The Assignment of CDMA Spreading Codes Constructed from Hadamard Matrices and Almost Bent Functions

Abstract

Almost bent functions and Hadamard matrices can be used to construct spreading codes for code-division multiple-access (CDMA) systems. Four specific Hadamard matrices can be constructed and each one can be divided into eight octants in such a way that spreading codewords from certain pairs of octants have zero correlation. It is possible to assign these octants to a regular tessellation of hexagonal cells in such a way that there is zero correlation between adjacent cells, small correlation between non-adjacent cells and a large codeword re-use distance. If synchronous CDMA is used in a satellite system, interference is reduced in comparison with the use of a single Hadamard matrix. In this case the regular hexagonal tessellation is usually a good model of the areas covered by satellite spot beams. The same approach can be advantageous when the Hadamard matrices are used to construct loosely synchronized codes for a terrestrial system. The tessellation of cells is unlikely to be a regular hexagonal tessellation and the question arises of whether an assignment to an irregular tessellation with these properties can be found. In this paper a positive answer is given to this question, confirming that the approach is applicable to a terrestrial system.