Beampattern Synthesis with Minimum Phase Quantization Bits via Kronecker Decomposition

In practical implementations, phase excitations are inherently discrete, and the number of phase quantization bits significantly affects hardware complexity and cost. To reduce the cost of array systems, this communication proposes a beampattern synthesis method with minimum phase quantization bits required. By exploiting the Vandermonde structure of the phase alphabet and properties of the Kronecker product/decomposition, we formulate an optimization method that minimizes phase quantization bits via mixed-integer programming (MIP). The method is further extended to dual-phase-shifter (DPS) structures by constructing a phase candidate matrix that represents combined branch excitations. Both formulations incorporate dimension reduction techniques to improve computational efficiency.