阵列信号处理在雷达和移动通信中的应用研究
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摘要
阵列信号处理是信号处理的一个年青的分支，属于现代信号处理的重要研究内容之一，其应用范围很广，可用于雷达、声呐、通信、地震勘察、射电天文和医用成像等众多领域。阵列信号处理是将一组传感器在空间的不同位置按一定规则布置形成的传感器阵列（尽管采用的传感器的类型可以不同，如天线、水听器、听地器、超声探头、X射线检测器，但是传感器的功能是相同的，它是连接信号处理器和感兴趣的空间纽带），用传感器阵列发射能量和（或）接收空间信号，获得信号源的观测数据并加以处理。阵列信号处理的目的是从这些观测数据中提取信号的有用特征，获取信号源的属性等信息。
目前，阵列信号处理在雷达及移动通信等领域有着广泛而重要的应用。在相控阵雷达体制中，自适应波束形成技术在抑制杂波干扰方面起着关键的作用。在移动通信中，基于阵列信号处理的波达方向估计技术，使移动通信进入一个崭新的阶段。
本论文首先介绍阵列信号处理的基础知识。在此基础上，着重讨论阵列波束形成技术，非理想线性阵列的雷达信号波达方向和多普勒频率估计，均匀圆形阵列的信号波达方向估计和复杂信号的波达方向及参数估计等四方面内容。这些内容都是阵列信号处理领域的研究热点。它们无论对阵列信号处理的理论发展还是实际应用，都有重要的意义。
目前，人们普遍关注在阵列响应矢量未知情况下，自适应波束形成问题，即盲自适应波束形成技术。本文第一方面介绍了最基本的阵列波束形成方法，
即最小均方误差波束形成器，线性约束最小方差波束形成器和基于特征空间的波束形成器（ESB）。在此基础上，提出一个基于特征空间的盲自适应波束形成算法。此算法首先根据高分辨波达方向估计方法，估计信号源的波达方向，然后以此方向形成约束导向矢量，进而计算出ESB波束形成算法的最优权矢量，最后，对期望目标形成笔状波束。此算法能够有效地抑制信号的对消现象，并且能够应用于在波束中有多个期望信号的场合。
当阵列存在各种误差时，一般高分辨波达方向估计方法（如MUSIC）的估计性能严重下降。在阵列存在各种误差情况下，如何高质量地估计信号源的波达方向是一个有待于解决的问题。本文第二方面重点讨论了这个问题，给出了三种估计方法：一是当阵元存在幅度误差时，估计信源的二维方向角和多普勒频率；二是当阵元存在一般阵列误差时，估计信源的一维方向角和多普勒频率；三是当阵元存在一般阵列误差时，估计信源的二维方向角和多普勒频率。这些方法首先应用DOA矩阵法或时空DOA矩阵法将多个信源分离，然后再采用总体最小二乘法估计单个信源的波达方向。三种估计方法相比较，第三种估计方法，其估计精度最高，对增益幅度误差和相位误差具有很强的鲁棒性，但是，对位置误差特别敏感。第二种估计方法，其估计精度次之，对增益幅度误差和相位误差具有一定的鲁棒性，并且在一定范围内，对位置误差不敏感。第一种估计方法，其估计精度最差，只对一定范围的增益幅度误差具有一定的鲁棒性。但是，此方法不需要解模糊运算。总之，对于这三种估计方法，且俯仰角和锥角的估计精度好于多普勒频率估计精度。
均匀圆形阵列具有许多优异特性，如何利用均匀圆阵的优异特性，估计信号波达方向也是人们关注的问题。在第三方面，本文首先针对雷达回波信号，给出两种波达方向和多普勒频率的估计方法，即基于相位模式激励法的间接法和基于均匀圆阵阵列流形的直接法。间接法是采用相位模式激励法将均匀圆阵的阵列流形变换成与均匀线阵的阵列流形相似的形式，然后再使用适用于均匀线阵的估计方法。直接法是直接利用均匀圆阵阵列流形的特点，采用适用于均匀圆阵的高分辨估计方法。通过理论分析和实验可知，直接利用均匀圆阵阵列流形，可以保留UCA阵列流形的优点，从而提高了估计精度，因而，直接法的估计精度明显高于变换法的估计精度。其次，本文基于均匀圆阵阵列流形，提出了多个信源的移动通信信号二维方向角的估计方法。此方法首先应用时空DOA矩阵法将多个信源分离，然后采用最小二乘法估计单个信源的波达方向。此方
法有很强的抗噪能力，尤其在低信噪比的情况下，仍能保持较好的估计精度。此方法对阵元的幅相误差都具有很强的鲁棒性。最后，针对均匀圆阵存在一般阵列误差的情况，提出单个信源的信号二维方向角估计方法。并分析了阵元幅相误差对空间角频率估计的影响，推导出估计值的渐近方差表达式，从理论上揭示了幅相误差与估计误差的关系。建立了阵元位置误差与载波频率扰动的模型，求出了一般阵列误差的协方差矩阵，采用加权总体最小二乘法估计信号二维方向角。此方法具有估计精度高，对阵列误差鲁棒性强的特点。并且各项性能都接近于CRB。
在许多实际应用场合，信源不能被假定为点目标信号源，如在移动通信中的角度扩展信号源或在雷达中的线性调频信号源。本文第四方面重点讨论了这个问题，给出了基于均匀圆阵的时变幅度信号源，角度扩展信号源和线性调频信号的波达方向及参数估计方法，并分析估计的性能。首先讨论了时变幅度信号源的波达方向互相关估计方法，并推出了有限和大样本两种情况下的互相关估计协方差函?
Array signal processing is a new field of signal processing, and it is a very important content of modern signal processing. Array signal processing has wide engineering application such as radar, sonar, weather predicting, land and ocean exploring, seismic and biomedical signal processing etc. On different spatial positions, a few of sensors are placed by some rules so that these sensors form an array of sensors. Though the type of these sensors may be different, such as antenna, sound sensor under water, sound sensor under earth, ultrasonic sensor, X-radial sensor etc, but the function of these sensors is the same, that is, the interested spatial information is connected to signal processor. By the array of sensors, the electromagnetic wave is sent or the spatial signal is received. So the information of spatial sources is gain by signal processor. The process above is called as array signal processing. The aim of array signal processing is to acquire the useful information of spatial sources form received signal.
Now, array signal processing has wide and important application in radar and mobile communication. To a radar being provided with phase control array, adaptive beamforming plays a very important role in noise and interference suppression. To a mobile communication, DOA estimation is a key technology in separation of signal sources.
In this paper, the basic theory of array signal processing is first introduced. Then, the four part contents, namely adaptive beamforming of array, DOA and Doppler frequency estimation of sources with non-ideal uniform line array (ULA), DOA estimation of sources with uniform circular array (UCA), DOA estimation or parameter estimation of complex signal sources, are detailedly discussed. These researches have important effects on the theory and application of array signal processing.
When the array response vector for the desired signal is not known, adaptive beamforming, that is blind adaptive beamforming, is a problem of people’ attention now. In 3rd chapter of this paper, a few of basic beamforming, such as minimum mean square error beamforming, linearly constrained minimum variance beamforming and Eigenspace-Based beamforming (ESB), are first introduced. Then, an algorithm of blind adaptive beamforming is proposed. In this method, the DOA of desired source with unknown array response vector is first estimated. The DOA of desired source is regarded as the constrained steer vector. The optimum weigh vector of ESB is further acquired. Finally, the beamforming to desired signal is formed. The advantage of this method is that it can eliminate the signal cancellation when a desired is contained in the correlation matrix. When there are a few of desired signals in beamforming, this algorithm can be applied.
In presence of general array errors, such as amplitude and phase error of sensors, setting position error of sensors etc, the performance of high-resolution estimator such as MUSIC will degrade drastically and even fail. To estimate DOA of sources in the presence of general array errors still is a difficult problem. The problem is detailedly discussed in 4th chapter. Three estimating algorithms are provided. The first one is the estimation of 2-D angle and Doppler frequency in the presence of gain amplitude errors of sensors. The second one is the estimation of 1-D angle and Doppler frequency in the presence of general array errors. The third one is the estimation of 2-D angle and Doppler frequency in the presence of general array errors. In these algorithms, the DOA matrix method or the time-spatial DOA matrix method firstly separates signal sources. Then, DOA of source is estimated by Total Least Squares. By comparison, the advantages of third algorithm are that the estimating accuracy is the highest of three algorithms and the robusticity to amplitude and phase errors of sensors is strong. But this algorithm is sensitive to setting position errors of sensors. The estimating accuracy of second algorithm and the robusticity to amplitude and phase errors of sensors ar
目前，阵列信号处理在雷达及移动通信等领域有着广泛而重要的应用。在相控阵雷达体制中，自适应波束形成技术在抑制杂波干扰方面起着关键的作用。在移动通信中，基于阵列信号处理的波达方向估计技术，使移动通信进入一个崭新的阶段。
本论文首先介绍阵列信号处理的基础知识。在此基础上，着重讨论阵列波束形成技术，非理想线性阵列的雷达信号波达方向和多普勒频率估计，均匀圆形阵列的信号波达方向估计和复杂信号的波达方向及参数估计等四方面内容。这些内容都是阵列信号处理领域的研究热点。它们无论对阵列信号处理的理论发展还是实际应用，都有重要的意义。
目前，人们普遍关注在阵列响应矢量未知情况下，自适应波束形成问题，即盲自适应波束形成技术。本文第一方面介绍了最基本的阵列波束形成方法，
即最小均方误差波束形成器，线性约束最小方差波束形成器和基于特征空间的波束形成器（ESB）。在此基础上，提出一个基于特征空间的盲自适应波束形成算法。此算法首先根据高分辨波达方向估计方法，估计信号源的波达方向，然后以此方向形成约束导向矢量，进而计算出ESB波束形成算法的最优权矢量，最后，对期望目标形成笔状波束。此算法能够有效地抑制信号的对消现象，并且能够应用于在波束中有多个期望信号的场合。
当阵列存在各种误差时，一般高分辨波达方向估计方法（如MUSIC）的估计性能严重下降。在阵列存在各种误差情况下，如何高质量地估计信号源的波达方向是一个有待于解决的问题。本文第二方面重点讨论了这个问题，给出了三种估计方法：一是当阵元存在幅度误差时，估计信源的二维方向角和多普勒频率；二是当阵元存在一般阵列误差时，估计信源的一维方向角和多普勒频率；三是当阵元存在一般阵列误差时，估计信源的二维方向角和多普勒频率。这些方法首先应用DOA矩阵法或时空DOA矩阵法将多个信源分离，然后再采用总体最小二乘法估计单个信源的波达方向。三种估计方法相比较，第三种估计方法，其估计精度最高，对增益幅度误差和相位误差具有很强的鲁棒性，但是，对位置误差特别敏感。第二种估计方法，其估计精度次之，对增益幅度误差和相位误差具有一定的鲁棒性，并且在一定范围内，对位置误差不敏感。第一种估计方法，其估计精度最差，只对一定范围的增益幅度误差具有一定的鲁棒性。但是，此方法不需要解模糊运算。总之，对于这三种估计方法，且俯仰角和锥角的估计精度好于多普勒频率估计精度。
均匀圆形阵列具有许多优异特性，如何利用均匀圆阵的优异特性，估计信号波达方向也是人们关注的问题。在第三方面，本文首先针对雷达回波信号，给出两种波达方向和多普勒频率的估计方法，即基于相位模式激励法的间接法和基于均匀圆阵阵列流形的直接法。间接法是采用相位模式激励法将均匀圆阵的阵列流形变换成与均匀线阵的阵列流形相似的形式，然后再使用适用于均匀线阵的估计方法。直接法是直接利用均匀圆阵阵列流形的特点，采用适用于均匀圆阵的高分辨估计方法。通过理论分析和实验可知，直接利用均匀圆阵阵列流形，可以保留UCA阵列流形的优点，从而提高了估计精度，因而，直接法的估计精度明显高于变换法的估计精度。其次，本文基于均匀圆阵阵列流形，提出了多个信源的移动通信信号二维方向角的估计方法。此方法首先应用时空DOA矩阵法将多个信源分离，然后采用最小二乘法估计单个信源的波达方向。此方
法有很强的抗噪能力，尤其在低信噪比的情况下，仍能保持较好的估计精度。此方法对阵元的幅相误差都具有很强的鲁棒性。最后，针对均匀圆阵存在一般阵列误差的情况，提出单个信源的信号二维方向角估计方法。并分析了阵元幅相误差对空间角频率估计的影响，推导出估计值的渐近方差表达式，从理论上揭示了幅相误差与估计误差的关系。建立了阵元位置误差与载波频率扰动的模型，求出了一般阵列误差的协方差矩阵，采用加权总体最小二乘法估计信号二维方向角。此方法具有估计精度高，对阵列误差鲁棒性强的特点。并且各项性能都接近于CRB。
在许多实际应用场合，信源不能被假定为点目标信号源，如在移动通信中的角度扩展信号源或在雷达中的线性调频信号源。本文第四方面重点讨论了这个问题，给出了基于均匀圆阵的时变幅度信号源，角度扩展信号源和线性调频信号的波达方向及参数估计方法，并分析估计的性能。首先讨论了时变幅度信号源的波达方向互相关估计方法，并推出了有限和大样本两种情况下的互相关估计协方差函?
Array signal processing is a new field of signal processing, and it is a very important content of modern signal processing. Array signal processing has wide engineering application such as radar, sonar, weather predicting, land and ocean exploring, seismic and biomedical signal processing etc. On different spatial positions, a few of sensors are placed by some rules so that these sensors form an array of sensors. Though the type of these sensors may be different, such as antenna, sound sensor under water, sound sensor under earth, ultrasonic sensor, X-radial sensor etc, but the function of these sensors is the same, that is, the interested spatial information is connected to signal processor. By the array of sensors, the electromagnetic wave is sent or the spatial signal is received. So the information of spatial sources is gain by signal processor. The process above is called as array signal processing. The aim of array signal processing is to acquire the useful information of spatial sources form received signal.
Now, array signal processing has wide and important application in radar and mobile communication. To a radar being provided with phase control array, adaptive beamforming plays a very important role in noise and interference suppression. To a mobile communication, DOA estimation is a key technology in separation of signal sources.
In this paper, the basic theory of array signal processing is first introduced. Then, the four part contents, namely adaptive beamforming of array, DOA and Doppler frequency estimation of sources with non-ideal uniform line array (ULA), DOA estimation of sources with uniform circular array (UCA), DOA estimation or parameter estimation of complex signal sources, are detailedly discussed. These researches have important effects on the theory and application of array signal processing.
When the array response vector for the desired signal is not known, adaptive beamforming, that is blind adaptive beamforming, is a problem of people’ attention now. In 3rd chapter of this paper, a few of basic beamforming, such as minimum mean square error beamforming, linearly constrained minimum variance beamforming and Eigenspace-Based beamforming (ESB), are first introduced. Then, an algorithm of blind adaptive beamforming is proposed. In this method, the DOA of desired source with unknown array response vector is first estimated. The DOA of desired source is regarded as the constrained steer vector. The optimum weigh vector of ESB is further acquired. Finally, the beamforming to desired signal is formed. The advantage of this method is that it can eliminate the signal cancellation when a desired is contained in the correlation matrix. When there are a few of desired signals in beamforming, this algorithm can be applied.
In presence of general array errors, such as amplitude and phase error of sensors, setting position error of sensors etc, the performance of high-resolution estimator such as MUSIC will degrade drastically and even fail. To estimate DOA of sources in the presence of general array errors still is a difficult problem. The problem is detailedly discussed in 4th chapter. Three estimating algorithms are provided. The first one is the estimation of 2-D angle and Doppler frequency in the presence of gain amplitude errors of sensors. The second one is the estimation of 1-D angle and Doppler frequency in the presence of general array errors. The third one is the estimation of 2-D angle and Doppler frequency in the presence of general array errors. In these algorithms, the DOA matrix method or the time-spatial DOA matrix method firstly separates signal sources. Then, DOA of source is estimated by Total Least Squares. By comparison, the advantages of third algorithm are that the estimating accuracy is the highest of three algorithms and the robusticity to amplitude and phase errors of sensors is strong. But this algorithm is sensitive to setting position errors of sensors. The estimating accuracy of second algorithm and the robusticity to amplitude and phase errors of sensors ar
引文
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30、W. A. Gardner. Simplification of MUSIC and ESPRIT by exploitation of cyclostationarity. Proc. IEEE trans.1998, 76(7):845-847.
31、Xu Guanghan. Direction-of-arrival estimation via exploitation of cyclostationarity - a Combination of temporal and spatial processing. IEEE Trans, on SP,1992, 40(7):1775-1785.
32、汪仪林，殷勤业，金梁，姚敏立. 利用信号的循环平稳特性进行相干源的波达方向估计. 电子学报，1999，27(9)：86-89.
33、黄知涛，周一宇，姜文利. 基于循环平稳特性的源信号到达角估计方法. 电子学报，2002, 30(3): 372-375。
34、黄知涛，王炜华，姜文利，周一宇. 基于循环互相关的非相干源信号方向估计方法. 通信学报，2003，24(2)：108-113.
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37、Ju-Hong Lee, Chia-Hsin Tung. Estimating the Bearings of Near-Field Cyclosationary Signals. IEEE Trans., on SP, 2002, 50(1):110-118.
38、A．Belouchrani, M. Amin. Blind Source Separation based on time-frequency signal representation. IEEE Trans, on SP, 1998, 46(11):2888-2898.
39、M. G. Awin. Spatial time–frequency distributions for direction finding and blind source separation. Proc. SPIE: Wavelet Applications IV, 1999, Vol.3723: 62-70.
40、A. Belouchrain, M. Amin. Time–frequency MUSIC. IEEE Signal processing Lett, 1999, 6(5):109-110.
41、Y. Zhang, W. Mu, M. G. Amin. Time-frequency maximum likelihood methods for direction finding. J.Franklin Inst., 2000, 337(4): 483-497.
42、金梁，殷勤业，李盈. 时频子空间拟合波达方向估计. 电子学报，2001，29(1)：71-74.
43、Y. Zhang, W. Mu, G. Amin. Subspace Analysis of Spatial Time-frequency Distribution Matrices. IEEE Trans, on SP, 2001, 49(4):747-759.
44、万群、杨万麟. 基于盲波束形成的分布式目标波达方向估计方法. 电子学报，2000，28(12)：90-93.
45、M. Ghogho, A Swami and T. Sdurrani. Frequency Estimation in the Presence of Doppler spread: Performance Analysis. IEEE Trans on SP, 2001, 49(4): 777-789.
46、O bensson, F vincent, P stoica, A B gershman. Approximate maximum likelihood estimator for array processing in multiplicative noise environments. IEEE Trans on SP, 2000, 48(9):2506-2518.
47、O besson, P stoica. Decoupled estimation of DOA and angular spread for a spatially distributed sources. IEEE Trans on SP, 2000, 48(7): 1872-1882.
48、O besson, P stoica, A B gershman. Simple and accurate direction of arrival estimation in the case of imperfect spatial coherence. IEEE Trans on SP, 2001, 49(4): 730-737.
49、M bengtson, B ottersten. Low-complexity estimation for distributed sources[J]. IEEE Trans on SP, 2000, 48(8): 2185-2194.
50、袁静，万群，彭应宁. 局部散射源参数估计的非线性算子方法，通信学报，2003，24(2)：102-107.
51、S. Shahbazpanahi, S. Valaee, M. H. Bastani. Distributed source localization using ESPRIT algorithm. IEEE Trans .on SP, 2001, 49(10):2169-2178.
52、M. Ghogho, O. Besson, A. Swami. Estimation of directions of arrival of multiple scattered sources. IEEE Trans .on SP, 2001, 49(11): 2467-2480.
53、Q.Y.Yin, R. Newcomb, S. Munjal and L. H. Zou. Relation Between the DOA Matrix Method
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66、E. G. Larsson and P. stoica. High-Resolution Direction Finding: The Missing Data Case. IEEE Trans. on SP, 2001, 49(5):950-958
67、万群，杨万麟. 增益幅度不一致条件下波达方向估计方法. 电子学报，2001，29(6)：730-732
68、陈志群，权太范，赵淑清. 一般阵列误差情况下空时谱分析的研究. 电子学报，2001，29(1)：93-95
69、陶建武，常文秀，石要武，非理想阵列的信号波达方向和多普勒频率估计. 系统工程与电子技术，2003，25(10)：1216-1218
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28、刘全. 一种新的二维快速波达方向估计方法—虚拟累量域波达方向矩阵法. 电子学报，2002，30(3)：351-353.
29、 Wu Q. and Wong K. M. Blind Adaptive Beamforming for cyclostationary Signals. IEEE Trans. On SP, 1996, 44(11): 2757-2767.
30、W. A. Gardner. Simplification of MUSIC and ESPRIT by exploitation of cyclostationarity. Proc. IEEE trans.1998, 76(7):845-847.
31、Xu Guanghan. Direction-of-arrival estimation via exploitation of cyclostationarity - a Combination of temporal and spatial processing. IEEE Trans, on SP,1992, 40(7):1775-1785.
32、汪仪林，殷勤业，金梁，姚敏立. 利用信号的循环平稳特性进行相干源的波达方向估计. 电子学报，1999，27(9)：86-89.
33、黄知涛，周一宇，姜文利. 基于循环平稳特性的源信号到达角估计方法. 电子学报，2002, 30(3): 372-375。
34、黄知涛，王炜华，姜文利，周一宇. 基于循环互相关的非相干源信号方向估计方法. 通信学报，2003，24(2)：108-113.
35、金梁、殷勤业，汪仪林. 广义谱相关子空间拟合DOA估计原理. 电子学报，2000，28(1)：60-63
36、J．Xin, A. Sano. Linear Prediction Approach to Direction Estimation of Cyclostationary Signals in Multipath Environment. IEEE Trans, on SP, 2001, 49(4):710-720.
37、Ju-Hong Lee, Chia-Hsin Tung. Estimating the Bearings of Near-Field Cyclosationary Signals. IEEE Trans., on SP, 2002, 50(1):110-118.
38、A．Belouchrani, M. Amin. Blind Source Separation based on time-frequency signal representation. IEEE Trans, on SP, 1998, 46(11):2888-2898.
39、M. G. Awin. Spatial time–frequency distributions for direction finding and blind source separation. Proc. SPIE: Wavelet Applications IV, 1999, Vol.3723: 62-70.
40、A. Belouchrain, M. Amin. Time–frequency MUSIC. IEEE Signal processing Lett, 1999, 6(5):109-110.
41、Y. Zhang, W. Mu, M. G. Amin. Time-frequency maximum likelihood methods for direction finding. J.Franklin Inst., 2000, 337(4): 483-497.
42、金梁，殷勤业，李盈. 时频子空间拟合波达方向估计. 电子学报，2001，29(1)：71-74.
43、Y. Zhang, W. Mu, G. Amin. Subspace Analysis of Spatial Time-frequency Distribution Matrices. IEEE Trans, on SP, 2001, 49(4):747-759.
44、万群、杨万麟. 基于盲波束形成的分布式目标波达方向估计方法. 电子学报，2000，28(12)：90-93.
45、M. Ghogho, A Swami and T. Sdurrani. Frequency Estimation in the Presence of Doppler spread: Performance Analysis. IEEE Trans on SP, 2001, 49(4): 777-789.
46、O bensson, F vincent, P stoica, A B gershman. Approximate maximum likelihood estimator for array processing in multiplicative noise environments. IEEE Trans on SP, 2000, 48(9):2506-2518.
47、O besson, P stoica. Decoupled estimation of DOA and angular spread for a spatially distributed sources. IEEE Trans on SP, 2000, 48(7): 1872-1882.
48、O besson, P stoica, A B gershman. Simple and accurate direction of arrival estimation in the case of imperfect spatial coherence. IEEE Trans on SP, 2001, 49(4): 730-737.
49、M bengtson, B ottersten. Low-complexity estimation for distributed sources[J]. IEEE Trans on SP, 2000, 48(8): 2185-2194.
50、袁静，万群，彭应宁. 局部散射源参数估计的非线性算子方法，通信学报，2003，24(2)：102-107.
51、S. Shahbazpanahi, S. Valaee, M. H. Bastani. Distributed source localization using ESPRIT algorithm. IEEE Trans .on SP, 2001, 49(10):2169-2178.
52、M. Ghogho, O. Besson, A. Swami. Estimation of directions of arrival of multiple scattered sources. IEEE Trans .on SP, 2001, 49(11): 2467-2480.
53、Q.Y.Yin, R. Newcomb, S. Munjal and L. H. Zou. Relation Between the DOA Matrix Method
and the ESPRIT Method . In Proc. IEEE ISCAS-90, 1990, pp:1561-1564.
54、潘士先. 谱估计和自适应滤波. 北京：北京航空航天大学出版社，1991.
55、陶建武，常文秀，石要武. 递推式空时自适应滤波器的研究. 兵工学报，2004.25(5):
56、O. L. frost. An Algorithm for Linearly Constrained Adaptive Processing. Proc. IEEE, 1972, 60(8):926-935.
57、L.Chang and C.C Yeh. Effect of Pointing Errors on the Performance of the Projection Beamformer. IEEE Trans, Antennas and propagation, 1993, 41(8):1045-1055
58、J. L. Yu and C.C Yeh. Generalized Eigenspace-based Beamformers. IEEE trans on SP 1995, 43(11):2453-2461
59、廖桂生，保铮，张林让. 基于特征结构的自适应波束形成新算法. 电子学报，1998，26(3)：23-26.
60、赵永波，刘茂仓，张守宏. 一种改进的基于特征空间自适应波束形成算法. 电子学报, 2000, 28(6):16-18.
61、张林让，廖桂生，保铮. 基于多普勒信号的盲自适应波束形成技术. 电子学报，1999，27(6)：36-39.
62、陶建武，常文秀，石要武. 预警雷达的盲自适应波束形成新算法. 仪器仪表学报，2003，24(2)：179-182.
63、Henry Cox, Robert M. Zeskind, and Mark M. Owen. Effects of Amplitude and Phase Errors on Linear Predicative Array Processors. IEEE Trans on ASSP, 1988,36(1):10-19.
64、B. Friedlander. A Sensitivity Analysis of the MUSIC Algorithm. IEEE Trans on ASSP 1990,38(10):1740-1751.
65、苏卫民，顾红，倪晋麟等. 通道幅相误差条件下MUSIC空域谱的统计性能. 电子学报，2000，28(6)：105-107。
66、E. G. Larsson and P. stoica. High-Resolution Direction Finding: The Missing Data Case. IEEE Trans. on SP, 2001, 49(5):950-958
67、万群，杨万麟. 增益幅度不一致条件下波达方向估计方法. 电子学报，2001，29(6)：730-732
68、陈志群，权太范，赵淑清. 一般阵列误差情况下空时谱分析的研究. 电子学报，2001，29(1)：93-95
69、陶建武，常文秀，石要武，非理想阵列的信号波达方向和多普勒频率估计. 系统工程与电子技术，2003，25(10)：1216-1218
70、陶建武，石要武，常文秀. 当增益幅度不同时信号二维方向角和多普勒频率的盲估计.航空学报，2002，23(4)：373-376
71、陶建武，石要武，常文秀. 一般阵列误差情况下信号二维方向角和多普勒频率的联合估计. 高技术通讯，2003，13(2)：10-14
72、J. J. Fuchs, On the Application of the Global Matched Filter to DOA Estimation with Uniform Circular Arrays. IEEE Trans. on SP, 2001, 49(4): 702-709
73、C. P. Mathews, M. D. Zoltowski. Eigenstructure Techniques for 2-D Angle Estimation with Uniform Circular Array. IEEE Trans. on SP, 1994, 42(9): 2395-2407
74、黄浩学,吴嗣亮.基于均匀圆阵的信号源DOA和多普勒频率估计算法.电子学报, 2001,29(5):619-621
75、陶建武,石要武,常文秀. 基于均匀圆阵的信号二维方向角和多普勒频率的盲估计. 计量学报, 2003, 24(3):231-235
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