Robust regularized blind system identification with application to adaptive speech dereverberation

The normalized multichannel frequency-domain least-mean square (NMCFLMS) algorithm is a prominent method for blind identification of multichannel acoustic systems. However, the NMCFLMS algorithm relies on a constant, determined by a block of microphone signals, to define the regularization parameter. This setup makes the algorithm sensitive to variations in speech segments and noise conditions. In this paper, we propose a variable regularization parameter that incorporates key factors, such as signal-to-noise ratio, output signal power, and filter length, to enhance the robustness of the algorithm against additive noise and the non-stationary nature of speech. Additionally, we introduce a mechanism to update the regularization parameter based on the mean-squared error of the adaptive filter, improving the ability of the algorithm to track time-varying systems. The proposed variable regularization NMCFLMS algorithm is then applied to speech dereverberation using the multichannel input-output inverse theorem method. Simulation results, using room impulse responses measured in real acoustic environments, demonstrate the effectiveness of the approach in both multichannel blind identification and speech dereverberation.