Extended total weighted squared correlation signature sequences of DS-CDMA systems in multipath channels

We analyze the extended total weighted squared correlation (ETWSC) for a given signature sequence set used in slow flat multipath channels and in the presence of colored noise. extended total square correlation (ETSC) and total squared correlation (TSC) are particular cases of ETWSC and are considered as well. The main results of this paper are: 1) the conditions on the channel such that the received multipath sequences are WBE (Welch bound Equality) sequences and 2) an iterative distributed method for obtaining real sequences that meet the Welch's lower bound on ETWSC. The method is based on majorization theory decreasing the weighted Frobenius norm associated with users' Sylvester channel matrices and noise covariance matrix. Numerical results for overloaded DS-CDMA systems are presented in order to support our analysis.