Large Sets of Orthogonal Sequences Suitable for Applications in CDMA Systems

TL;DR

This paper introduces a novel method using semi-bent functions to generate large sets of orthogonal sequences, significantly increasing user capacity in CDMA systems with hexagonal cell tessellations.

Contribution

The paper presents a new approach to create orthogonal sequences from semi-bent functions, enabling more users per cell in CDMA networks compared to existing methods.

Findings

Number of users per cell is doubled for certain parameters.

Orthogonal sets can be assigned regardless of codeword length parity.

Method improves capacity without complex cell allocation problems.

Abstract

In this paper, we employ the so-called semi-bent functions to achieve significant improvements over currently known methods regarding the number of orthogonal sequences per cell that can be assigned to a regular tessellation of hexagonal cells, typical for certain code-division multiple-access (CDMA) systems. Our initial design method generates a large family of orthogonal sets of sequences derived from vectorial semi-bent functions. A modification of the original approach is proposed to avoid a hard combinatorial problem of allocating several such orthogonal sets to a single cell of a regular hexagonal network, while preserving the orthogonality to adjacent cells. This modification increases the number of users per cell by starting from shorter codewords and then extending the length of these codewords to the desired length. The specification and assignment of these orthogonal sets to a regular tessellation of hexagonal cells have been solved regardless of the parity and size of $m$ (where $2^m$ is the length of the codewords). In particular, when the re-use distance is $D=4$ the number of users per cell is $2^{m-2}$ for almost all $m$, which is twice as many as can be obtained by the best known methods.