Signature sequence selection in a CDMA system with orthogonal coding

In code-division multiple-access (CDMA) systems, recent attention has focused on the use of orthogonal coding to provide spreading. Each signal is coded with the same orthogonal or biorthogonal code, followed by a modulo-2 addition of a unique signature sequence. The set of signature sequences used determines how much signals interfere with each other at a receiver, thus determining the performance of the system. An analysis is presented to determine the properties of an optimal set of signature sequences for such a system. Using a Kerdock code, a set of signature sequences is presented which optimizes performance in a direct sequence CDMA system with (a) synchronous transmission, (b) no multipath time dispersion, and (c) orthogonal or biorthogonal Walsh-Hadamard coding as a means of spreading the information signal. For a length-N-binary code (where N is an even power of two), the set contains N/2 signature sequences. Approaches are discussed for the cases when N is an odd power of two and when more sequences are needed