非圆信号参数估计方法研究
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摘要
非圆信号是现代无线通信中常见的一种信号，例如AM、MASK、UQPSK、BPSK、MSK、GMSK和OQPSK信号。本文研究非圆信号的参数估计技术，包括非圆信号的TDOA估计、基于非相参阵列的非圆信号DOA估计、以及非圆信号的稳健Capon波束形成。与圆信号情况下只利用信号的相关统计信息相比，非圆信号参数估计研究的关键在于如何联合利用信号的相关和共轭相关统计信息来提高参数估计的性能。本文的主要工作概括如下：
1.在高斯非圆复信号和高斯圆噪声的模型下推导了TDOA估计的最大似然算法和CRB。与互相关和共轭互相关算法相比，最大似然算法更全面的利用了非圆信号的二阶统计信息，因此在非圆信号情况下有更好的估计性能。同时，针对非圆信号提出了一种改进传统循环算法的方案，新方案可以同时利用信号的循环相关和共轭循环相关信息。
2.从信息论的角度出发，在高斯和拉普拉斯两种实信号假设下对比了基于联合熵和互信息两个准则的实信号TDOA估计算法。然后，在非圆高斯复信号和圆高斯复噪声的模型下推导了基于互信息准则的TDOA估计算法。
3.研究了基于非相参阵列的非圆信号渐进最优二阶DOA估计算法。首先，在非圆高斯复信号和圆高斯噪声的假设下推导了非相参阵列DOA估计的最大似然算法和闭式CRB。接着，提出了改进的广义最小二乘算法，此算法对高斯或非高斯圆信号都是渐进最小方差的二阶算法。随后，提出了一种非圆信号的渐进最小方差二阶算法。
4.研究了非相参阵列的MUSIC类DOA估计算法，提出了只使用第一协方差矩阵的子阵加权MUSIC算法（w-MUSIC），并把w-MUSIC算法扩展到非圆信号。同时，对比分析了w-MUSIC算法和文献[85]中MUSIC算法的渐进估计方差。
5.针对SOI和干扰信号都可能是非圆信号的情况提出了稳健的自适应波束形成方法NC-RCB。NC-RCB不但对阵列方向向量误差和协方差矩阵估计误差是稳健的，同时对SOI非圆系数的估计误差也是稳健的。在SOI是非圆信号的情况下，NC-RCB与只利用第一协方差矩阵的稳健Capon波束形成方法相比具有显著的性能提升。
Noncircular signals are usually encountered in radio communications, such as AM,MASK, UQPSK, BPSK, MSK, GMSK and OQPSK signals. This dissertation addressesthe parameter estimation issue for noncircular signals, including time difference ofarrival (TDOA) estimation for noncircular signals, direction of arrival (DOA)estimation for noncircular signals with multiple noncoherent subarrays, and robustCapon beamforming for noncircular signals. Compared to utilizing only thecross-correlation statistics of a signal in the case of circular signals, the key point of theresearch on parameter estimation for noncircular signals is how to jointly utilize thecross-correlation and conjugate cross-correlation statistics of a noncircular singal toimprove the estimation perforamce. The main work and contibutions of this dissertationare as follows.
1. The maximum likelihood (ML) estimator and the Cramer–Rao lower bound(CRB) of TDOA estimation for Gaussian noncircular signals in Gaussian circular noiseis derived. Compared to the cross-correlation and conjugate cross-correlation estimators,the ML estimator utilizes the second-order statistics (SOS) information of a noncircularsignal more comprehensively and thus has better performance. Then, based on thecyclostationarity of man-made signals, a scheme to modify the traditionalsignal-selective TDOA methods for noncircular signals is proposed. This schemeexploits simultaneously the information contained in both the cyclic cross-correlation(CCC) and the conjugate CCC of a noncircular signal.
2. For real-valued Gaussian and Laplacian signal models, the TDOA estimatorsusing the two information-theoretic measures, joint entropy and mutual information(MI), have been compared. Then, a method employing the MI to exploit thesecond-order (SO) noncircularity of noncircular signals has been proposed.
3. The asymptotically-minimum-variance (AMV) SO estimation of DOA fornoncircular sources with multiple noncoherent subarrays has been addressed. First, theML estimator and the closed-form CRB for this problem are derived for noncircularGaussian complex signals and circular Gaussian complex noise. Subsequently, themodified generalized least-squre estimator is proposed, which is anasymptotically-minimum-variance (AMV) SO estimator for both Gaussian and non-Gaussian circular sources. Then, an AMV SO estimator for noncircular sources ispresented.
4. The MUSIC-like DOA estimation algorithms for multiple noncoherent subarrayshave been studied. A weighted MUSIC (w-MUSIC) algorithm for noncoherentsubarrays using only the first covariance matrix is proposed, and it is subsequentlyextended for noncircular sources. The asymptotic performance of the w-MUSICalgorithm and a previously introduced MUSIC algorithm in [85] for noncoherentsubarrays are analyzed and compared.
5. A robust Capon beamformer for noncircular signals (termed NC-RCB) has beenproposed for the generalized case with possibly noncircular signal-of-interesting (SOI)and/or noncircular interferences. The NC-RCB exploits the SO noncircularity of theSOI and interferences simultaneously and is robust against the errors in the steeringvector, sample covariance matrix and noncircular parameter of the SOI. For noncircularSOI, the NC-RCB shows distinctly better performance than the robust Caponbeamformer using only the first covariance matrix.
1.在高斯非圆复信号和高斯圆噪声的模型下推导了TDOA估计的最大似然算法和CRB。与互相关和共轭互相关算法相比，最大似然算法更全面的利用了非圆信号的二阶统计信息，因此在非圆信号情况下有更好的估计性能。同时，针对非圆信号提出了一种改进传统循环算法的方案，新方案可以同时利用信号的循环相关和共轭循环相关信息。
2.从信息论的角度出发，在高斯和拉普拉斯两种实信号假设下对比了基于联合熵和互信息两个准则的实信号TDOA估计算法。然后，在非圆高斯复信号和圆高斯复噪声的模型下推导了基于互信息准则的TDOA估计算法。
3.研究了基于非相参阵列的非圆信号渐进最优二阶DOA估计算法。首先，在非圆高斯复信号和圆高斯噪声的假设下推导了非相参阵列DOA估计的最大似然算法和闭式CRB。接着，提出了改进的广义最小二乘算法，此算法对高斯或非高斯圆信号都是渐进最小方差的二阶算法。随后，提出了一种非圆信号的渐进最小方差二阶算法。
4.研究了非相参阵列的MUSIC类DOA估计算法，提出了只使用第一协方差矩阵的子阵加权MUSIC算法（w-MUSIC），并把w-MUSIC算法扩展到非圆信号。同时，对比分析了w-MUSIC算法和文献[85]中MUSIC算法的渐进估计方差。
5.针对SOI和干扰信号都可能是非圆信号的情况提出了稳健的自适应波束形成方法NC-RCB。NC-RCB不但对阵列方向向量误差和协方差矩阵估计误差是稳健的，同时对SOI非圆系数的估计误差也是稳健的。在SOI是非圆信号的情况下，NC-RCB与只利用第一协方差矩阵的稳健Capon波束形成方法相比具有显著的性能提升。
Noncircular signals are usually encountered in radio communications, such as AM,MASK, UQPSK, BPSK, MSK, GMSK and OQPSK signals. This dissertation addressesthe parameter estimation issue for noncircular signals, including time difference ofarrival (TDOA) estimation for noncircular signals, direction of arrival (DOA)estimation for noncircular signals with multiple noncoherent subarrays, and robustCapon beamforming for noncircular signals. Compared to utilizing only thecross-correlation statistics of a signal in the case of circular signals, the key point of theresearch on parameter estimation for noncircular signals is how to jointly utilize thecross-correlation and conjugate cross-correlation statistics of a noncircular singal toimprove the estimation perforamce. The main work and contibutions of this dissertationare as follows.
1. The maximum likelihood (ML) estimator and the Cramer–Rao lower bound(CRB) of TDOA estimation for Gaussian noncircular signals in Gaussian circular noiseis derived. Compared to the cross-correlation and conjugate cross-correlation estimators,the ML estimator utilizes the second-order statistics (SOS) information of a noncircularsignal more comprehensively and thus has better performance. Then, based on thecyclostationarity of man-made signals, a scheme to modify the traditionalsignal-selective TDOA methods for noncircular signals is proposed. This schemeexploits simultaneously the information contained in both the cyclic cross-correlation(CCC) and the conjugate CCC of a noncircular signal.
2. For real-valued Gaussian and Laplacian signal models, the TDOA estimatorsusing the two information-theoretic measures, joint entropy and mutual information(MI), have been compared. Then, a method employing the MI to exploit thesecond-order (SO) noncircularity of noncircular signals has been proposed.
3. The asymptotically-minimum-variance (AMV) SO estimation of DOA fornoncircular sources with multiple noncoherent subarrays has been addressed. First, theML estimator and the closed-form CRB for this problem are derived for noncircularGaussian complex signals and circular Gaussian complex noise. Subsequently, themodified generalized least-squre estimator is proposed, which is anasymptotically-minimum-variance (AMV) SO estimator for both Gaussian and non-Gaussian circular sources. Then, an AMV SO estimator for noncircular sources ispresented.
4. The MUSIC-like DOA estimation algorithms for multiple noncoherent subarrayshave been studied. A weighted MUSIC (w-MUSIC) algorithm for noncoherentsubarrays using only the first covariance matrix is proposed, and it is subsequentlyextended for noncircular sources. The asymptotic performance of the w-MUSICalgorithm and a previously introduced MUSIC algorithm in [85] for noncoherentsubarrays are analyzed and compared.
5. A robust Capon beamformer for noncircular signals (termed NC-RCB) has beenproposed for the generalized case with possibly noncircular signal-of-interesting (SOI)and/or noncircular interferences. The NC-RCB exploits the SO noncircularity of theSOI and interferences simultaneously and is robust against the errors in the steeringvector, sample covariance matrix and noncircular parameter of the SOI. For noncircularSOI, the NC-RCB shows distinctly better performance than the robust Caponbeamformer using only the first covariance matrix.
引文
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