Performance of Orthogonal CDMA Codes for Quasi-Synchronous Communication Systems

In this paper, the performance of quasi-synchronous direct-sequence CDMA communication systems based on diierent sets of orthogonal codes is investigated. We search for sets of sequences that minimize the probability of bit detection error, given that there is imperfect synchronization among the signals. Orthogonal sequences based on the Sylvester-type Hadamard matrices (Walsh functions) are shown to provide a large improvement over the case where an orthogonal set is chosen at random. For these sequences we derive closed form expressions for the average bit error rate. Computer searches indicate that this set of codes has special properties with respect to minimizing the average cross-correlations between the diierent signals for small errors in chip synchronization. It appears that these codes are optimal. We also discuss a multi-carrier signalling scheme designed to help synchronize the CDMA signals at the chip level.