Determination of the Integrated Sidelobe Level of Sets of Rotated Legendre Sequences

TL;DR

This paper introduces a method to compute the Integrated Sidelobe Level (ISL) for sets of rotated Legendre sequences, aiding in the design of sequences with low correlation for communication and sensing applications.

Contribution

It provides a novel method for calculating the ISL of rotated Legendre sequence sets and derives their asymptotic expression, advancing sequence design techniques.

Findings

Derived the asymptotic ISL expression for rotated Legendre sequences.

Established a computational method for ISL evaluation.

Enhanced understanding of correlation properties in sequence sets.

Abstract

Sequences sets with low aperiodic auto- and cross-correlations play an important role in many applications like communications, radar and other active sensing applications. The use of antipodal sequences reduces hardware requirements while increases the difficult of the task of signal design. In this paper we present a method for the computation of the Integrated Sidelobe Level (ISL), and we use it to calculate the asymptotic expression for the ISL of a set of sequences formed by different rotations of a Legendre sequence.