Synthesis of Minimally Subarrayed Linear Array With Partially Clustered Array Architecture via New TVPDD Framework

In this letter, the synthesis of a partially subarrayed linear array is studied to obtain as few subarrays as possible. For the partially clustered array (PCA), the amplifiers are placed at the subarray level, while the phase shifters are placed at the element level. By performing a matrix transformation on the equivalent excitation amplitude vector, the original synthesis problem of PCA is reformulated as a minimization problem of l0-norm. It is nonconvex and cannot be solved by the existing convex methods. Then, a new penalty dual decomposition (PDD) framework is proposed to address the task. The new approach can directly optimize the subarray number and simultaneously guarantee that the elements of subarrays are physically contiguous, while the excitation matching (EM) methods cannot. Numerical simulations show that the proposed method can get as few subarrays as possible in the synthesis of PCA.