采用随机矩阵理论的水声阵列SMI-MVDR空间谱估计技术
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摘要
对角加载MVDR技术是一种经典的空间谱估计技术,在水声阵列信号处理中有着广泛的应用。该技术之所以具有较好的性能是由于其通过对角加载使样本协方差矩阵的特征值分散度减小。提出了基于随机矩阵理论的MVDR空间谱估计技术,具体思路是利用随机矩阵特征值的极限性质实现样本协方差矩阵噪声的抑制,以达到类似对角加载能够实现的特征值分散度减小的效果。仿真表明所提出的方法与对角加载方法达到了同样的目的,且当快拍数一定,而信噪比由小变大时,该方法可以达到与对角加载MVDR技术相当的性能;当信噪比设为定值,快拍数由小变大时,其与对角加载技术具有相同的DOA估计成功概率变化趋势,且在小样本情况下,此方法优势较为明显。
Minimum variance distortionless response(MVDR) with diagonal loading is a conventional spatial spectrum estimation method,it has a wide application in underwater acoustic array signal processing. The good performance of the above method is attributed to it reduce the eigenvalue spread of sample covariance matrix by diagonal loading. The underwater acoustic array sampling matrix inversion(SMI) minimum variance distortionless response(MVDR) beamforming technique is proposed based on random matrix theory(RMT),limit properties of RMT eigenvalue is used to noise suppression of sample covariance matrix,in order ot reach the same performance as diagonal loading,namely reducing the eigenvalue spread of sample covariance matrix. Simulation results show that the proposed method has achieved the same performance as diagonal loading,as a certain number of snapshots and signal to noise ratio(SNR)from small to large. At the same time,when the number of snapshots from small to large,and SNR set value,it has the same trends of success probability of DOA estimation,and in the case of small sample,the advantages of the proposed method are obvious.
Minimum variance distortionless response(MVDR) with diagonal loading is a conventional spatial spectrum estimation method,it has a wide application in underwater acoustic array signal processing. The good performance of the above method is attributed to it reduce the eigenvalue spread of sample covariance matrix by diagonal loading. The underwater acoustic array sampling matrix inversion(SMI) minimum variance distortionless response(MVDR) beamforming technique is proposed based on random matrix theory(RMT),limit properties of RMT eigenvalue is used to noise suppression of sample covariance matrix,in order ot reach the same performance as diagonal loading,namely reducing the eigenvalue spread of sample covariance matrix. Simulation results show that the proposed method has achieved the same performance as diagonal loading,as a certain number of snapshots and signal to noise ratio(SNR)from small to large. At the same time,when the number of snapshots from small to large,and SNR set value,it has the same trends of success probability of DOA estimation,and in the case of small sample,the advantages of the proposed method are obvious.
引文
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[2]CAPON J.High-resolution frequency-wavenumber spectrum analysis[J].Proceedings of the IEEE,1969,57(8):1408-1418.
[3]乔永雯.大孔径拖线阵的自适应波束形成研究[D].西安:西北工业大学,2007:34-37.
[4]CARLSON B D.Covariance matrix estimation errors and diagonal loading in adaptive arrays[J].Aerospace and Electronic Systems,IEEE Transactions on,1988,24(4):397-401.
[5]许林.高维协方差矩阵结构检验[D].长春:东北师范大学,2014:1-2.
[6]曾杏元.生成于四种流形上的大维随机矩阵的谱分布[D].长沙:中南大学,2013:1-6.
[7]王小英.大维样本协方差矩阵的线性谱统计量的中心极限定理[D].长春:东北师范大学,2009:2-8.
[8]李冰娜.基于RMT去噪法股票投资组合风险优化研究[D].哈尔滨:哈尔滨工业大学,2013:45-46.
[9]鄢社锋,马远良.传感器阵列波束优化设计及应用[M].北京:科学出版社,2009:53-62.