Phased-array beampattern synthesis with a tradeoff between sparsity and sidelobe level

Abstract

This paper addresses the problem of joint sparse array beampattern synthesis and sidelobe control for arbitrary array configurations. In particular, a new cost function, which can balance the tradeoff between the sparsity of the array and sidelobe level, is proposed in this paper by combining sidelobe level with the weighted l1 norm. The constraints concerning the magnitude response deviation within the mainlobe region are also incorporated, which makes the optimization problem nonconvex and hard to solve. In order to make the optimization process efficient, the original nonconvex optimization problem is decomposed into several subproblems by introducing auxiliary variables, and the weight vector is iteratively obtained by employing the alternating direction penalty method (ADPM). A remarkable feature of the proposed method is that the penalty term can be forced to approach zero to ensure convergency even though with unbounded penalty parameters. Moreover, it is also proven in this paper that the converged solution is Karush-Kuhn–Tucker (KKT) optimal with some necessary conditions. The effectiveness of the proposed method is verified via simulation experiments.