Mean periodic correlation of sequences in CDMA

In CDMA systems, pseudo-random codes are used to distinguish between different users. The codes in an ideal CDMA system would have zero crosscorrelation, and pulse-like autocorrelation with a nonzero value at the origin and a zero value elsewhere. In the paper we prove that both requirements can not be met simultaneously. Different authors, e.g., Sidelnikov 1971, Welch 1974, Sarwate 1979, have derived lower bounds on the maximal correlation (crosscorrelation and out-of-phase autocorrelation) of codes. However, the maximal correlation is not the only relevant criteria in a code set design process. In a real CDMA system the mean value of the correlation of codes is important and should be considered as well. In the paper the derivation of the lower bounds of the mean correlation moments of codes is given. The results are very useful for evaluation of different code sets in CDMA systems.