Novel On-Line Adaptive Learning Algorithms for Blind Deconvolution Using the Natural Gradient Approach

Abstract

Blind deconvolution is an important task for numerous applications in control, signal processing, and communications. In this paper, the efficient natural gradient [Amari et. al. (1996)] or relative gradient [Cardoso and Laheld (1996)] is extended to derive a set of on-line adaptive algorithms for single channel and combined multichannel linear blind source separation and time-domain deconvolution/equalization of additive, convolved signal mixtures. The single-channel algorithms are based on Bussgang blind error criteria, and the multichannel algorithm is based on a modified maximum entropy formulation. Both algorithms possess the so-called “equivariance property᾿ [Cardoso and Laheld (1996)] such that their convergence properties are independent of the mixing characteristics of the unknown channel. Simulations indicate the abilities of the proposed algorithms to perform single-channel or simultaneous multichannel signal deconvolution and source separation.