Two-channel variable-step-size forward-and-backward adaptive algorithms for acoustic noise reduction and speech enhancement

This paper addresses the problem of speech enhancement and acoustic noise reduction by adaptive filtering algorithms. Recently, forward-and-backward (FB) blind-source-separation (BSS) structures have been proposed to solve acoustic noise reduction and speech enhancement problems. The FB structures use the least-mean-square (LMS) algorithm in combination with two BSS structures and are implemented with fixed-step-size to control the convergence behavior of the cross-coupling adaptive filters. In this paper, we propose two new two-channel variable-step-size FB algorithms (2C-VSSF and 2C-VSSB) that improve the previous LMS-based algorithm in the transient and the steady-state phases. These two new proposed FB algorithms are based on recursive formulas, which lead to efficient estimation of the optimal step-sizes of the cross-coupling filters. These proposed algorithms show significant improvement in the steady-state and transient mean-square-error (MSE) values. We present simulation results of the proposed 2C-VSSF and 2C-VSSB algorithms that confirm the superiority and good performance in comparison with the original versions, which use fixed-step-sizes.