Spectrally compatible multiple-input multiple-output radar waveform design based on alternating direction method of multipliers

Multiple-input multiple-output (MIMO) radar waveform design in a spectrally crowded environment is a challenging problem. In this study, the issue of MIMO radar waveform design in coexistence with communication systems is investigated by maximising the output signal-to-interference-plus-noise ratio (SINR) of the MIMO radar under transmit energy, similarity and spectral compatibility constraints. Different from the existing alternating direction method of multipliers (ADMM) proposed in a single-antenna scenario, a novel ADMM algorithm for spectrally compatible MIMO radar waveform design is proposed to efficiently tackle the non-convex optimisation problem in both single-antenna and multi-antenna scenarios. Due to the decomposability of ADMM, only a few quadratic programming subproblems need to be solved during each iteration in the authors' algorithm, which reduces the computational complexity. In numerical simulations, the proposed ADMM algorithm is compared with the semidefinite relaxation algorithm and the existing ADMM algorithm in a single-antenna scenario and a multi-antenna scenario, respectively. It shows that the proposed ADMM algorithm can achieve almost the same performance as the two existing algorithms; however, it is computationally more efficient.