On Shift Sequences for Interleaved Construction of Sequence Sets with Low Correlation

TL;DR

This paper improves the construction of low-correlation signal sets for CDMA by relaxing conditions on shift sequences, increasing their number, and solving an open problem on maximum correlation bounds.

Contribution

It demonstrates that previous conditions on shift sequences are overly restrictive and provides a more general condition, also solving an open problem on maximum correlation bounds.

Findings

More shift sequences are possible under relaxed conditions.

The open problem on maximum correlation bound v+2 is solved.

Enhanced construction methods for low-correlation signal sets are proposed.

Abstract

Construction of signal sets with low correlation property is of interest to designers of CDMA systems. One of the preferred ways of constructing such sets is the interleaved construction which uses two sequences a and b with 2-level autocorrelation and a shift sequence e. The shift sequence has to satisfy certain conditions for the resulting signal set to have low correlation properties. This article shows that the conditions reported in literature are too strong and gives a version which results in more number of shift sequences. An open problem on the existence of shift sequences for attaining an interleaved set with maximum correlation value bounded by v+2 is also taken up and solved.