Some theoretical observations on spread-spectrum communications

We consider a simple direct-sequence model of spread-spectrum communications over a bandwidth W using signals of duration T. In addition to the dimension n − 2WT of signal space, the other parameters of interest are the number (u + 1) of simultaneous users of the system, the error rate Pe(u), and the number M of subscribers, or potential users. We investigate the relationships between these parameters, and, in particular, study the validity of the usual Gaussian approximation often used to compute Pe(u). Basically, we conclude that, if Mis larger than n
²
/2, then the Gaussian approximation is not a guaranteed error rate for (u + 1) users, but rather an average over all possible (u + 1) users. If Mis somewhat less than this number (the exact value is not known), codes can be assigned so that a uniform performance at least as good as Pe(u) can be obtained, where, again, Pe(u) is calculated from the Gaussian approximation. Uniform performance guarantees are given for any value of M, but they (for M targe) permit fewer simultaneous users that the Gaussian approximation predicts. These bounds explicitly use the maximum cross-correlation between the signals of the different subscribers. This quantity played no role in the Gaussian approximation.