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 <inline-formula> <tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm minimization, which encourages the sparsity of array pattern. An <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula> 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 <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math> </inline-formula>-IPC algorithm is devised, in which a sparsity-enhanced scheme is utilized to convert the <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm to a new cost function that more closely resembles <inline-formula><tex-math notation="LaTeX">$\ell _0$</tex-math></inline-formula>-norm. Numerical results are presented to demonstrate the effectiveness of the proposed approach in different scenarios.