低信噪比下相干信号的DOA估计的白噪声滤除方法

在波达方向估计中，“相干”和“信噪比”一直引人关注。相干会使多重信号分类等算法失效，究其原因就是信源协方差矩阵的秩亏缺。低信噪比使阵列协方差矩阵的主次特征值区分困难，造成信号和噪声的子空间划分错误。针对相干，人们往往都是从“解相干”的角度出发，通过各种手段使信源的协方差矩阵能够满秩，但并未对秩亏缺特性加以利用。基于此，本文给出了一种在低信噪比下对相干源的波达方向估计的噪声消除方法，在仅有加性白噪声的环境下，利用相干信号协方差矩阵不能满秩的特点，通过求解方程组，用求的值代替估计的协方差矩阵的相关对角元素（即对角加载处理），置换被噪声污染的对角元素，进而可以滤除掉白噪声的影响。仿真结果证实了方法的有效性。 

A White Noise Filtering Method for DOA Estimation of Coherent Signals under Low SNR

The coherence and signal-to-noise ratio (SNR) are always more attractive on the studies of the direction-of-arrival (DOA) estimation. The coherence disables traditional algorithm such as multiple signal classification (MUSIC) which is caused by deficient-rank of the covariance matrix of the source. It is difficult to distinguish the primary and the secondary eigenvalue after eigenvalue decomposition (EVD) of the array covariance matrix because of the decreased SNR, and low-SNR will lead to faulty subspace partition of signal and noise. According to coherence, the traditional way is based on decoherence and to obtain the full rank covariance matrix of the coherent signals by all means, which are not taking the advantage of this mathematical characteristics. Based on this, in the paper, we propose a white noise filtering method for the DOA estimation of completely coherent or partially coherent sources under low SNR environments. Only the additive white noise is considered here, firstly, we can demarcate a number of diagonal matrices in the array covariance matrix. According to that the rank of the coherent signals covariance matrix is not full, each determinant of the diagonal matrices is equal to zero, and we have related equations which correspond to the determinants. By resolving the determinant equations, one can obtain new diagonal elements which do not involve the noise components. Then, through substituting the new diagonal elements for original diagonal elements (i.e. diagonal loading processing), we can obtain the new array covariance matrix without noise components. Finally, the DOA can be estimated further by means of forward-backward spatial smoothing (FBSS) and MUSIC or some other algorithms. Simulation results confirm the validity of the proposed method.