Blind adaptation of stable discrete-time IIR filters in state-space form

Blind deconvolution consists of extracting a source sequence and impulse response of a linear system from their convolution. In the presence of system zeros close to the unit circle, which give rise to very long impulse responses, infinite-impulse-response (IIR) adaptive structures are of use, whose adaptation should be carefully designed in order to guarantee stability. In this paper, we propose a blind-type discrete-time IIR adaptive filter structure realized in state-space form that, with a suitable parameterization of its coefficients, remains stable. The theory is first developed for a two-pole filter, whose numerical behavior is investigated via numerical experiments. The proposed structure/adaptation theory is then extended to a multipole structure realized as a cascade of two-pole filters. Computer-based experiments are proposed and discussed, which aim at illustrating the behavior of the filter cascade on several cases of study. The numerical results obtained show the proposed filters remain stable during adaptation and provide satisfactory deconvolution results