Sparse Array Beamforming Design With Proximinal Set Constraints

Abstract

Sparse array beamforming design with sidelobe level suppression and set constraints is considered in this paper. A novel algorithmic framework named Dual Descent Variable Smoothing ADMM (DDVS-ADMM) is proposed that can incorporate a class of application-oriented constraints including power limit and constant modulus as special cases. Instead of applying any convex or nonconvex relaxations, we stick to the strict sparsity constraint while avoiding any expensive combinatorial procedures. In contrast to relevant literature on sparse array beamforming, we develop rigorous convergence guarantees in lieu of any impractical assumptions based on the recent idea of dual descent for nonconvex constrained programming. Furthermore, by adopting the variable smoothing technique, the DDVS-ADMM admits efficient closed-form gradient based variable updates. Several typical set constraints fitting DDVS-ADMM are discussed in detail and the empirical advantages of DDVS-ADMM over competing methods are demonstrated via extensive experiments.