Hybrid Constructions of Binary Sequences with Low Autocorrelation Sidelobes

TL;DR

This paper introduces hybrid heuristic algorithms for designing binary sequences with minimal autocorrelation sidelobes, successfully finding optimal sequences for various lengths and demonstrating their effectiveness through extensive experiments.

Contribution

It presents novel hybrid heuristic algorithms that efficiently generate PSL-optimal binary sequences, including for lengths previously only accessible via exhaustive search.

Findings

Successfully found PSL-optimal sequences for all lengths previously studied

Discovered record-breaking PSL values for sequences of lengths 106 to 300

Outlined strategies for constructing highly competitive binary sequences

Abstract

In this work, a classical problem of the digital sequence design, or more precisely, finding binary sequences with optimal peak sidelobe level (PSL), is revisited. By combining some of our previous works, together with some mathematical insights, few hybrid heuristic algorithms were created. During our experiments, and by using the aforementioned algorithms, we were able to find PSL-optimal binary sequences for all those lengths, which were previously found during exhaustive searches by various papers throughout the literature. Then, by using a general-purpose computer, we further demonstrate the effectiveness of the proposed algorithms by revealing binary sequences with lengths between 106 and 300, the majority of which possess record-breaking PSL values. Then, by using some well-known algebraic constructions, we outline few strategies for finding highly competitive binary sequences, which could be efficiently optimized, in terms of PSL, by the proposed algorithms.