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Controlling peak side-lobe level (PSL) is of great importance in high-resolution applications of multiple input multiple output (MIMO) radars. In this paper, designing sequences with good autocorrelation properties are studied. The PSL of the autocorrelation is regarded as the main merit and is optimized through newly introduced cyclic algorithms, namely, PSL minimization quadratic approach, PSL minimization algorithm where the smallest rectangular, and PSL optimization cyclic algorithm. It is revealed that minimizing PSL results in better sequences in terms of autocorrelation side lobes when compared with traditional integrated side-lobe level minimization. In order to improve the performance of these algorithms, fast-randomized singular value decomposition is utilized. To achieve waveform design for MIMO radars, this algorithm is applied to the waveform generated from a modified Bernoulli chaotic system. The numerical experiments confirm the superiority of the newly developed algorithms compared to high-performance algorithms in monostatic and MIMO radars. [ABSTRACT FROM AUTHOR]