Sequence pairs with asymptotically optimal aperiodic correlation

TL;DR

This paper constructs complex sequence pairs with unit magnitude entries that asymptotically achieve the optimal Pursley-Sarwate criterion of 1, indicating minimal combined aperiodic autocorrelation and crosscorrelation.

Contribution

It introduces new sequence pairs using Chu sequences that asymptotically reach the optimal correlation criterion, advancing sequence design for signal processing.

Findings

Sequence pairs with unit magnitude entries approach Pursley-Sarwate criterion of 1 as length increases

Use of Chu sequences in constructing optimal correlation pairs

Sequences exhibit minimal combined aperiodic autocorrelation and crosscorrelation

Abstract

The Pursley-Sarwate criterion of a pair of finite complex-valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic crosscorrelations of the two sequences. It is known that this quantity is always at least 1 with equality if and only if the sequence pair is a Golay pair. We exhibit pairs of complex-valued sequences whose entries have unit magnitude for which the Pursley-Sarwate criterion tends to 1 as the sequence length tends to infinity. Our constructions use different carefully chosen Chu sequences.