Joint Antenna Selection and Beamforming for Area Surveillance With Spatially Distributed Array Radar

This article addresses the joint optimization problem of antenna selection and beamforming design for a spatially distributed array radar (SDAR) used for area surveillance, while meeting spatial response and surveillance requirements. We first derive the mathematical relationships between detection probability and key SDAR parameters, including antenna selection and beamforming weights. The surveillance area, defined as a portion of a hemisphere delimited in azimuth and polar angles, is split into a grid of smaller cells that can each be covered by a single beam. For each angular cell, we then seek to minimize the number of antennas being employed for irradiation, while achieving a desired spatial response and target detection probability. As the formulated optimization problem is a nonconvex mixed-integer nonlinear programming problem, we propose a joint antenna selection and beamforming design algorithm based on the alternating direction method of multipliers (ADMM) to solve it effectively. Specifically, the optimization problem is transformed into an augmented Lagrangian problem based on the ADMM framework by introducing a series of auxiliary variables. We proceed by decomposing the resulting problem into two intertwined subproblems for which an iterative solution is developed, hence enabling an efficient solution of the overall problem wherein both beamforming weights and antenna selection are optimized jointly. Simulation results show that the proposed algorithm can deliver excellent performance in terms of minimizing the antenna resource while reliably meeting the given spatial response and surveillance requirements.