Estimation of the complex-valued mixing matrix by single-source-points detection with less sensors than sources

ABSTRACT This paper essentially considers the direction‐of‐arrival (DOA) estimation of far‐field source signals in the underdetermined blind separation, where the mixing matrix is complex‐valued. By distinguishing single‐source‐points (SSPs) from multi‐source‐points in the time‐frequency domain, a novel estimation algorithm is proposed based on the detection of SSPs, where only single source contributes and samples all correspond to one of the mixing column vectors. To further enhance the estimation accuracy, a modified version of the proposed algorithm is also presented, which utilizes the probability density distribution of the already detected SSPs and reselects those reliable SSPs with most likely probabilities. Finally, the mixing matrix as well as the DOAs can be obtained by performing the K‐means clustering algorithm on samples at selected SSPs. The results of numerical simulations validate the efficiency of both the two estimation algorithms. One of the outstanding superiorities for the SSPs‐based idea is that it can distinguish multiple DOAs using only two sensors; the other is that it relaxes the signal sparsity requirement to allow SSPs to merely occur at a small number of time‐frequency locations. Copyright © 2011 John Wiley & Sons, Ltd. Using only two sensors, both the proposed algorithm and the modified algorithm can distinguish multiple directions of arrival whenever the source number increases from 3 to 6. Their estimation accuracy is acceptable, and the root mean square of the modified algorithm is especially satisfying, which can stay less than 1° even for the six sources case.