Iterative construction of optimum signature sequence sets in synchronous CDMA systems

Recently, optimum signature sequence sets that maximize the capacity of sin gle-cell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correla tion (TSC); they form a set of orthogonal sequences, if the number of users is less than or equal to the processing gain, and a set of Welch bound equ ality (WBE) sequences, otherwise. We present an algorithm where users updat e their transmitter signature sequences sequentially, in a distributed fash ion, by using available receiver measurements. We show that each update dec reases the TSC of the set, and produces better signature sequence sets prog ressively. We prove that the algorithm converges to a set of orthogonal sig nature sequences when the number of users is less than or equal to the proc essing gain. We observe and conjecture that the algorithm converges to a WE E set when the number of users is greater than the processing gain. At each step, the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error (MMSE) receiver corresponding to that signature sequence. Since the MMSE filter can be obtained by a distributed algorithm for each user, the proposed algorithm is amenable to distributed implementation.