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.