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Constant-modulus sequence set with low peak side-lobe level is a necessity for enhancing the performance of modern active sensing systems like Multiple Input Multiple Output (MIMO) RADARs. In this paper, we consider the problem of designing a constant-modulus sequence set by minimizing the peak side-lobe level, which can be cast as a non-convex minimax problem, and propose a Majorization-Minimization technique based iterative monotonic algorithm named as the PSL minimizer. The iterative steps of our algorithm are computationally not very demanding and they can be efficiently implemented via Fast Fourier Transform (FFT) operations. We also establish the convergence of our proposed algorithm and discuss the computational and space complexities of the algorithm. Finally, through numerical simulations, we illustrate the performance of our method with the state-of-the-art methods. To highlight the potential of our approach, we evaluate the performance of the sequence set designed via our approach in the context of probing sequence set design for MIMO RADAR angle-range imaging application and show results exhibiting good performance of our method when compared with other commonly used sequence set design approaches.
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