Improved least mean square algorithm with application to adaptive sparse channel estimation

Least mean square (LMS)-based adaptive algorithms have attracted much attention due to their low computational complexity and reliable recovery capability. To exploit the channel sparsity, LMS-based adaptive sparse channel estimation methods have been proposed based on different sparse penalties, such as ℓ1-norm LMS or zeroattracting LMS (ZA-LMS), reweighted ZA-LMS, and ℓp-norm LMS. However, the aforementioned methods cannot fully exploit channel sparse structure information. To fully take advantage of channel sparsity, in this paper, an improved sparse channel estimation method using ℓ0-norm LMS algorithm is proposed. The LMS-type sparse channel estimation methods have a common drawback of sensitivity to the scaling of random training signal. Thus, it is very hard to choose a proper learning rate to achieve a robust estimation performance. To solve this problem, we propose several improved adaptive sparse channel estimation methods using normalized LMS algorithm with different sparse penalties, which normalizes the power of input signal. Furthermore, Cramer-Rao lower bound of the proposed adaptive sparse channel estimator is derived based on prior information of channel taps' positions. Computer simulation results demonstrate the advantage of the proposed channel estimation methods in mean square error performance.