Beampattern Synthesis for Frequency Diverse Array via Reweighted $\ell _1$ Iterative Phase Compensation

This paper addresses the issue of beampattern synthesis with flexible magnitude response and low sidelobe in a frequency diverse array radar. It is formulated as an optimization problem in terms of $\ell _1$ -norm minimization, which encourages the sparsity of array pattern. An $\ell _1$ iterative phase compensation (IPC) technique is employed to transform the nonconvex constraint to phase compensation form. Then, to further reduce the sidelobe level, a reweighted $\ell _1$ -IPC algorithm is devised, in which a sparsity-enhanced scheme is utilized to convert the $\ell _1$ -norm to a new cost function that more closely resembles $\ell _0$ -norm. Numerical results are presented to demonstrate the effectiveness of the proposed approach in different scenarios.