On the Generation of Long Binary Sequences with Record-Breaking PSL Values

TL;DR

This paper introduces a new efficient method for generating long binary sequences with record-breaking low peak sidelobe levels, outperforming existing sequences in PSL values with minimal computational resources.

Contribution

The paper presents a novel, simple, and efficient algorithm for generating long binary sequences with unprecedented low PSL values, outperforming traditional sequences like Legendre and Rudin-Shapiro.

Findings

Achieved PSL values strictly less than √n for various sequence lengths.

The algorithm has linear time and memory complexity, making it highly efficient.

Record-breaking PSL values were obtained in less than a second.

Abstract

Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this paper, a method to generate long binary sequences (LBS) with low peak sidelobe level (PSL) value is proposed. Having an LBS with length $n$, both the time and memory complexities of the proposed algorithm are $\mathcal{O}(n)$. During our experiments, we repeatedly reach better PSL values than the currently known state of art constructions, such as Legendre sequences, with or without rotations, Rudin-Shapiro sequences or m-sequences, with or without rotations, by always reaching a record-breaking PSL values strictly less than $\sqrt{n}$. Furthermore, the efficiency and simplicity of the proposed method are particularly beneficial to the lightweightness of the implementation, which allowed us to reach record-breaking PSL values for less than a second.