Multichannel blind deconvolution and equalization using the natural gradient

Multichannel deconvolution and equalization is an important task for numerous applications in communications, signal processing, and control. We extend the efficient natural gradient search method of Amari, Cichocki and Yang (see Advances in Neural Information Processing Systems, p.752-63, 1995) to derive a set of on-line algorithms for combined multichannel blind source separation and time-domain deconvolution/equalization of additive, convolved signal mixtures. We prove that the doubly-infinite multichannel equalizer based on the maximum entropy cost function with natural gradient possesses the so-called "equivariance property" such that its asymptotic performance depends on the normalized stochastic distribution of the source signals and not on the characteristics of the unknown channel. Simulations indicate the ability of the algorithm to perform efficient simultaneous multichannel signal deconvolution and source separation.