Stability And Performance Of Adaptive Algorithms For Multichannel Blind Separation And Deconvolution

The problem of blind source separation is reviewed and the properties of stability and performance of the classic adap# tive algorithms are derived. In case of an unstable separat# ing solution, a stabilization procedure is proposed. These #ndings are then extended to the problems of single-channel and multichannel blind deconvolution. It is shown that the algorithms for all these problems can be stabilized for any situation of nonlinearities and source distributions. 1 INTRODUCTION In the Multi-Channel Blind Deconvolution #MCBD# prob# lem we observe a signal vector x = #x1;x 2;x 3;::: ;x N # T that is formed from zero-mean source signals s = #s1 ;s 2;s 3;:::;s N # T by mixing and convolution #9#. Mathe# matically,inthez-domain this is represented by x#z#=A#z#s#z# ; #1# where A#z# is an invertible N # N matrix of polynomi# als. The goal is to recover the sources through the demix# ing#deconvolution process u#z#=W#z#x#z#=W#z#A#z#s#z#: #2# The N # N matrix W#z# is such that..