A design and flexible assignment of orthogonal binary sequence sets for (QS)-CDMA systems

Boolean functions naturally induce binary sequences of length \(2^m\) and a large number of such orthogonal sequences is required in the design of code-division multiple-access (CDMA) systems. In this paper, Boolean functions are used to construct nonlinear phase orthogonal sequence sets for CDMA communications. For even m, employing carefully designed an m-variable Boolean function with five-valued Walsh spectra, one can get 16 different orthogonal sequence sets with sequence length \(2^m\). These sequence sets are assigned to a lattice of regular hexagonal cells, and we can ensure the orthogonality of adjacent cells. Moreover, the cross-correlation values between the sequences in a given cell and the sequences in non-neighbouring cells belong to \(\{0,\pm 2^{\frac{m}{2}}, \pm 2^{\frac{m}{2}+1}\}\). On the other hand, the cardinality of the sequences sets is \(2^{m-3}\) thus implying a trade-off between the quality of communication and the number of users assigned to each cell. This method can be improved so that the number of users is increased to \(2^{m-2}\) in one half of the network while preserving the orthogonality between adjacent cells and the same level of low cross-correlation values to the non-neighbouring cells.