MIMO Radar Waveform Design for Quasi-Equiripple Transmit Beampattern Synthesis via Weighted $l_p$-Minimization

In this paper, under the peak-to-average power ratio (PAR) and energy constraints on the transmit waveforms, a new efficient weighted $\ell _p$ -norm metric (with $p\geq 2$ ) is introduced for colocated wideband/narrowband multiple-input multiple-output radar transmit beampattern matching design. The proposed metric can achieve quasi-equiripple beampattern, which is desirable to improve the robustness of radar systems with imprecise direction information of targets and reduce radar clutter. In addition, mainlobe ripple control, peak sidelobe suppression, and deep null/notch formation can be obtained. On the other hand, the PAR and energy constraints cause the radar waveform losing the degree of freedom to match arbitrary pattern shape, and the desired pattern usually lies in matching an appropriately scaled version of the shape. Thus, a scaling factor is introduced into the proposed metric to tackle the scaling ambiguity problem. The resultant optimization problems are difficult to solve due to the higher order polynomial objective function with coupled scaling factor and waveform matrix, and also the nonconvex PAR constraint. To develop a fast and efficient algorithm, by utilizing the majorization–minimization technique, we decouple the scaling factor and radar waveform matrix variables by a majorization step, derive a new quadratic majorizer to tackle the quadratic function with the matrix variable, and surrogate the nonsmooth nonconvex functions by convex functions. Numerical examples show that the devised approach can synthesize beampattern with lower peak sidelobe level and more flat mainlobe compared to the existing algorithms.