Antenna Selection for Array Synthesis Problems

The problem of choosing a set of N antennas from M possible radiators to optimize the performances of antenna arrays is addressed. Solving this combinatorial problem by evaluating all possible choices is untractable unless both N and M are small. Convex relaxations are proposed to solve approximately this antenna selection problem and quickly get bounds on the performance that can be achieved over all possible antenna combinations. Two approaches are also presented to rapidly construct, from these approximated results, good suboptimal solutions, i.e., good antenna selections. For (N, K) = (30, 10), i.e., 1030 possible antenna arrays, the methods can be carried out in a few seconds on a laptop. The proposed approaches are applied to solve various representative numerical instances, and they provide quickly valuable information for antenna array designers.