SLOPE: A monotonic algorithm to design sequences with good autocorrelation properties by minimizing the peak sidelobe level

Abstract

Sequences with low autocorrelation sidelobes has applications in various fields like wireless communications, radar, sonar, cryptography to name a few. In this paper, we propose an approach to construct sequences, in particular unimodular sequences, by directly minimizing the peak sidelobe level (PSL) metric. The underlying optimization problem involved is a minimax problem which is in general difficult to tract. We address this issue and propose an iterative algorithm named Sequence with LOw Peak sidelobE level (SLOPE) based on the technique of Majorization Minimization, which can be implemented efficiently using the Fast Fourier Transform tool. Further, we also discuss the extension of SLOPE to incorporate energy, peak-to-average-power ratio (PAPR) and spectral constraints on the sequence. We show through numerical simulations that the proposed algorithm can generate sequences of considerably longer lengths with lower peak sidelobe level when compared to the state-of-the-art algorithms and in the end we also evaluate the performance of the sequences designed via SLOPE in the context of channel estimation application.