Norm Constrained Noise-free Algorithm for Sparse Adaptive Array Beamforming

• Published in: Applied Computational Electromagnetics Society journal Vol. 34; no. 5; p. 709
• Main Authors: Shi, Wanlu, Li, Yingsong, Sun, Laijun, Yin, Jingwei, Zhao, Lei
• Format: Journal Article
• Language: English
• Published: Pisa River Publishers 2019
• Subjects: Acceptable noise levels; Adaptive algorithms; Algorithms; Beamforming; Constraints; Error signals; Lagrange multiplier; Mean square values; Sparsity
• ISSN: 1054-4887; 1943-5711

In this paper, a reweighted l1-norm constrained noise-free normalized least mean square (NLMS) (RL1- CNFLMS) algorithm is proposed for dealing with sparse adaptive array beamforming. The proposed RL1-CNFLMS algorithm integrates a reweighted l1-norm penalty into the traditional objective function of constrained least mean square least mean square (LMS) (CLMS) algorithm to drive the weighted coefficient vector to sparsity. Besides, the Lagrange multiplier (LM) method and the gradient descent principle are employed during the derivation procedure for getting the update equation. Additionally, we utilize the l1-l2 optimization method to acquire the noise-free a posteriori error signal in normalizing process to achieve a quicker convergence speed, a better signal to interference plus noise ratio (SINR) performance as well as a higher array sparsity with an acceptable computational complexity. Simulation results turn out that by using the noise-free and norm constraint techniques, a fairly comparable beampattern is achieved by using only 38.4%, 39.4% and 69.4% antenna elements in contrast to the constrained NLMS (CNLMS), reweighted l1-norm constrained LMS (RL1- CLMS) and reweighted l1-norm constrained normalized LMS (RL1-CNLMS) algorithms, respectively.