A Multi-Objective Quantum Genetic Algorithm for MIMO Radar Waveform Design

Aiming at maximizing waveform diversity gain when designing a phase-coded multiple-input multiple-output (MIMO) radar waveform set, it is desirable that all waveforms are orthogonal to each other. Hence, the lowest possible peak cross-correlation ratio (PCCR) is expected. Meanwhile, low peak auto-correlation side-lobe ratio (PASR) is needed for good detection performance. However, it is difficult to obtain a closed form solution to the waveform set from the expected values of the PASR and PCCR. In this paper, the waveform set design problem is modeled as a multi-objective, NP-hard constrained optimization problem. Unlike conventional approaches that design the waveform set through optimizing a weighted sum objective function, the proposed optimization model evaluates the performance of multi-objective functions based on Pareto level and obtains a set of Pareto non-dominated solutions. That means that the MIMO radar system can trade off each objective function for different requirements. To solve this problem, this paper presents a multi-objective quantum genetic algorithm (MoQGA) based on the framework of quantum genetic algorithm. A new population update strategy for the MoQGA is designed based on the proposed model. Compared to the state-of-the-art methods, like BiST and Multi-CAN, the PASR and PCCR metrics of the waveform set are 0.95–3.91 dB lower with the parameters of the numerical simulation. The MoQGA is able to minimize PASR and PCCR of the MIMO radar waveform set simultaneously.