A Novel Blind Source Separation Algorithm using Bussgang Criterion and Natural Gradient

Abstract

Objectives: In this paper, a novel algorithm based on Transform Domain Least Mean Square (TDLMS) is proposed for Blind Source Separation (BSS). The proposed algorithm is compared with several other BSS algorithms in detail and the results are discussed extensively. Methods/Statistical Analysis: To solve the problem of BSS employing the present approach, the ordinary gradient used in conventional LMS algorithm is replaced by natural gradient on the Stiefel manifold. The natural gradient is computed from a cost function based on Bussgang criterion. The proposed algorithm is compared with previously reported LMS type and Recursive Least Square (RLS) type algorithms for four different performance criteria – cross–talk error convergence, harmonic distortion in recovered signals, average deviation from orthogonality of demixing matrix and time complexity. Findings: Using simulations it is found that the proposed algorithm has best cross-talk error-convergence and least harmonic distortion as compared to other algorithms. However, the average deviation from orthogonality for demixing matrix and average simulation time for the proposed algorithm are comparable to LMS-type algorithms and estimates 35% as compared to RLS-type algorithms. Application/Improvements: The use of natural gradient and the pre-whitening process improves the performance of the algorithm. This algorithm is applied to separate signals from its mixture.Keywords: Bussgang Criterion, Bind Source Separation (BSS), Cost-Function, LMS type BSS, Natural Gradient, RLS type BSS