Parallel interference cancellation (PIC) is a promising detection technique
for code division multiple access (CDMA) systems. It has previously been s
hown that the weighted multistage PIC can be seen as an implementation of t
he steepest descent algorithm used to minimize the mean squared error (MSE)
. Following this interpretation, a unique set of weights, based on the eige
nvalues of the correlation matrix, was found to lead to the minimum achieva
ble 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 wei
ghts for systems using long codes. The weights are dependent on moments of
the eigenvalues of the correlation matrix, exact expressions of which can b
e derived, This set of weights is optimal in the sense that it minimizes th
e ensemble averaged MSE over all code-sets. The loss incurred by averaging
rather than using the optimal, time-varying weights is practically negligib
le, since the eigenvalues of sample correlation matrices are tightly cluste
red in most cases of interest. The complexity required for computing the we
ights increases linearly with the number of users but is independent of the
processing gain, hence on-line weight updating is possible in a dynamic sy
stem. Simulation results show that a few stages is usually sufficient for n
ear-MMSE performance.