Multichannel blind deconvolution of nonminimum-phase systems using filter decomposition

In this paper, we present a new filter decomposition method for multichannel blind deconvolution of nonminimum-phase systems. With this approach, we decompose a doubly finite impulse response filter into a cascade form of two filters: a causal finite impulse response (FIR) filter and an anticausal FIR filter. After introducing a Lie group to the manifold of FIR filters, we discuss geometric properties of the FIR filter manifold. Using the nonholonomic transform, we derive the natural gradient on the FIR manifold. By simplifying the mutual information rate, we present a very simple cost function for blind deconvolution of nonminimum-phase systems. Subsequently, the natural gradient algorithms are developed both for the causal FIR filter and for the anticausal FIR filter. Simulations are presented to illustrate the validity and favorable learning performance of the proposed algorithms.