  We investigate the detection dynamics of a soft parallel interference
canceller (soft-PIC), which includes a hard-PIC as a special case, for
code-division multiple-access (CDMA) multiuser detection, applied to a randomly
spread, fully synchronous base-band uncoded CDMA channel model with additive
white Gaussian noise under perfect power control in the large-system limit. We
analyze the detection dynamics of some iterative detectors, namely soft-PIC,
the Onsager-reaction-cancelling parallel interference canceller (ORC-PIC) and
the belief-propagation-based detector (BP-based detector), by the generating
functional analysis (GFA). The GFA allows us to study the asymptotic behavior
of the dynamics in the infinitely large system without assuming the
independence of messages. We study the detection dynamics and the stationary
estimates of an iterative algorithm.
  We also show the decoupling principle in iterative multiuser detection
algorithms in the large-system limit. For a generic iterative multiuser
detection algorithm with binary input, it is shown that the multiuser channel
is equivalent to a bank of independent single-user additive non-Gaussian
channels, whose signal-to-noise ratio degrades due to both the multiple-access
interference and the Onsager reaction, at each stage of the algorithm. If an
algorithm cancels the Onsager reaction, the equivalent single-user channels
coincide with an additive white Gaussian noise channel. We also discuss ORC-PIC
and the BP-based detector.
