Reconfigurable Sparse Array Synthesis With Phase-Only Control via Consensus-ADMM-Based Sparse Optimization

In this work, we consider the problem of joint sparse array antenna design and phase-only beampattern shaping with reconfigurability. Our design objective is to reduce the cost of the antenna system for the unmanned aerial vehicle (UAV) radar with a large-aperture array. We formulate this co-design problem as a sparse optimization problem with angular response and binary-like modulus constraints. To solve the resultant NP-hard nonconvex problem, we propose a consensus alternating direction method of multipliers (ADMM) based algorithm. This method transforms the original problem into a higher-dimensional one by introducing two categories of auxiliary variables. By doing so, the problem can be effectively tackled via alternately solving several subproblems, meanwhile the tricky binary modulus constraints can be well handled by utilizing the geometric property of the subproblem. We further prove that the proposed algorithm converges to the KKT points of the original problem. In addition, we extend our methodology to the discrete phase case to handle the practical finite-bit phase quantization. The devised algorithm is capable of generating phase-only weight vector meanwhile automatically selecting appropriate antenna elements according to the specific beam shape. Numerical examples are given to demonstrate the effectiveness of the proposed approach.