# 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.

## Key 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.