Linear parallel interference cancellation in long-code CDMA multiuser detection

Parallel interference cancellation (PIC) is a promising detection technique for code division multiple access (CDMA) systems. It has previously been shown that the weighted multistage PIC can be seen as an implementation of the steepest descent algorithm used to minimize the mean squared error (MSE). Following this interpretation, a unique set of weights, based on the eigenvalues of the correlation matrix, was found to lead to the minimum achievable MSE for a given number of stages in a short-code system. In this paper, we introduce a method for finding an appropriate set of time-invariant weights for systems using long codes. The weights are dependent on moments of the eigenvalues of the correlation matrix, exact expressions of which can be derived. This set of weights is optimal in the sense that it minimizes the ensemble averaged MSE over all code-sets. The loss incurred by averaging rather than using the optimal, time-varying weights is practically negligible, since the eigenvalues of sample correlation matrices are tightly clustered in most cases of interest. The complexity required for computing the weights increases linearly with the number of users but is independent of the processing gain, hence on-line weight updating is possible in a dynamic system. Simulation results show that a few stages is usually sufficient for near-MMSE performance.