations 46
3.6.1 Benedetto and Biglieri’s Digital Nonlinear Satellite Channel Model 46
3.6.2 Communication System with Nonlinear Transmit Amplifier Model 50
Chapter 4 Conclusions 58
Appendix A. The Matrix Inversion Lemma 59
Appendix B. Time Update for the Tap-Weight Vector 60
Appendix C. Recursive Implementation 61
Appendix D. Givens Rotations 64
Appendix E. Filter Update Derivation 67
Appendix F. Inverse QR Derivation 71
Appendix F. Updating the Angle Parameters 74
References 77

References

[1] A. A. M. Saleh, “Frequency-Independent and Frequency-Dependent Nonlinear Models of TWT Amplifiers,” IEEE Trans. on Commun., vol. COM-29, no.11, pp. 715–1720, Nov. 1981.
[2] S. Benedetto, E. Bigilieri, and R. Daffara “Modeling and Evaluation of Nonlinear Satellite Links-A Volterra Series Approach,” IEEE Trans. on Aerosp. Electron. Syst., vol. AES-15, pp.494-506, Jul. 1979.
[3] S. Benedetto, E. Bigilieri, “Nonlinear Equalizeration of Digital Satellite Channels,” IEEE Journal on Selected Area in Communications, vol. SAC-1, no.1, pp.57-62, Jan. 1983.
[4] M. Schetzen, The Volterra and Wiener Theories of the Nonlinear Systems, New York, Wiley, 1980.
[5] G. Karam and H. Sari, “Analysis of Predistortion, Equalization, and ISI Cancellation Techniques in Digital Radio Systems with Nonlinear Transmit Amplifiers,” IEEE Trans. on Commun. vol.37, pp.1245-1253, Dec. 1989.
[6] Changsoo Eun and Edward J. Powers, “A New Volterra Predistorter Based on the Indirect Learning Architecture,” IEEE, Trans. on Signal Processing, vol. 45, no.1, pp.223-227, Jan. 1997.
[7] S. J. Chern and C. H. Huang, “ Nonlinear Adaptive Equalizer Based Upon an Inverse QRD-RLS Volterra Filter,” Proc. of 1997 IEEE MICC/ISPACS'97, Nov. 11-13, Hotel Nikko, Kuala Lumpur, Malaysia, pp.S24.1.1- S24.1.5, Nov. 1997.
[8] S. Haykin, Adaptive Filter Theory, 3rd Ed. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1995.
[9] S. J. Chern and K. T. Hsu, “Adaptive LMS Volterra Filtering Based Equalizer with Lattice Pre-filter,” Proc. of 1999 IEEE International Symposium on Intelligent Signal Processing and Communication Systems, Phuket Arcadia Hotel & Resort, Phuket, Thailand, Dec. 8-10, pp.457-460, Dec. 1999.
[10] S. Haykin, Adaptive Filter Theory, 2nd Ed. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1991.
[11] J. M. Cioffi and T. Kailath, “Fast RLS Transversal Filter for Adaptive Filtering,”IEEE Trans. on Acoust., Speech, Signal Proce. vol.ASSP-32, pp.304-337, Jun. 1984.
[12] J. M. Cioffi, “Limited Precision Effects for Adaptive Filtering,” IEEE Trans. on Circuits and Syst., vol CAS-34, pp. 821-833, Jul. 1987.


[13] C. M. Rader and A.O. Steinhardt, ”Hyperbolic Householder Transformations,” IEEE Trans. on Acoust., Speech, Signal Processing, vol. ASSP-34, pp.1589-1602, Dec.1986.
[14] W. M. Gentleman and H. T. Kung, “Matrix Triangulariztion by Systolic Arrays,” Proc. SPIE, Int. Soc. Opt. Eng., vol.298, pp.19-26, 1981.
[15] S.T. Alexander, A. L. Ghirnikar, “A Method for Recursive Least Squares Filtering Based Upon an Inverse QR Decomposition” IEEE Trans. on Signal Processing, vol. 41, no.1, pp.20-30, Jan. 1993.
[16] G. Lazzarin, S. Pupolin, and A. Sarti, “Nonlinearity Compensation in Digital Radio Systems,” IEEE Trans. on Commun., vol 42, pp.988-999, Feb. 1994.
[17] D. Psaltis, A. Sideris, and A. A. Yamamura, “A Multilayer Neural Network Controller”, IEEE Contr. Syst. Mag., pp.17–21, Apr. 1988.
[18] S. H. Leung and C. C. Chu, “Adaptive LMS Digital Filter with Lattice Pre-filter”, IEE Electronics Letters, vol.33, no.1, pp.34-35, Jan. 1997.
[19] J. Lee and V. J. Mathew, ”A Fast Recursive Least Squares Adaptive Second-Order Volterra Filter and Its Performance Analysis,” IEEE Trans. Signal Processing, vol. 41, no.3, pp.1087-1102, Mar. 1993.
[20] Sungbin Im and Powers, E.J., “A Block LMS Algorithm for Third-Order Frequency-Domain Volterra Filters,” IEEE Signal Processing Letters , vol.4, Issue 3, pp.75–78, Mar. 1997.
[21] Nam, S.W., Kim, S.B.and Powers, E.J., “Utilization of Digital Polyspectral Analysis to Estimate Transfer Functions of Cubically Nonlinear Systems with NonGaussian Inputs,” ICASSP-89., vol.4, pp.2306 -2309, 1989.
[22] Sergio Benedetto, Ezio Biglieri and Valentino Catellani, “Digital Transmission Theory,” Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1987.
[23] Dokic M.V., Clarkson P.M., “Performance characteristics of a third order adaptive Volterra filter,” ISCAS '92. Proceedings., 1992 IEEE International Symposium on , Volume: 6 , pp.2785 –2788, 1992