Low SPSL Transmit Beampattern Design for MIMO Radar via Lp-Norm Smoothing

For transmit beampattern design, low spatial autocorrelation peak sidelobe level (SPSL) is essential for synthetic waveforms to prevent the masking of weak targets by strong scattering points. In this article, an effective low SPSL transmit beampattern design scheme is proposed. First, we formulate the SPSL model for the synthetic waveform. Second, we establish an optimization problem aimed at minimizing the SPSL of synthetic waveforms and controlling the transmit beampattern, resulting in a nonconvex, nonsmooth min-max problem. To address this issue, we transform it into a fourth-order polynomial optimization problem using the majorization model of the ${L}_{p}$ -norm. Subsequently, we introduce an auxiliary variable to convert the fourth-order polynomial optimization problem into a quadratic polynomial optimization problem. Numerical results demonstrate the effectiveness of the proposed scheme in achieving transmit beampattern with low SPSL (TB-SPSL).