可適性波束成型技術是透過調整各個天線陣列上的權重係數，來達到提取欲接收信號並消除干擾信號和雜訊的技術，主要可以分為兩種類型，第一種所需要的已知資訊為欲接收信號的入射角方向，此種類型稱作是指引式波束成型技術，例如linearly constrained minimum variance beamformer (LCMV)，而近年來發展出了另一種，不需要知道欲接收信號入射角方向，其運用信號的某些特徵，像是週期恆定性(cyclostationary)，來達到波束成型，此類型稱作是盲目式波束成型技術，而本論文會根據此兩種波束成型技術來發展出多種具快速收斂性且強健式的技術，以對抗非理想效應的影響。
本論文大致可分為兩個部分，第一部分為第三章，我們利用改良式的average cyclic correlation matrix algorithm (ACCM)，此方法是用迭代平均的方式(Iterative Averaging, IA)估計出在週期頻率誤差影響下最接近真實的週期共軛自相關矩陣，接著我們將Full Data-Dependent Loading方法引入改善此演算法的收斂性，如此便可發展出一套新的具快速收斂性及強健性的波束成型技術，並且我們以實驗模擬的方式證明了此方法的有效性。
第二部分為第四章以後，我們將原本僅用於單一接收信號的支持向量機-波束成型技術，推廣到多重接收信號也能使用，且由文獻中我們了解到支持向量機-波束成型技術的好處是他可以結合許多已知的強健式波束成型技術，幫助這些方法達到更好的收斂性(本論文中所提到的良好收斂性指的是使用少量資料點即可達到不錯的array output signal-to-interference-plus-noise ratio (Output SINR))甚至還會增強其效能(本論文所提到的效能是以Output SINR來評斷)，故我們的貢獻主要是將支持向量機-波束成型技術推廣為支持向量機-多重波束成型技術，並且結合了許多已知對抗非理想環境的強健式波束成型技術，如Cheng’s method、ACCM、Efficient Robust Array Beamforming(ERAB)、Compesaion method等等 ，發展在非理想環境下具有快速收斂性及強健式的波束成型技術。

Adaptive array beamforming which can extract signals of interest from specific angles while suppress interferences and noise by adjusting weights on the array elements. And they can be classified into two types. The first type we call it conventional beamforming. For conventional beamforming, the a priori information is the direction of the desired signal, and this kind of technique is also called steered-beam beamforming, for example linearly constrained minimum variance beamformer (LCMV). In recent years, another kind of adaptive array beamforming without the knowledge of the direction of the desired signal has been widely presented. It utilizes some characteristic of the signals to achieve beamforming, for example, signal cyclostationary and thus it is called “blind” beamformer. The purpose of this thesis is mainly to develop several fast convergent and robust techniques for both steered-beam beamformer and blind beamformer using cyclostationary in order to tackle the performance degradation under non-ideal enviroments.
This thesis can be divided into two parts. Chapter 3 is the first part of this thesis. To deal with the cycle frequency error (CFE), we present an iterative averaging (IA) scheme in conjunction with average cyclic correlation matrix algorithm (ACCM) to estimate the actual cyclic correlation matrix. In addition, we apply Fully Data-Dependent method to improve the convergence of the proposed method. In this way, we would expect that the propsed method will be a fast convergent and robust beamforming techniques. We will present the simulation results to show the effectiveness of the proposed method.
From the forth chapter, we present a new sheme of the suppert vectoe machines beamformer(SVM-beamformer) which can deal with multiple signals of interest (SOIs). The advantages of using SVM-beamformer (which is use to handle single SOI) are that it can combine with the existing robust array beamforming techniques and improve their convergence and performance. (In this thesis, the fast convergence means that we can use less data to get good performance, and the performance means the array output signal-to-interference-plus-noise ratio (SINR)). Besides, we note that it can also be applied to the environment of multiple SOIs. Therefore, we combine several robust array beamforming techiques with the SVM-beamformer to deal with the problem of array beamforming under multiple SOIs and non-ideal enviroments.

目錄
誌謝 i
摘要 ii
ABSTRACT iii
目錄 v
圖目錄 x
表目錄 xiv
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 論文架構 4
第二章 天線陣列的基本概念 6
2.1 天線陣列基本架構與數學模型 6
2.2 自相關矩陣介紹 8
2.2.1 自相關矩陣的數學定義 8
2.2.2 自相關矩陣的特徵分解 10
2.3 傳統可適性陣列波束成型技術 11
2.4 信號週期恆定特性介紹 13
2.4.1 信號週期恆定特性 13
2.4.2 週期自相關函數 14
2.4.3 LS-SCORE演算法介紹 16
2.4.4 CAB演算法介紹 17
第三章 重建自相關矩陣之盲目式波束成型技術 20
3.1 簡介 20
3.2 已開發之盲目式波束成型技術 21
3.2.1 Constrained-CAB Algorithm 21
3.2.2 ERAB Algorithm 22
3.2.3 Compensation Method 23
3.2.4 ACCM Algorithm 25
3.3 在有限資料點以及週期頻率誤差情況下之解決方法 26
3.3.1 Fully Data-Dependent Loading technique 26
3.3.2 Iteration ACCM 27
3.3.3 Cyclic constraint method 29
3.3.4 Proposed method 31
3.4 模擬分析 33
3.5 結論 50
第四章 解決角度不匹配問題之支持向量機強健式多重波束成型技術 51
4.1 簡介 51
4.2 運用支持向量機之多重波束成型技術討論 51
4.2.1 運用支持向量機之多重波束成型技術 52
4.2.2 Iterative reweighted least-squares Procedure (IRWLS) 57
4.3 已開發之強健式多重波束成型技術介紹 61
4.3.1 ESB method 61
4.3.2 Cheng’s method 62
4.4 運用支持向量機之新式強健式多重波束成型技術 65
4.5 模擬分析 66
4.6 結論 76
第五章 利用信號週期恆定特性且結合方位估計及支持向量機之盲目式波束成型技術 77
5.1 簡介 77
5.2 利用信號週期恆定特性之盲目式波束成型技術介紹 78
5.2.1 CAB Algorithm 78
5.2.2 ACCM Algorithm 79
5.2.3 ERAB method 80
5.2.4 Compensation method 82
5.2.5 IACCM Algorithm 84
5.3 結合支持向量機之新式盲目式波束成型技術 85
5.3.1 ACCM-SVM 86
5.3.2 ERAB-SVM 95
5.3.3 Com-SVM 95
5.3.4 IACCM-SVM 95
5.4 結合支持向量機及方位估測之新式盲目式波束成型技術 96
5.4.1 Cyclic MUSIC and Conjugate Cyclic MUSIC 96
5.4.2 EMUSIC-SVM 97
5.4.2 IAMUSIC-SVM 99
5.5 模擬分析 102
5.6 結合支持向量機之新式盲目式多重波束成型技術 122
5.6.1 多重接收信號情況下的CCAB演算法 122
5.6.2 多重接收信號情況下的LS-SCORE演算法 122
5.6.3 多重接收信號情況下的ERAB演算法 123
5.6.4 MEMUSIC-SVM 129
5.6.5 多重接收信號情況下的Com-SVM 131
5.6.6 MComMUSIC-SVM 133
5.7 多重接收信號環境下各方法模擬分析 135
5.8 結論 147
第六章 解決欲接收信號同調問題之多重波束成型技術 149
6.1 簡介 149
6.1 問題描述 149
6.2 解決信號同調問題的方位估測技術 150
6.2.1 Spatial Smoothing Technique with CMUSIC or PSB 150
6.2.2 Partial Henkel approximation method 154
6.3 解決信號同調問題之多重波束成型技術介紹 155
6.4 模擬分析 165
6.5 結論 174
第七章 解決隨機週期頻率誤差之強健式波束成型技術 175
7.1 簡介 175
7.2 問題描述 175
7.3 現有對抗RCFE的方法介紹 176
7.3.1 Subspace Projection Method 176
7.3.2 Conventional Method 177
7.3.3 Huang’s Method 177
7.4 解決RCFE問題之新式波束成型技術 179
7.4.1 Huang’s Method with SVM 179
7.4.2 CMUSIC-SVM 180
7.5 模擬分析 180
7.6 結論 186
第八章 總結與未來研究方向 187
REFERENCE 190

[1]B. D. Van Veen and K. M. Buckley, "Beamforming: A versatile approach to spatial filtering, " IEEE ASSP Magazine, pp. 4-24, Apr. 1998.
[2]L. C. Godara, "Application of antenna arrays to mobile communication, partII: beamforming and direction-of-arrival considerations, " Proceedings of the IEEE, vol. 85, pp. 1195-1245, Aug. 1997.
[3]P. W. Howells, "Explorations in Fixed and adaptive Resolution at GE and SURC, " IEEE Trans. Antennas Propagat., vol. AP-24, pp. 575-584, Sep. 1976.
[4]S. P. Applebaum and D. J. Chapman, "Adaptive Arrays, " IEEE Trans. Antenna Propagat., vol. AP-24, no. 5, pp. 650-662, Sep. 1976.
[5]B. Windrow and S. D. Strearns, ADAPTIVE SIGNAL PROCESSING, Prentice Hall, Englewood Gliffs, NEW YORK, 1988.
[6]R. T. Comptom, Jr., ADAPTIVE ANTENNA, CONCEPT AND PERFORMANCE, Englewood Gliffs, NEW YORK, 1988.
[7]R. A. Monzingo and T. W. Miller, Introduction to Adaptive Arrays. New York: Wiley, 1980.
[8]Q. Wu and K. M. Wong, "Blind adaptive beamforming for cyclostationary signals," Signal Processing, IEEE Transactions on , vol. 44, no. 11, pp. 2757-2767, Nov. 1996.
[9]J.-H. Lee, Y.-T. Lee, W.-H. Shih, "Efficient robust adaptive beamforming for cyclostationary signals," Signal Processing, IEEE Transactions on , vol. 48, no. 7, pp. 1893-1901, Jul. 2000.
[10]J.-H Lee, C.-C. Huang, "Robust cyclic adaptive beamforming using a compensation method, " Signal Processing, vol. 92, no. 4, pp. 954-962, Apr. 2012.
[11]J.-H. Lee, C.-C. Huang, "Blind Adaptive Beamforming for Cyclostationary Signals: A Subspace Projection Approach," Antennas and Wireless Propagation Letters, IEEE , vol. 8, pp. 1406-1409, 2009.
[12]M. Wax, T. Kailath, "Detection of signals by information theoretic criteria," Acoustics, Speech and Signal Processing, IEEE Transactions on , vol. 33, no. 2, pp. 387-392, Apr. 1985.
[13]J. Zhang, G. Liao, J. Wang, "Robust direction finding for cyclostationary signals with cycle frequency error, " Signal Processing, vol. 85, issue. 12, pp. 2386-2393, Dec. 2005.
[14]W. Wang, R. Wu, and J. Liang, "A novel diagonal loading method for robust adaptive beamforming," Progress In Electromagnetics Research C, vol. 18, pp. 245-255, 2011.
[15]F. Vincent, O. Besson, "Steering vector errors and diagonal loading," Radar, Sonar and Navigation, IEE Proceedings , vol. 151, no. 6, pp. 337-343, Dec. 2004
[16]Gu. J., "Robust beamforming based on variable loading," Electronics Letters , vol. 41, no. 2, pp. 55-56, Jan. 2005.
[17]C.-C. Huang and J.-H. Lee, "Robust adaptive beamforming using a fully data-dependent loading technique," Progress In Electromagnetics Research B, vol. 37, pp. 307-325, 2012.
[18]J. –H. Lee, Y.-T. Lee, "Robust adaptive array beamforming for cyclostationary signals under cycle frequency error," Antennas and Propagation, IEEE Transactions on , vol. 47, no. 2, pp. 233-241, Feb. 1999.
[19]黃家成, "Techniques for Adaptive Array Beamforming Under Scenario Mismatch, " 國立臺灣大學電信工程學研究所博士論文, Jul. 2012.
[20]V. N. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
[21]Santamaria, I.; Pantaleon, C.; Vielva, Luis; Ibanez, J., "Blind equalization of constant modulus signals using support vector machines," Signal Processing, IEEE Transactions on , vol. 52, no. 6, pp. 1773-1782, Jun. 2004.
[22]駱文城, "Robust Array beamforming Using Support Vector Machines Under Non-ideal Environments, " 國立臺灣大學電信工程學研究所碩士論文, Jan. 2013.
[23]Ramon, M.M.; Nan Xu; Christodoulou, C.G., "Beamforming using support vector machines," Antennas and Wireless Propagation Letters, IEEE , vol. 4, no. , pp.439-442, 2005.
[24]Gaudes, C.C.; Santamaria, I.; Via, J.; Gomez, E.M.M.; Paules, T.S., "Robust Array Beamforming With Sidelobe Control Using Support Vector Machines," Signal Processing, IEEE Transactions on , vol. 55, no. 2, pp. 574-584, Feb. 2007.
[25]F. Perez-Cruz, A. Navia-Vazquez, P. Alarcon-Diana, and A. Artes-Rodriguez, "An IRWLS procedure for SVR, ". In Proc. EUPSICO 2000, Tampere, Finland, vol. 2, pp. 833-839., Sep. 2000.
[26]F. Perez-Cruz, C. Bousono-Calzon, A. Artes-Rodriguez, "Convergence of the IRWLS procedure to the support vector machine solution,"Neural Comput., vol. 17, pp.7-18, Jan. 2005.
[27]Boyd, Stephen Poythress, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
[28]L. Chang and C.-C. Yeh, "Performance of DMI and eigenspace-based beamformers," Antennas and Propagation, IEEE Transactions on , vol. 40, no. 11, pp. 1336-1347, Nov. 1992.
[29]J.-H. Lee, C.-C. Wang, K.-P. Cheng, "Robust adaptive array beamforming under steering angle mismatch, " Signal processing, vol.86, issue 2, pp. 296-309, Feb. 2006.
[30]鄭光鵬, "在非理想環境下的強健式可適性多重波束成型技術, " 國立臺灣大學電信工程學研究所碩士論文, Jun. 2003.
[31]M. Wax, T. Kailath, "Detection of signals by information theoretic criteria," Acoustics, Speech and Signal Processing, IEEE Transactions on , vol. 33, no. 2, pp. 387-392, Apr. 1985.
[32]B. G. Agee, S. V. Schell, and W. A. Gardner, "Spectral self-coherence restoral: a new approach to blind adaptive signal extraction using antenna arrays," Proceedings of the IEEE, vol. 78, pp. 753-767, Apr. 1990.
[33]Er, M. -H; Ng, B.C., "A new approach to robust beamforming in the presence of steering vector errors," Signal Processing, IEEE Transactions on , vol. 42, no. 7, pp. 1826-1829, Jul. 1994.
[34]Schell, Stephan V., et al. "Cyclic MUSIC algorithms for signal-selective direction estimation." Acoustics, Speech, and Signal Processing, 1989. ICASSP-89., 1989 International Conference on. IEEE, 1989.
[35]T. J. Shan and T. Kailath, "Adaptive beamforming for coherent signals and interference, " IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. 38, no. 3, pp. 527-536, Jun. 1985.
[36]K. M. Duvall, "Signal cancellation phenomena in adaptive antenna: causes and cures" IEEE Trans. On Antennas and Propagation, vol. 30, no. 3, pp. 469-478, May 1982.
[37]T. J. Shan , M. Wax and T. Kailath, "On spatial smoothing for direction-of-arrival estimation of coherent signals, " IEEE Trans. Acoust., Speech, and Signal Processing, vol. 33, pp. 806-811, Aug. 1985.
[38]Yung-Ting Lee and Ju-Hong Lee, "Direction-finding methods for cyclostationary signals in the presence of coherent sources," Antennas and Propagation, IEEE Transactions on , vol. 49, no. 12, pp. 1821-1826, Dec. 2001.
[39]Ju-Hong Lee, Yung-Ting Lee, "A novel direction-finding method for cyclostationary signals", Signal Processing, vol. 81, issue 6, pp. 1317-1323, Jun. 2001.
[40]W. A. Gardner, W. A. Brown, III, and C,-K. Chen, "Spectral correlation of modulated signals: Part II – digital modulation, " IEEE Trans. Communications, vol. 36, pp. 595-601, Jun. 1987.
[41]R. O. Schmidt, "Multiple emitter location and signal parameter estimation, " IEEE Trans. Antennas and Propagation, vol. 34, pp. 276-280, Mar. 1986.
[42]J. Capon, "High-resolution frequency-wavenumber spectrum analysis, " Proceedings of the IEEE, vol. 57, no. 8, pp. 1408-1418, Aug. 1969.
[43]O. L. Frost III, " Analgorithm for linearly constraines adaptive array processing, "Proceedings of the IEEE, vol. 60, no. 8, pp. 926-935, Aug. 1972.
[44]W. A. Gardner, "Exploitation of spectral redundancy in cyclostationary signals, " Signal Processing Magazine, IEEE. vol. 8, pp.14-36, Apr. 1991.
[45]J. -H. Lee and C. –C. Huang, "Robust adaptive beamforming for multiple signals of interest with cycle frequency error, " EURASIP Journal on Advances in Signal Processing, vol. 2010, pp. 1-7, Dec. 2010.
[46]Y. –T. Lee and J. –H. Lee, "Robust adaptive aray beamforming with random error in cycle frequency, " IEE Proceedings-Radar, Sonar and Navigation, vol. 148, no. 4, pp. 193-199, Aug. 2001.
[47]Gibra I. N., Probability and statistical inference for scientists and engineers, Prentice Hall, 1973.
[48]H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Teory, John and Wiley Sons, Inc., New York, U.S.A., 2002.
[49]詹皓翔, "Adaptive Array Signal Processing using Cyclostationary property under Non-ideal Situations, " 國立臺灣大學電信工程學研究所碩士論文, Jun. 2008.