An Efficient Design of LPI Transmit Beampattern for MIMO Radar via $L_{p}$-Norm Smoothing

The design of a transmit beampattern may generate large instantaneous amplitude fluctuations in the synthesized waveforms at the probed region, which distorts the low probability of intercept (LPI) performance of multi-input–multi-output (MIMO) radar systems. To avoid the radar signal being intercepted and identified by electronic interception measures, it is crucial to design an LPI transmit beampattern with a smoothed amplitude. In this article, an effective LPI transmit beampattern design scheme is proposed for MIMO radar systems. First, we formulate the peak-to-average power ratio model of the synthetic waveform. Second, we establish an LPI transmit beampattern scheme to minimize the instantaneous amplitude fluctuations of the synthesized waveform and control the transmit beampattern, which is a nonconvex nonsmooth min–max problem. To smooth the min–max problem, we approximate the max function by using the $L_{p}$-norm. Then, we propose a majorization method for the $L_{p}$-norm, which transforms the $L_{p}$-norm into a quadratic polynomial. Finally, to solve the min–max problem efficiently, a quadratic function majorization method is proposed. Numerical results demonstrate that the proposed method designs an LPI transmit beampattern efficiently.