Sparse Array Beampattern Synthesis via Majorization Based ADMM

In this paper, the problem of beampattern synthesis for sparse array is investigated. By properly devising the transmitting weight vector, the synthesized beampattern is able to match the desired pattern with minimum array elements. Compared with the commonly used $\ell_1$-norm approach, the Shannon entropy function is first introduced to enhance the sparsity of array configurations. Then, a novel method which combines the majorization minimization and alternating direction multiplier method (M-ADMM) is developed to tackle the formulated nonconvex problem. Simulation results demonstrate the effectiveness and practicality of the proposed method.