We characterize the Total Generalized Squared Correlation (TGSC) for a given signature sequence set used in uplink synchronous code division multiple access (S-CDMA) when channel state information is known perfectly at bothtransmitter and receiver. We give a definition of the TGSC based on the eigenvalues of Gram matrix associated to signature sequences set for multipath channels in the presence of the colored noise. Total Squared Correlation (TSC) and Total Weighted Squared Correlation (TWSC) measures are particular cases of TGSC. We present a method for minimizing TGSC (TSC, TWSC) in multipath channels and in the presence of the colored noise. Numerical results for overloaded synchronous CDMA systems are presented in order to support our analysis.