OPTIMAL PHASES FOR A FAMILY OF QUADRIPHASE CDMA SEQUENCES

Signature sequences with both good even and odd (or polyphase) correla tions are crucial for asynchronous code-division multiple access (CDMA ), When the data sequence is random, the even and odd (or polyphase) c orrelations are equally important, However, for most known signature s equences, only their even correlations were analyzed. It appears that determining the odd (or the polyphase) correlations is generally a ver y hard problem since the odd (or the polyphase) correlations depend on the phases of the signature sequences. Sole, Boztas, Hammons, and Kum ar found a family of quadriphase sequences that are asymptotically opt imal. These sequences gain a factor root 2 in terms of their maximum p eriodic even correlations when compared with the best possible binary phase-shift keying (BPSK) sequences. In this paper, we find the optima l phases of these sequences. The optimality is in the sense that at th ese phases, the mean square values of the even, odd, and the polyphase correlations are minimal, and achieve the Welch-Bound-Equality simult aneously. Furthermore, we show that at these phases, the average user interference of these sequences is always smaller than that of the ide al random signature sequences. Comprehensive analytical and numerical results show that good phase sequences can offer nonnegligible amount of gains over bad phase sequences at modest and high signal-to-noise r atios.