Shaped-Beam Pattern Synthesis With Sidelobe Level Minimization via Nonuniformly-Spaced Sub-Array

Abstract

This article deals with the low-sidelobe shaped-beam pattern synthesis (SBPS) problem using two nonuniformly spaced subarray configurations, including amplitude and amplitude–phase subarray configurations. An optimization model is proposed for the SBPS problem to minimize the peak sidelobe level by jointly optimizing the subarray configuration and element excitations/positions. A typical advantage of the proposed model is to reduce the system control points while maintaining the benign array performance. However, the formulated problem is a mixed-integer nonconvex one, which makes it challenging. Besides, this problem cannot be directly solved due to the existence of coupling optimization variables. Thus, a set of auxiliary variables is introduced to move the coupling optimization variables into equality constraints. These equality constraints are converted into quadratic penalty forms and are added to the objective function. Then, an efficient iterative algorithm is proposed using the penalty-based optimization method, which solves the original problem by iteratively solving a series of subproblems based on the inexact block coordinate descent technique. Numerical examples with different beam patterns are performed to verify the effectiveness of the proposed algorithm.