One optimized LMF algorithm in low SNR

Abstract

There is a need to improve the capability of the adaptive filtering algorithm against Gaussian or multiple types of non-Gaussian noises, time-varying system, and systems with low SNR. In this paper, we propose an optimized least mean absolute fourth (Optimized-LMF) algorithm, especially for a time-varying unknown system with low signal-noise-rate (SNR). The optimal step-size of LMF is obtained by minimizing the mean-square deviation (MSD) at any given moment in time. In addition, the mean convergence and steady-state error of Optimized-LMF are derived. Also the theoretical computational complexity of Optimized-LMF is analyzed. Furthermore, the simulation experiment results of system identification are used to illustrate the principle and efficiency of the Optimized-LMF algorithm. The performance of the algorithm is analyzed mathematically and validated experimentally. Simulation results demonstrate that the proposed Optimized-LMF is superior to the normalized LMF (NLMF) and variable step-size of LMF using quotient form (VSSLMFQ) algorithms.