Phased array beamforming with practical constraints

Abstract

This paper deals with the design of the weighted coefficients (WCs) for the phased array to synthesize a received beam. Two new optimization problems accounting for non-quantitative and quantitative WCs cases are developed via maximizing array gain in the constraints on absolute dynamic range (ADR)/quantization for WCs and non-normalized power pattern level (NNPPL). The resulting problems are non-convex constrained quadratic fractional programming that falls into a class of NP-hard problems. We reformulate them into a new unified ADMM form via introducing a series of auxiliary variables, where each iteration is executed via solving a series of small tractable subproblems. To deal with the combinatorial constraints on quantization, we formulate the update of WCs as a Euclid projection form to obtain the closed-form solutions. Finally, some simulation results highlight that the proposed approach can synthesize beams that meet the requirements of narrow mainlobe or both low sidelobe and high array gain or wide notch and can deal with the deterioration of the beam performance due to the quantization operation and the nonisotropy of the array.