Title :
-Constrained Normalized LMS Algorithms for Adaptive Beamforming
Author :
de Andrade, Jose Francisco ; de Campos, Marcello L. R. ; Apolinario, Jose Antonio
Author_Institution :
Programa de Eng. El trica, Univ. Fed. do Rio de Janeiro, Rio de Janeiro, Brazil
Abstract :
We detail in this paper an L1-norm Linearly constrained normalized least-mean-square (L1-CNLMS) algorithm and its weighted version (L1-WCNLMS) applied to solve problems whose solutions have some degree of sparsity, such as the beamforming problem in uniform linear arrays, standard hexagonal arrays, and (non-standard) hexagonal antenna arrays. In addition to the linear constraints present in the CNLMS algorithm, the L1-WCNLMS and the L1-CNLMS algorithms take into account an L1-norm penalty on the filter coefficients, which results in sparse solutions producing thinned arrays. The effectiveness of both algorithms is demonstrated via computer simulations. When employing these algorithms to antenna array problems, the resulting effect due to the L1-norm constraint is perceived as a large aperture array with few active elements. Although this work focuses the algorithm on antenna array synthesis, its application is not limited to them, i.e., the L1-CNLMS is suitable to solve other problems like sparse system identification and signal reconstruction, where the weighted version, the L1-WCNLMS algorithm, presents superior performance compared to the L1-CNLMS algorithm.
Keywords :
antenna arrays; array signal processing; least mean squares methods; signal reconstruction; CNLMS algorithm; L1-constrained normalized LMS algorithms; L1-norm penalty; active elements; adaptive beamforming; beamforming problem; filter coefficients; large aperture array; least mean square; nonstandard hexagonal antenna arrays; signal reconstruction; sparse system identification; standard hexagonal arrays; thinned arrays; uniform linear arrays; weighted version; Antenna arrays; Array signal processing; Convergence; Least mean square algorithms; Sensor arrays; Signal processing algorithms; $L_1$ -norm; CNLMS algorithm; constrained adaptive beamforming; sparse sensor arrays; thinned arrays;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2015.2474302