Improved Combined Step-size Sign Subband Adaptive Filter Algorithms with Variable Mixing Factors

This paper proposes improved combined step-size sign subband adaptive filter (ICSS-SSAF) algorithms with variable mixing factors robust to non-Gaussian noises such as impulsive noise. The CSS scheme is adopted to resolve a trade-off problem of step size in the SSAF, combining two adaptive filters with a large step size for a fast convergence rate and a small step size for low steady-state misalignment. Variable mixing factors (VMFs), whose values are changed at every iteration, are introduced to combine the two adaptive filters. To design the VMFs, a modified sigmoidal or arctangent function is employed. They are updated indirectly to minimize the power of approximated system output error, unlike the conventional algorithm using the $\ell_{1}$ norm of the error vector composed of error signals divided by subbands. The recursive forms of VMFs are acquired by adopting the gradient method. The simulation results show that the proposed algorithms perform better than conventional algorithms in system identification scenarios.

1. Introduction

In the signal processing, various filters are utilized to estimate an unknown system and predict the signals [1] –[4]. Among them, adaptive filtering algorithms have been studied and applied to various fields such as channel estimation, network echo cancellation, active noise control, and biosignal processing [5] –[8]. Among them, the least mean square (LMS) and the normalized least mean square (NLMS) algorithms are widely utilized because of their simple structure and good performance [9] –[12]. However, the LMS-type algorithms have a slow convergence rate when the input is highly correlated. Affine projection (AP) algorithms that use previous input signals together are proposed to overcome the defect of LMS-type algorithms. The AP algorithms have a faster convergence rate than the LMS-type algorithms when the input is correlated.