Constant Modulus MIMO Radar Waveform Design with Minimum Peak Sidelobe Transmit Beampattern

This paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple-input multiple-output radar systems. Two new methods are proposed to achieve it via designing constant modulus (CM) waveforms directly: One is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level (PSL) without specifying pattern masks, and another is to minimize PSL under the mainlobe ripple and unspecified waveform modulus constraints. The resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double-sided quadratic constraints and unknown waveform modulus in the latter. For the former, we decouple the numerator and denominator by equivalent transformation and introduction of boundary-type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently. For the latter, we simplify the coupled double-sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem. Numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the CM constraints.