Cross-correlation based under-modelled multichannel blind acoustic system identification with sparsity regularization

Abstract

In room acoustics, the under-modelled blind system identification (BSI) problem arises when the identified room impulse response (RIR) is shorter than the real one. Conventional BSI methods can perform poorly under these circumstances. In this paper, we propose an algorithm for multichannel BSI in under-modelled situations. Instead of minimizing the cross-relation error, a new optimization criterion is formulated, which is based on maximizing a cross-correlation criterion. We show that under the statistical model of reverberant signals, the cross-correlation based criterion helps to reduce the adverse effects of system under-modelling on BSI. Moreover, the optimization problem is regularized by including a sparsity term in the cost function. The optimization problem is finally solved based on the split Bregman method in the least-mean-square (LMS) framework. Experimental results show that the proposed method can perform effectively in the under-modelled situations in which conventional methods fail.