Minimizing Excitation Quantization Bits in Pattern Synthesis via Mixed-Integer Programming

This paper addresses the problem of minimizing excitation quantization bits in pattern synthesis to reduce costs while meeting performance requirements on beampattern. To achieve this task, we propose a framework leveraging mixed-integer programming (MIP), which models problems by introducing both continuous and discrete variables. The proposed method is applicable to various pattern synthesis scenarios and general array geometries, with the capability to minimize the quantization bits for both excitation phase and excitation amplitude. Additionally, the method supports joint optimization, allowing for optimal beampattern performance while minimizing quantization bits. The optimality of the proposed MIP model is theoretically guaranteed, and it can be efficiently solved using off-the-shelf solvers. Our approach differs from existing methods that predetermine quantization bits, as it obtains the minimal excitation quantization bits under the given beampattern specifications. Extensive simulations are presented to demonstrate the effectiveness and superiority of the proposed method.