A two-stage design approach is proposed to address the sparse antenna array design for multiple-input multiple-output radar. In\nthe first stage, the cyclic algorithm (CA) is used to establish a covariance matrix that satisfies the beam pattern approximation\nfor a full array. In the second stage, a sparse antenna array with a beam pattern is designed to approximate the desired beam\npattern. This paper focuses on the second stage. The optimization problem for the sparse antenna array design aimed at beam\npattern synthesis is formulated, where the peak side lobe (PSL) is weakly constrained by the mean squared error. To solve this\noptimization problem, the differential evolution (DE) algorithm with multi strategy is introduced and PSL suppression is treated\nas an inequality constraint. However, in doing so, a new multiobjective optimization problem is created. To address this new\nproblem, a multiobjective differential evolution algorithm based on Pareto technique is proposed.Numerical examples are provided\nto demonstrate the advantages of the proposed approach over state-of-the-art methods, including DE and genetic algorithm.
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