A General Scheme of a Branch-and-Bound Approach for the Sensor Selection Problem in Near-Field Broadband Beamforming

This paper is devoted to the sensor selection problem. A broadband receiver beamforming working in a near-field is considered. The system response should be as close as possible to the desired one, which is optimized in the sense of L2 norm. The problem considered is at least NP-hard. Therefore, the branch-and-bound algorithm is developed to solve the problem. The proposed approach is universal and can be applied not only to microphone arrays but also to antenna arrays; that is, the methodology for the generation of consecutive solutions can be applied to different types of sensor selection problems. Next, for a larger microphone array, an efficient metaheuristic algorithm is constructed. The algorithm implemented is a hybrid genetic algorithm based on the ITÖ process. Numerical experiments show that the proposed approach can be successfully applied to the sensor selection problem.