ADMM-based transmit beampattern synthesis for antenna arrays under a constant modulus constraint

Abstract

Transmit beampattern synthesis for antenna arrays is addressed in this paper. In pursuit of high radiation efficiency, most phased array radar systems utilize nonlinear power amplifiers, which leads to a constant modulus constraint for transmit weight vector optimization. Existing methods to solve this hard nonconvex problem (unit-modulus quadratic program) generally have high computational cost and large memory burden, which may increase dramatically as the array size increases. To that end, we propose a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework. By introducing auxiliary variables, the original problem is decomposed into several subproblems with closed-form solutions. The transmit weight vector and the phase response of the desired beampattern is updated alternately so that the cost function value can be monotonically reduced. With bounded penalty parameters, the proposed ADMM-based algorithm can guarantee to converge. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker conditions of the nonconvex optimization problem. Numerical simulation results confirm the effectiveness of the proposed method.