Robust Normalized Subband Adaptive Filter Algorithm with a Sigmoid-Function-Based Step-Size Scaler and Its Convex Combination Version

Zijie Shen,Li Yang,Lin Tang,Laurent Mevel

doi:10.1155/2021/9924179

Abstract

In this paper, by inserting the logarithm cost function of the normalized subband adaptive filter algorithm with the step-size scaler (SSS-NSAF) into the sigmoid function structure, the proposed sigmoid-function-based SSS-NSAF algorithm yields improved robustness against impulsive interferences and lower steady-state error. In order to identify sparse impulse response further, a series of sparsity-aware algorithms, including the sigmoid L0 norm constraint SSS-NSAF (SL0-SSS-NSAF), sigmoid step-size scaler improved proportionate NSAF (S-SSS-IPNSAF), and sigmoid L0 norm constraint step-size scaler improved proportionate NSAF (SL0-SSS-IPNSAF), is derived by inserting the logarithm cost function into the sigmoid function structure as well as the L0 norm of the weight coefficient vector to act as a new cost function. Since the use of the fix step size in the proposed SL0-SSS-IPNSAF algorithm, it needs to make a trade-off between fast convergence rate and low steady-state error. Thus, the convex combination version of the SL0-SSS-IPNSAF (CSL0-SSS-IPNSAF) algorithm is proposed. Simulations in acoustic echo cancellation (AEC) scenario have justified the improved performance of these proposed algorithms in impulsive interference environments and even in the impulsive interference-free condition.

Highlights

Adaptive filtering is famous for its numerous practical applications, such as system identification, acoustic echo cancellation, channel equalization, and signal denoising [1,2,3,4,5]
Simulations in the acoustic echo cancellation (AEC) scenario with impulsive interference have justified the improved performance of these proposed algorithms
While whenever impulsive interferences occur, the subband error signal ei,D(k) will be very large, so does the value of JSSS−normalized SAF (NSAF)(k), and S(k) approaches to constant one, which result in the termination of iteration of the SL0-SSSNSAF algorithm. is demonstrates that the proposed sigmoid-function-based algorithms retain the outstanding performance of the original step-size scaler (SSS)-NSAF algorithm in the noise-free impulsive condition and possess strong robustness against impulsive noise

Summary

Introduction

Adaptive filtering is famous for its numerous practical applications, such as system identification, acoustic echo cancellation, channel equalization, and signal denoising [1,2,3,4,5]. The main disadvantage of these two algorithms is that they have a slower convergence speed in case the input signal is colored. For settling this issue, the subband adaptive filter (SAF) structure has been presented. Is is because the colored input signal can be decomposed into multiple mutually independent white subband signals by the analysis filter bank [6]. Based on this structure and by solving a multiple-constraint optimization problem, the normalized SAF (NSAF) algorithm has been generated to speed up the convergence rate of the NLMS algorithm [7]. For improving the convergence behavior of the NSAF algorithm in a sparse system, a family of proportionate NSAF algorithms [10, 11], such as proportionate NSAF (PNSAF), μ-law proportionate NSAF (MPNSAF), and improved proportionate NSAF (IPNSAF), have been proposed, wherein each tap of the filter is updated independently by allocating different step sizes which are in proportion to the magnitude of the estimated filter coefficient

Results

Discussion

Conclusion