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In this paper, we aim at designing sets of binary sequences with good aperiodic/periodic auto- and cross-correlation functions for multiple-input multiple-output (MIMO) radar systems. We show that such a set of sequences can be obtained by minimizing a weighted sum of peak sidelobe level (PSL) and integrated sidelobe level (ISL) with the binary element constraint at the design stage. The sets of designed sequences are neighboring the lower bound on ISL and have a better PSL than the best-known structured sets of binary sequences. To formulate the problem, we introduce a Pareto-objective of weighted auto- and cross-correlation functions by establishing a multi-objective NP-hard constrained optimization problem. Then, by using the block coordinate descent framework, we propose an efficient monotonic algorithm based on fast Fourier transform, to minimize the multi-dimensional objective function. Numerical results illustrate the superior performance of the proposed algorithm in comparison with the state-of-the-art methods.
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