Int J Performability Eng ›› 2020, Vol. 16 ›› Issue (9): 1374-1382.

### A Square-Root Variable Step Size with a lp-Norm Penalty LMS Algorithm for Sparse Channel Estimation

Aihua Zhanga,*, Wanming Haob, Qiyu Zhouc, and Bing Ninga

1. aSchool of Electronic and Information Engineering, Zhongyuan University of Technology, Zhengzhou, 450007, China;
bSchool of Information Engineering, Zhengzhou University, Zhengzhou, 450001, China;
cSchool of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China
• Submitted on  ;  Revised on  ; Accepted on
• Contact: * E-mail address: zhah@zut.edu.cn

Abstract: To improve the performance of the channel estimation in the cascaded scenario, we propose a sparsity-aware LMS algorithm by using a new cost function with a variable step size and lp norm constraint. The step size is updated according to the square root of the estimated error each iteration, which allows the adaptive filter to track the changes in the channel to produce a small steady-state error. By exploiting the sparsity of the channels, the proposed algorithm integrates the lp norm penalty, which imposes a zero attraction of the sparse channel coefficients. Next, the convergence performance of the proposed algorithm is analyzed, and the stability condition is derived. Our theoretical analysis shows that the proposed algorithm effectively decreases the amount of mis-adjustment and improves the channel estimation accuracy. Finally, the simulation results demonstrate that the proposed algorithm can converge quickly, while its performance outperforms that of the conventional LMS-based identification algorithm.