Constant Modulus Waveform Design for MIMO Radar Transmit Beampattern

Abstract

A multiple-input multiple-output radar has great flexibility to design the transmit beampattern via selecting the probing waveform. The idea of current transmit beampattern design is to approximate the disired transimit beampattern and minimize the cross-correlation sidelobes. In this paper, under the constant modulus constraint, two algorithms are proposed to design the probing waveform directly. In the first algorithm, the optimization criterion is minimizing the squared-error between the designed beampattern and the given beampattern. Since the objective function is a nonconvex fourth-order polynomial and the constant modulus constraint can be regarded as many nonconvex quadratic equality constraints, an efficient alternating direction method of multipliers (ADMM) algorithm, whose convergence speed is very fast, is proposed to solve it. In the second algorithm, the criterion is minimizing the absolute-error between the designed beampattern and the given beampattern. This nonconvex problem can be formulated as $l_1$ -norm problem, which can be solved through a double-ADMM algorithm. Finally, we assess the performance of the two proposed algorithms via numerical results.