Approximate belief propagation, density evolution, and statistical neurodynamics for CDMA multiuser detection

We present a theory to analyze the performance of the parallel interference canceller (PIC) for code-division multiple-access (CDMA) multiuser detection, applied to a randomly spread, fully synchronous baseband uncoded CDMA channel model with additive white Gaussian noise under perfect power control in the large-system limit. We reformulate PIC as an approximation to the belief propagation algorithm for the detection problem. We then apply the density evolution framework to analyze its detection dynamics. It turns out that density evolution for PIC is essentially the same as statistical neurodynamics, a theory to describe dynamics of a certain type of neural network model. Adopting this correspondence, we develop the density evolution framework for PIC using statistical neurodynamics. The resulting formulas, however, are only approximately correct for describing detection dynamics of PIC even in the large-system limit, because we ignore the Onsager reaction terms in the derivation. We then propose a modified PIC algorithm, in which we subtract the Onsager reaction terms algorithmically, for which the density evolution formulas give a correct description of the detection dynamics in the large-system limit.