恒定束宽波束形成及宽带DOA估计应用研究
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摘要
高分辨方位估计是现代信号处理的重要内容之一，随着微电子集成及数字技术的发展，其在声纳、雷达等许多领域有着很好的应用前景。高分辨算法最初都是在窄带信号的假设条件下提出的，由于宽带信号含有更丰富的信息，有利于目标检测、参量估计和目标特征提取，因此，对于宽带信号处理的研究越来越多。恒定束宽波束形成和宽带源方位估计是宽带阵列信号处理的重要研究内容。论文从实际工程应用的角度出发，系统研究了恒定束宽波束形成和宽带高分辨阵列信号处理的相关理论和实现技术，主要研究内容包括：
1．系统概要地论述了阵列信号处理的基本概念和理论，给出了宽带阵列信号处理的模型。
2．研究了宽带恒定束宽波束形成器的两种设计思想，并重点分析了计算阵元权系数的最小二乘法和空间重采样法，比较了二者的性能，分析了恒定束宽波束形成器的频域和时域实现原理。
3．研究了宽带高分辨阵列信号处理的典型算法——相干信号子空间算法(CSSM：Coherent Signal Subspace Method)。分析了CSSM方法分辨相干源的实质，即通过频域平均消除了相关函数矩阵的奇异性；分析比较了几种不同聚焦矩阵对算法性能的影响。
4．研究了宽带信号波束域处理技术。分析比较了波束域处理与阵元域处理的分辨能力以及估计性能，并从降低分辨门限和估计方差角度考虑，给出了转换矩阵的构造方法。
对于转换矩阵(恒定束宽波束形成矩阵)正交化过程对恒定束宽性能的损失提出了一种补偿措施，即在正交化过程中对不同频率对应的波束进行加权，称之为加权正交化恒定束宽波束形成矩阵。并且仿真实验验证了加权正交化恒定束宽波束形成矩阵既具有良好的恒定束宽性能，又具有与一般正交化恒定束宽波束形成矩阵相近的分辨性能和估计性能。
5．完成了恒定束宽波束形成以及宽带源方位估计算法在DSP硬件系统中的实现。分析了系统的硬件结构，介绍了ADSP21160的结构特点和软件设计方法。采用模块化设计方法，完成了系统软件的设计、调试。针对系统对于算法实时性的要求，对于计算量集中的子模块设计了合理的实现方案。进行了基于DSP硬件系统的仿真实验和实验室实验，实现了3路恒定束宽波束形成和宽带
相干源波束域DOA估计的实时处理。
As an important part of the modern signal processing, high-resolution direction of arrival estimation technique has a promising perspective in many fields such as radar and sonar, with the development of the microelectronic and digital techniques. The analysis of wideband signals will improve the resolution capability and accuracy of estimation, for more frequency components can be synthetically used. Constant beam-width beam-former and direction of arrival of sources for wideband signals are the important parts of wideband array signal processing. Aiming at the practical applications on engineering, the dissertation studies the theories and application technologies of constant beam-width beam-former and DOA estimation for wideband signals. The main results and achievements are summarized as follows:
1. The fundamental concepts and theories of array signal processing are discussed summarily, and the model of wideband array signal processing is set up.
2. The two thoughts of designing constant beam-width beam-former are studied, and the least square method and spatial resample method to calculate the weighting coefficients of the array elements are analyzed and compared, and the constant beam-width beam-former is designed, both in frequency and time domains.
3. The typical wideband high-resolution method-the coherent signal subspace method (CSSM) is studied. We analyzed its nature of resolving coherent sources and compared the influence of different focusing matrices. Simulations are conducted to test the performance of these focusing matrices.
4. The wideband beam-space high-resolution technique is studied. The differences on resolution capability and the performance of estimation between beam-space processing and element-space processing are analyzed. Transforming matrices are designed for the consideration of depressing the resolution threshold and estimation variance.
A method is proposed to make for the loss of the orthogonal converting matrix's performance on constant beam-width, that is giving different frequency components different weighing values during orthogonal process, which is called weighted orthogonal converting matrix. Simulation results show that the weighted orthogonal converting matrix not only has good performance on constant
beam-width, but also has the same performance on resolution and estimation as those of common orthogonal converting matrix.
5. The constant beam-width beam-former and wideband DOA estimation algorithms are realized in the DSP hardware systems. The system hardware architecture is analyzed, and the properties of ADSP2116x and the methodology of software development are presented. The system software is developed and debugged in modularization. Reasonable designing scenarios are proposed for the key modules, for the consideration of algorithms' being performed in real time. The simulation results based on the target board show that the system running properly.
1．系统概要地论述了阵列信号处理的基本概念和理论，给出了宽带阵列信号处理的模型。
2．研究了宽带恒定束宽波束形成器的两种设计思想，并重点分析了计算阵元权系数的最小二乘法和空间重采样法，比较了二者的性能，分析了恒定束宽波束形成器的频域和时域实现原理。
3．研究了宽带高分辨阵列信号处理的典型算法——相干信号子空间算法(CSSM：Coherent Signal Subspace Method)。分析了CSSM方法分辨相干源的实质，即通过频域平均消除了相关函数矩阵的奇异性；分析比较了几种不同聚焦矩阵对算法性能的影响。
4．研究了宽带信号波束域处理技术。分析比较了波束域处理与阵元域处理的分辨能力以及估计性能，并从降低分辨门限和估计方差角度考虑，给出了转换矩阵的构造方法。
对于转换矩阵(恒定束宽波束形成矩阵)正交化过程对恒定束宽性能的损失提出了一种补偿措施，即在正交化过程中对不同频率对应的波束进行加权，称之为加权正交化恒定束宽波束形成矩阵。并且仿真实验验证了加权正交化恒定束宽波束形成矩阵既具有良好的恒定束宽性能，又具有与一般正交化恒定束宽波束形成矩阵相近的分辨性能和估计性能。
5．完成了恒定束宽波束形成以及宽带源方位估计算法在DSP硬件系统中的实现。分析了系统的硬件结构，介绍了ADSP21160的结构特点和软件设计方法。采用模块化设计方法，完成了系统软件的设计、调试。针对系统对于算法实时性的要求，对于计算量集中的子模块设计了合理的实现方案。进行了基于DSP硬件系统的仿真实验和实验室实验，实现了3路恒定束宽波束形成和宽带
相干源波束域DOA估计的实时处理。
As an important part of the modern signal processing, high-resolution direction of arrival estimation technique has a promising perspective in many fields such as radar and sonar, with the development of the microelectronic and digital techniques. The analysis of wideband signals will improve the resolution capability and accuracy of estimation, for more frequency components can be synthetically used. Constant beam-width beam-former and direction of arrival of sources for wideband signals are the important parts of wideband array signal processing. Aiming at the practical applications on engineering, the dissertation studies the theories and application technologies of constant beam-width beam-former and DOA estimation for wideband signals. The main results and achievements are summarized as follows:
1. The fundamental concepts and theories of array signal processing are discussed summarily, and the model of wideband array signal processing is set up.
2. The two thoughts of designing constant beam-width beam-former are studied, and the least square method and spatial resample method to calculate the weighting coefficients of the array elements are analyzed and compared, and the constant beam-width beam-former is designed, both in frequency and time domains.
3. The typical wideband high-resolution method-the coherent signal subspace method (CSSM) is studied. We analyzed its nature of resolving coherent sources and compared the influence of different focusing matrices. Simulations are conducted to test the performance of these focusing matrices.
4. The wideband beam-space high-resolution technique is studied. The differences on resolution capability and the performance of estimation between beam-space processing and element-space processing are analyzed. Transforming matrices are designed for the consideration of depressing the resolution threshold and estimation variance.
A method is proposed to make for the loss of the orthogonal converting matrix's performance on constant beam-width, that is giving different frequency components different weighing values during orthogonal process, which is called weighted orthogonal converting matrix. Simulation results show that the weighted orthogonal converting matrix not only has good performance on constant
beam-width, but also has the same performance on resolution and estimation as those of common orthogonal converting matrix.
5. The constant beam-width beam-former and wideband DOA estimation algorithms are realized in the DSP hardware systems. The system hardware architecture is analyzed, and the properties of ADSP2116x and the methodology of software development are presented. The system software is developed and debugged in modularization. Reasonable designing scenarios are proposed for the key modules, for the consideration of algorithms' being performed in real time. The simulation results based on the target board show that the system running properly.
引文
[1] 李贵斌，声纳基阵设计原理，第一版，北京：海洋出版社，1995
[2] 李启虎，声纳信号处理引论，第一版，北京：清华大学出版社，1988
[3] 智婉君、李志舜，“空间重采样法恒定束宽波束形成器设计”，中国船舶科技报告，1997
[4] 程云鹏，矩阵论，第二版，西安，西北工业大学出版社，2000
[5] 张贤达，现代信号处理，北京清华大学出版社，1995
[6] 宗引德、胡广书，数字信号处理，第一版，清华大学出版社，1988
[7] 孙超、李斌，加权子空间拟合算法理论与研究，西北工业大学出版社，1996
[8] 智婉君、李志舜，“宽带源波束域空间谱估计算法”，中国船舶科技报告，1997
[9] 智婉君，“水下宽带阵列信号处理的高分辨技术研究”，西北工业大学博士论文，1998
[10] 陈剑锋，水下高分辨定向关键技术研究，西北工业大学博士学位论文，1999
[11] [美]S．M．凯依 著，黄建国，武延祥，杨世兴 译，现代谱估计原理与应用，北京：科学出版社，1994
[12] 秦洪峰，水下多目标定位关键技术研究，博士论文。
[13] R. O. Schmidt, " A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation ", Ph.D. Dissertation, Stanford University, 1981.
[14] R. Kumaresan and D. W.Tuifts, "Estimation the Angles of Anrrival of Multiple Plane Waves", IEEE Trans. on Aerospace and Electronic Systems, Vol.19, No.l, pp. 134-139,1983.
[15] R. Roy and T. Kailath, "ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques" ,IEEE Trans. ASSP, Vol.37, No.7, pp.984-995,1989.
[16] Bhaskr D. Rao and K. V. S. Hari, "Performance Analysis of Root-MUSIC",IEEE Trans.ASSE., Vol. 37,pp. 1939-1949,No. 12,Dec., 1989
[17] Tiejun Shah, Marl Wax and T. Kailath, "On spatial smoothing for direction-of-arrival estimation of coherent signals", IEEE. ASSE Vol.33,No.4,pp.806-811, Aug.,1985
[18] S.Unnikfishna Pillai and Byung Ho Kwon, "Forward/backward spatial smoothing techniques for coherent signal identification", IEEE. ASSE Vol.37,No.1,pp.8-15, Jan.,1989.
[19] Marl Wax, Tiejun Shan and T. Kailath, "Spatio-Temporal Spectral Analysis by Eigenstructure Methods", IEEE Trans ASSE Vol.32, pp.817-827, Aug. 1984.
[20] H. Wang and M. Kaveh, "Coherent Signal-Subspce Processing for the Detection and Estimation of Angles of Multiple Wide-Band Sources ", IEEE Trans. ASSP, Vol.33, No.4, pp.823-831,Aug., 1985.
[21] Yoram Bresler, Vellenki U. Reddy and Thomas Kailath, "Optimum Beamforming for Coherent Signal and Interferences", IEEE Trans ASSP, Vol.36, No.6, pp.833-843, Jum.,1988.
[22] H. Hung and M. Kaveh, "A New Class of Focusing Matrices for Coherent Signal-Subspace Method ", IEEE ICASSP, pp.2284-2287,1988.
[23] H. Hung and M. Kaveh, "Focusing Matrices for Coherent Signal-Subspace Processing ",IEEE Trans ASSP,Vol.36,No.8,pp. 1272-1281,1988.
[24] H. Hung and C. Mao, "Robust Coherent Signal-Subspace Processing for Direction-of-Arrival Estimation of Wideband Sources", IEE Proc. Radar, Sonar & Navigation, Vol. 141, No.5, pp256-262, Oct. 1994.
[25] Hong and A. H. Tewfik, "Focusing Matrices for Wide-Band Array Processing with no a Priori Angle Estimation", IEEE ICASSR,pp. Ⅱ493-500,1992.
[26] A. Doron & A. J. Weiss, " On Focusing Matrices for Wide-band Array Processing ", IEEE Trans. on SE., Vol.42,pp. 1295-1302,No.6,Jun., 1992
[27] H. Hung & C. Mao, "Robust Coherent Signal-Subspace Processing for Direction-of-Arrival Estimation of Wide-Band Sources", IEEE Proc. Radar, Sonar &Navigation, Vol. 141, No., 5,pp256-262, Oct.1994
[28] Ng, M. H. Er and C. Kot, "A MUSIC Approach for Estimation of Direction of Arrival of Multiple Narrowband and Broadband ",Signal Processing 40,pp.319-323, 1994
[29] Harry B. Lee and Michael S. Wenrovitz, "Resolution Threshold of Beamspace MUSICfor Two Closely Spaced Emitters ", IEEE Trans ASSP, Vol.38,No.9, pp. 1545-1559,Sep.,1990.
[30] Xiao Liang Xu and Kevin M. Buckley, "Statistical Performance Comparison of MUSIC in Element-Space and Beam-Space ",IEEE ICASSEpp.2124-2127,1989
[31] Hagit Messer, Yosef Rockah and Peter M. Schultheiss, "Localization in the presence of Coherent Interference ",IEEE Trans ASSR, Vol.38,No. 12,pp.2025-2032, Dec., 1990
[32] Harry L. Van Trees, Optimum Array Processing, John Wiley & Sons,Inc. 2002
[33] Wax and I.Ziskind, "Detection of the Number Coherent Signals by the MDL Principle ",IEEE Trans.ASSEVol.37,pp. 1190-1196,1991
[34] Eyaal Doron and Miriam A. Doron, "Coherent Wideband Array Processing ",IEEE ICASSP. pp. Ⅱ1497-500,1992
[35] Hui Liu and Fu Li, "Statistical Evaluation of Beam-Space Direction-of-Arrival Estimations ",IEEE ICASSP. pp. Ⅴ389-392,1992
[36] M. Wax and T. Kailath, "Detection of Signals by Information Theoretic Criteria", IEEE Trans ASSP, Vol.33,No.2,pp.387-392,Apr., 1985
[37] H. Wang and M. Kaveh, "On the Performance of Signal-Subspace Processing——Part Ⅱ: Coherent Wide-Band Systems", IEEE Trans ASSP ,Vol.35, No.2, pp.1583-1591, Nov., 1987
[38] 陈剑锋，黄建国，张群飞，一种宽容的宽带加权聚焦定向算法，声学学报，25卷1期，2000．1
[39] 杨益新，卓颉，孙超，朱治富，基于恒定束宽波束输出的宽带相干源高分辨测向，声学技术，20卷1期，2001
[40] Analog devices, inc., ADSP-21160 SHARK DSP hardware reference, 2002.3
[41] Analog devices, inc., ADSP-21160 SHARK DSP instruction set reference, 1999.11
[42] Analog devices, inc., VisualDSP＋＋3.0 assembler and preprocessor manual for SHARK DSPs, 2003.1
[43] Analog devices, inc., VisualDSP＋＋3.0 C/C＋＋ compiler and library manual for SHARK DSPs, 2003.1
[44] Analog devices, inc., VisualDSP＋＋3.0 linker and utilities manual for SHARK DSPs, 2003.1
[45] 彭启琮，DSP与实时数字信号处理，电子科技大学出版社，1995.4
[46] 彭启琮，李玉柏，DSP技术，电子科技大学出版社，1997.11
[47] [法]H．J．努斯鲍默著，胡光锐译，快速傅里叶变换和卷积算法，上海科学技术文献出版社，1984.12
[48] [英]J．H．威尔金森著，石钟慈，邓健新译，代数特征值问题，科学出版社，2001
[2] 李启虎，声纳信号处理引论，第一版，北京：清华大学出版社，1988
[3] 智婉君、李志舜，“空间重采样法恒定束宽波束形成器设计”，中国船舶科技报告，1997
[4] 程云鹏，矩阵论，第二版，西安，西北工业大学出版社，2000
[5] 张贤达，现代信号处理，北京清华大学出版社，1995
[6] 宗引德、胡广书，数字信号处理，第一版，清华大学出版社，1988
[7] 孙超、李斌，加权子空间拟合算法理论与研究，西北工业大学出版社，1996
[8] 智婉君、李志舜，“宽带源波束域空间谱估计算法”，中国船舶科技报告，1997
[9] 智婉君，“水下宽带阵列信号处理的高分辨技术研究”，西北工业大学博士论文，1998
[10] 陈剑锋，水下高分辨定向关键技术研究，西北工业大学博士学位论文，1999
[11] [美]S．M．凯依 著，黄建国，武延祥，杨世兴 译，现代谱估计原理与应用，北京：科学出版社，1994
[12] 秦洪峰，水下多目标定位关键技术研究，博士论文。
[13] R. O. Schmidt, " A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation ", Ph.D. Dissertation, Stanford University, 1981.
[14] R. Kumaresan and D. W.Tuifts, "Estimation the Angles of Anrrival of Multiple Plane Waves", IEEE Trans. on Aerospace and Electronic Systems, Vol.19, No.l, pp. 134-139,1983.
[15] R. Roy and T. Kailath, "ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques" ,IEEE Trans. ASSP, Vol.37, No.7, pp.984-995,1989.
[16] Bhaskr D. Rao and K. V. S. Hari, "Performance Analysis of Root-MUSIC",IEEE Trans.ASSE., Vol. 37,pp. 1939-1949,No. 12,Dec., 1989
[17] Tiejun Shah, Marl Wax and T. Kailath, "On spatial smoothing for direction-of-arrival estimation of coherent signals", IEEE. ASSE Vol.33,No.4,pp.806-811, Aug.,1985
[18] S.Unnikfishna Pillai and Byung Ho Kwon, "Forward/backward spatial smoothing techniques for coherent signal identification", IEEE. ASSE Vol.37,No.1,pp.8-15, Jan.,1989.
[19] Marl Wax, Tiejun Shan and T. Kailath, "Spatio-Temporal Spectral Analysis by Eigenstructure Methods", IEEE Trans ASSE Vol.32, pp.817-827, Aug. 1984.
[20] H. Wang and M. Kaveh, "Coherent Signal-Subspce Processing for the Detection and Estimation of Angles of Multiple Wide-Band Sources ", IEEE Trans. ASSP, Vol.33, No.4, pp.823-831,Aug., 1985.
[21] Yoram Bresler, Vellenki U. Reddy and Thomas Kailath, "Optimum Beamforming for Coherent Signal and Interferences", IEEE Trans ASSP, Vol.36, No.6, pp.833-843, Jum.,1988.
[22] H. Hung and M. Kaveh, "A New Class of Focusing Matrices for Coherent Signal-Subspace Method ", IEEE ICASSP, pp.2284-2287,1988.
[23] H. Hung and M. Kaveh, "Focusing Matrices for Coherent Signal-Subspace Processing ",IEEE Trans ASSP,Vol.36,No.8,pp. 1272-1281,1988.
[24] H. Hung and C. Mao, "Robust Coherent Signal-Subspace Processing for Direction-of-Arrival Estimation of Wideband Sources", IEE Proc. Radar, Sonar & Navigation, Vol. 141, No.5, pp256-262, Oct. 1994.
[25] Hong and A. H. Tewfik, "Focusing Matrices for Wide-Band Array Processing with no a Priori Angle Estimation", IEEE ICASSR,pp. Ⅱ493-500,1992.
[26] A. Doron & A. J. Weiss, " On Focusing Matrices for Wide-band Array Processing ", IEEE Trans. on SE., Vol.42,pp. 1295-1302,No.6,Jun., 1992
[27] H. Hung & C. Mao, "Robust Coherent Signal-Subspace Processing for Direction-of-Arrival Estimation of Wide-Band Sources", IEEE Proc. Radar, Sonar &Navigation, Vol. 141, No., 5,pp256-262, Oct.1994
[28] Ng, M. H. Er and C. Kot, "A MUSIC Approach for Estimation of Direction of Arrival of Multiple Narrowband and Broadband ",Signal Processing 40,pp.319-323, 1994
[29] Harry B. Lee and Michael S. Wenrovitz, "Resolution Threshold of Beamspace MUSICfor Two Closely Spaced Emitters ", IEEE Trans ASSP, Vol.38,No.9, pp. 1545-1559,Sep.,1990.
[30] Xiao Liang Xu and Kevin M. Buckley, "Statistical Performance Comparison of MUSIC in Element-Space and Beam-Space ",IEEE ICASSEpp.2124-2127,1989
[31] Hagit Messer, Yosef Rockah and Peter M. Schultheiss, "Localization in the presence of Coherent Interference ",IEEE Trans ASSR, Vol.38,No. 12,pp.2025-2032, Dec., 1990
[32] Harry L. Van Trees, Optimum Array Processing, John Wiley & Sons,Inc. 2002
[33] Wax and I.Ziskind, "Detection of the Number Coherent Signals by the MDL Principle ",IEEE Trans.ASSEVol.37,pp. 1190-1196,1991
[34] Eyaal Doron and Miriam A. Doron, "Coherent Wideband Array Processing ",IEEE ICASSP. pp. Ⅱ1497-500,1992
[35] Hui Liu and Fu Li, "Statistical Evaluation of Beam-Space Direction-of-Arrival Estimations ",IEEE ICASSP. pp. Ⅴ389-392,1992
[36] M. Wax and T. Kailath, "Detection of Signals by Information Theoretic Criteria", IEEE Trans ASSP, Vol.33,No.2,pp.387-392,Apr., 1985
[37] H. Wang and M. Kaveh, "On the Performance of Signal-Subspace Processing——Part Ⅱ: Coherent Wide-Band Systems", IEEE Trans ASSP ,Vol.35, No.2, pp.1583-1591, Nov., 1987
[38] 陈剑锋，黄建国，张群飞，一种宽容的宽带加权聚焦定向算法，声学学报，25卷1期，2000．1
[39] 杨益新，卓颉，孙超，朱治富，基于恒定束宽波束输出的宽带相干源高分辨测向，声学技术，20卷1期，2001
[40] Analog devices, inc., ADSP-21160 SHARK DSP hardware reference, 2002.3
[41] Analog devices, inc., ADSP-21160 SHARK DSP instruction set reference, 1999.11
[42] Analog devices, inc., VisualDSP＋＋3.0 assembler and preprocessor manual for SHARK DSPs, 2003.1
[43] Analog devices, inc., VisualDSP＋＋3.0 C/C＋＋ compiler and library manual for SHARK DSPs, 2003.1
[44] Analog devices, inc., VisualDSP＋＋3.0 linker and utilities manual for SHARK DSPs, 2003.1
[45] 彭启琮，DSP与实时数字信号处理，电子科技大学出版社，1995.4
[46] 彭启琮，李玉柏，DSP技术，电子科技大学出版社，1997.11
[47] [法]H．J．努斯鲍默著，胡光锐译，快速傅里叶变换和卷积算法，上海科学技术文献出版社，1984.12
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