Pattern synthesis with minimum mainlobe width via sparse optimization

Abstract

This paper presents a pattern synthesis algorithm achieving minimum mainlobe width via sparse optimization. The problem of synthesizing a pattern with minimum mainlobe width is formulated as a sparse optimization problem with l0 norm by introducing a slack variable. To solve the sparse optimization problem, three existing relaxations for l0 norm are presented. Moreover, a novel log-sum-exp penalty function is proposed to replace l0 norm to be minimized in this paper, leading to a convex problem which can be solved directly and do not need to solve a sequence of sparse optimization problems compared with the iterative reweighted l1 norm. Both the focused beam pattern and shaped beam pattern for arbitrary arrays can be synthesized utilizing the proposed algorithm. Besides, the mainlobe width of pattern synthesized by the proposed algorithm is minimum. Simultaneously, it brings an extra advantage that it is no longer necessary to accurately determine the mainlobe region without synthesis performance degradation. Numerical examples are presented to verify the effectiveness and superiority of the proposed algorithm.