Performance of orthogonal CDMA codes for quasi-synchronous communication systems

TLDR: 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.

Abstract: In this paper, the performance of quasi-synchronous direct-sequence CDMA communication systems based on different sets of orthogonal codes is investigated. The authors 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 closed form expressions are derived 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 different signals for small errors in chip synchronization. It appears that these codes are optimal. A multi-carrier signalling scheme designed to help synchronize the CDMA signals at the chip level is also discussed.