Least Mean Square Algorithm with Application to Improved Adaptive Sparse Channel Estimation

Least mean square (LMS) based adaptive algorithms have been attracted much attention since their low computational complexity and robust recovery capability. To exploit the channel sparsity, LMS-based adaptive sparse channel estimation methods, e.g., L1-norm LMS or zero-attracting LMS (sparse LMS or ZA-LMS), reweighted zero attracting LMS (RZA-LMS) and Lp-norm LMS (LP-LMS), have been proposed based on Lp-norm constraint (0 ≤ p ≤ 1). However, the above methods cannot exploit channel sparse structure information fully. To further improve estimation performance, in this paper, we introduce a L0-norm LMS (L0-LMS) algorithm with application sparse channel estimation to full take advantage of the sparsity. In addition, due to LMS-based channel estimation methods have a common drawback which is sensitive to the scaling of random training signal. Therefore, it is very hard to choose a proper learning rate to achieve robust estimation performance. To solve this problem, we propose several improved adaptive sparse channel estimation methods by using normalized LMS algorithm (NLMS), which normalizes the power of input signal, with different sparse penalties, e.g., Lp-norm and L0-norm. Computer simulation results demonstrate the advantage of the proposed channel estimation methods in estimation performance. Keyword Least Mean Square (LMS); Adaptive Sparse Channel Estimation; Normalized LMS (NLMS); Sparse Penalty; Compressive Sensing (CS).