The Construction of Orthogonal Variable Spreading Factor Codes from Semi-Bent Functions

In a recent paper spreading codes for CDMA systems were constructed based on Hadamard matrices and semi-bent functions. These codes were applicable to synchronous CDMA systems and to quasi-synchronous CDMA systems when a loosely-synchronized code is used. The codes consist of the union of rows of four Hadamard matrices. The codes can be assigned to a regular tessellation of hexagonal cells in such a way that the correlation between codewords assigned to adjacent cells is zero, while the correlation between codewords assigned to non-adjacent cells is small. The use of codewords from four Hadamard matrices allows greater codeword re-use distances than the use of codewords from a single Hadamard matrix. This has advantages for both satellite and terrestrial systems. These codes only support a single data rate. The current paper shows how orthogonal variable spreading factor codes can be created from them by a careful selection of the semi-bent functions used.