Phase orthogonal sequence sets for (QS)CDMA communications

Abstract

For various quasi-synchronous (QS) CDMA systems, to reduce or eliminate the multiple access interference and multipath interference, it is required to design a set of spreading sequences which are mutually orthogonal within a designed shift zone. In this article, we demonstrate that a concept of irregular spatial assignment, with flexibility to assign different number of users to different cells, can be used to provide the maximal number of orthogonal sequences in any three adjacent cells in networks with a regular tessellation of hexagonal cells. We first consider p-phase spreading sequences of length $p^m$ (thus nonbinary p-valued sequences) suitable for synchronous (S)-CDMA applications, for $p>3$, and give an efficient design method for reaching the maximal cardinality achievable (being $p^m$). A simple solution for a flexible assignment of our orthogonal sets of spreading sequences to the cells in hexagonal networks is given. To address QS-CDMA applications as well, an efficient method to combine these orthogonal sequences with Zadeoff–Chu sequences is proposed for the purpose of designing sets of zero correlation zone (ZCZ) sequences (within a certain shift zone) with optimal parameters, thus reaching the Tang–Fan–Matsufuji bound. A similar design framework, based on the use of some special classes of Boolean functions, is then employed for the binary case to provide the maximum cardinality of pairwise orthogonal sequences of length $2^m$ through this irregular spatial assignment. This improves upon the best known results achieved in Zhang et al. (IEEE Trans Inf Theory 62:3757–3767, 2016), which assigns $2^{m-2}$ orthogonal sequences (users) per cell, by doubling the number of users in one third of the network.