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.

Underdetermined Blind Source Separation from Time-delayed Mixtures Based on Prior Information Exploitation

“…The estimated mixing matrix is  as in (41), with E A equals to -19.5298dB. [20] and the algorithms proposed by Reju [16] and Lihui [18]. When the SNR increases, the estimation errors of all the algorithms reduce.…”

“…Among the existing algorithms, Single-Source-Point (SSP) detection [16][17][18] is a kind of simple and efficient method for mixing matrix estimation, which achieves good performance in both over and underdetermined cases. Specifically, it sets no conditions on the stationarity, independence or non-Gaussianity of the sources, which made it be widely used.…”

“…In general, Reju's method is simple and practicable, but it works only when the elements of mixing matrix are real-valued, which limits their applications. Lihui et al [18] determined another criterion to identify SSPs. After that, binary masking and K-means clustering methods are implemented to get the clustering centers.…”

Underdetermined Blind Source Separation of Synchronous Orthogonal Frequency Hopping Signals Based on Single Source Points Detection

“…Since the mixing matrix of FH signals is complex-valued, some methods that deal with complex-valued mixing matrix estimation are discussed. Li and Nie considered the complex-valued mixing matrix estimation problem in [ 35 , 36 ] based on SSPs detection. Li introduced that the normalizations of coefficients of the Vandermonde mixing matrix were equal to one and the corresponding mixing coefficients could be calculated by utilizing a matrix inverse operation, so the mixing matrix estimation could be estimated by k-means clustering algorithm [ 35 ].…”

“…Li and Nie considered the complex-valued mixing matrix estimation problem in [ 35 , 36 ] based on SSPs detection. Li introduced that the normalizations of coefficients of the Vandermonde mixing matrix were equal to one and the corresponding mixing coefficients could be calculated by utilizing a matrix inverse operation, so the mixing matrix estimation could be estimated by k-means clustering algorithm [ 35 ]. A similar theorem was introduced based on the inherent property of the Vandermonde mixing matrix in [ 36 ].…”