Partial Correlation Effects in Direct-Sequence Spread-Spectrum Multiple-Access Communication Systems

Nearly all previous analytical results on the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems are restricted to systems in which the periodp of the signature sequence is equal to the number N of chips per data symbol. In many applications, however, it is necessary to employ signature sequences whose periodp is much larger than N. Thus, successive N-chip segments of the signature sequence are used to phase-code tbe carrier during the transmission of successive data symbols. The performance of such systems depends on thepartidcorrelation properties of the signature sequences (rather than the aperiodic correlation properties as in the case when N = p). In this paper , we consider the performance of a DS/SSMA system for arbitrary values of p and N. As special cases of OUT results, we determine the effects of partial correlation In three classes of systems: those for which N =p, those for which Nandp are relatively prime, and those for which N is a divisor of p. We also provide two methods for the design of sequences for systems for which N is a divisor of p. HE performance of direct-sequence spread-spectrum multiple-access communication (DSfSSMA) systems in the presence of additive white Gaussian noise has been thoroughly analyzed for systems in which the number N of chips per data symbol is equal to the period p of each signature sequence measures that have been considered include the mean-square value of the multiple-access interference, the average signal-to-noise ratio at the output of a correiation receiver, and the average probability of error. In many applications, however, it is necessary to employ signature sequences whose period p is much larger than N. Thus, successive N-chip segments of the signature sequence are used to phase-code the carrier [71 during the transmission of successive data symbols. Such changing of the code sequence from data symbol t o symbol is of importance in combatting certain types of multipath interference and certain types of jamming and spoofing threats [4]. Unfortunately, very little analysis has been done for such systems because of the additional complexity required to obtain quantitative results on the performance of DS/SSMA systems for which p exceeds N. In this paper, we analyze the performance of DS/SSMA systems for arbitrary N and p. The performance measure that we consider is the mean-square value p(x, y) (as defined in (7) below) of certain partial cross-correlation functions for the signature sequences …