Frequency-domain under-modelled blind system identification based on cross power spectrum and sparsity regularization

Abstract

In room acoustics, under-modelled multichannel blind system identification (BSI) aims to estimate the early part of the room impulse responses (RIRs), and it can be widely used in applications such as speaker localization, room geometry identification and beamforming based speech dereverberation. In this paper we extend our recent study on under-modelled BSI from the time domain to the frequency domain, such that the RIRs can be updated frame-wise and the efficiency of Fast Fourier Transform (FFT) is exploited to reduce the computational complexity. Analogous to the cross-correlation based criterion in the time domain, a frequency-domain cross power spectrum based criterion is proposed. As the early RIRs are usually sparse, the RIRs are estimated by jointly maximizing the cross power spectrum based criterion in the frequency domain and minimizing the l 1 -norm sparsity measure in the time domain. A two-stage LMS updating algorithm is derived to achieve joint optimization of these two targets. The experimental results in different under-modelled scenarios demonstrate the effectiveness of the proposed method.