Asymptotic optimality of random PSK signature ensembles

Selection of a proper signature ensemble is the point of a special care in designing code division multiple access (DS CDMA) systems. When the receiver complexity beyond that of a single user algorithm is not affordable, Welch-bound ensembles minimizing intensity of the multiple access interference (MAI) are optimal. In this paper we show that for random signature sets the mean square deviation of MM power from the Welch bound drops in nearly inverse proportion with growth of K/N, where K is number of users and N is the spreading factor. Thereby, the fact of asymptotic (K≫N) convergence in probability of random sets to the Welch-bound ones is demonstrated.