Generating functional analysis of CDMA detection dynamics

TL;DR

This paper introduces a generating functional analysis (GFA) method to accurately evaluate the detection dynamics of the parallel interference canceller in CDMA systems, especially when traditional density evolution predictions fail.

Contribution

The paper develops a GFA approach that precisely models CDMA detection dynamics without relying on Gaussian assumptions, improving accuracy in non-convergent scenarios.

Findings

GFA predictions align well with simulations across all conditions.

DE predictions deviate during transient and non-convergent dynamics.

GFA provides a more accurate analysis of detection dynamics in CDMA systems.

Abstract

We investigate the detection dynamics of the parallel interference canceller (PIC) for code-division multiple-access (CDMA) multiuser detection, applied to a randomly spread, fully syncronous base-band uncoded CDMA channel model with additive white Gaussian noise (AWGN) under perfect power control in the large-system limit. It is known that the predictions of the density evolution (DE) can fairly explain the detection dynamics only in the case where the detection dynamics converge. At transients, though, the predictions of DE systematically deviate from computer simulation results. Furthermore, when the detection dynamics fail to convergence, the deviation of the predictions of DE from the results of numerical experiments becomes large. As an alternative, generating functional analysis (GFA) can take into account the effect of the Onsager reaction term exactly and does not need the Gaussian assumption of the local field. We present GFA to evaluate the detection dynamics of PIC for CDMA multiuser detection. The predictions of GFA exhibits good consistency with the computer simulation result for any condition, even if the dynamics fail to convergence.