This study considers designing constant-modulus waveforms for multiple-input-multipleoutput radar in spectrally crowded environment. The mutual information is used as the waveform design metric. A constant-modulus constraint is imposed on the waveforms to improve the hardware efficiency. To enhance the spectral compatibility of the transmit waveforms, a precise control on the interference energy produced on each reserved bandwidth is considered. To tackle the multi-spectrally constrained waveform design problem, a minorisation-maximisation based method is developed, and a quadratic function to minorise the objective function is derived. Then an alternating direction method of multipliers is used to tackle the quadratically constrained quadratic programming problem at each iteration. The effectiveness of the presented algorithm is demonstrated via simulation results. K E Y W O R D Salternating direction method of multipliers (ADMM), constant-modulus, MIMO radar, minorisationmaximisation (MM), mutual information, spectrally crowded environment, waveform designThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

In this paper, the waveform design for Rician target detection with multiple-inputmultiple-output radar is addressed. The relative entropy between the distributions of the observations under two hypotheses is employed as the design metric. Due to the difficulty of tackling the non-convex waveform design problem, a novel algorithm based on minorisation-maximisation is developed. Since a simple quadratic function is established to minorise the objective function, the presented algorithm has lower computational complexity than its counterparts. Moreover, it can be extended to design waveforms under many practical constraints, including the constant-envelope constraint, the similarity constraint, and the constant-envelope and similarity constraints. Numerical results are provided to show the effectiveness of the proposed algorithm for detecting Rician targets. Moreover, the designed waveforms can be used to enhance the detection performance of a Swerling 0 target in the presence of angle mismatch.