A New Family of Perfect Polyphase Sequences with Low Cross-Correlation

TL;DR

This paper introduces a new family of perfect polyphase sequences with low cross-correlation, significantly increasing the number of such sequences available for spread spectrum systems, especially for even periods.

Contribution

It establishes a novel connection between generalized Frank sequences and Florentine arrays to construct larger families of perfect sequences with low cross-correlation.

Findings

Family size can reach the square root of the period for even periods.

Number of perfect sequences with low cross-correlation for even periods is greater than one.

Improves upon previous limitations of having only one such sequence for even periods.

Abstract

Spread spectrum multiple access systems demand minimum possible cross-correlation between the sequences within a set of sequences having good auto-correlation properties. Through a connection between generalised Frank sequences and Florentine arrays, we present a family of perfect sequences with low cross-correlation having a larger family size, compared with previous works. In particular, the family size can be equal to the square root of the period when the period of the perfect sequences is even. In contrast, the number of the perfect sequences of even period with low cross-correlation is equal to one in all previous works.