Coefficient-Gradient-Based Individualized Stepsize Adaptation Mechanism for Robust System Identification

Abstract

To efficiently reduce the impact of the trading-off between the convergence rate and the quality of identifying a system, and also to improve the robustness of the algorithm against unknown sparsity levels, a Modified Absolute Weighted Input using Log function (MAWILOG) for NLMS algorithm is proposed. The essence of the proposed algorithm is to assign, individually, each coefficient of the adaptive filter a variable stepsize that adapts according to a Log-term that takes advantage of the input power and the input signal underlying each filter coefficient, and adapts to the gradient value of each coefficient magnitude. Due to these attributes, the proposed approach outperforms the proportionate NLMS (PNLMS)-family regardless of sparsity level that is achieved by using the gradient of each coefficient individually to allocate large stepsize values for high gradient coefficients without directly inserting a sparse-aware constraint. Additionally, this technique is capable of overcoming the high computational complexity and high steady-state mean-square-deviation of the (PNLMS)-family. Simulation results of the proposed algorithm versus the comparable algorithms such as the NLMS, PNLMS, improved PNLMS, block-sparse PNLMS, and block-sparse IPNLMS are presented. Results have demonstrated that the proposed algorithm outperforms others in maintaining the lowest steady-state mean-square-deviation while attaining a fast convergence rate under various types of systems.