Beampattern Synthesis via the Constrained Subarray Layout Optimization

This article deals with a joint design of subarray layout vector (LV) and weighted coefficient of radiation element (RE) to achieve desired beampattern for a new array architecture. We first present an architecture of thinned array composed of multiple regular subarrays (ACMRS) and establish corresponding subarray layout and beampattern models. Then, we formulate a new optimization problem aiming to minimize the peak sidelobe level (PSL) and the LV norm under the constraints of power beampattern and subarray layout. The resulting problem is quite challenging to solve due to the highly nonconvex discrete LV and double-sided quadratic constraints. In this respect, we formulate the resultant hybrid optimization problem into a new alternating direction method of multipliers (ADMM) form via introducing a series of auxiliary variables, and propose an approximation algorithm based on ADMM. In each iteration of the proposed ADMM, the tractable and small-sized subproblems are globally or locally solved in parallel. Finally, numerical simulations show that the proposed method can obtain a lower PSL beampattern and a thinner (i.e., fewer REs or subarrays) array while satisfying the given constraints. Furthermore, fullwave simulation also shows that it has good reliability in the application of beampattern synthesis for real array.