Iterative channel and data estimation: Framework and analysis via replica method

The large system analysis of a randomly spread direct-sequence code-division multiple-access system operating over a frequency-selective fading channel is considered. Iterative multiuser detection and decoding based on generalized posterior mean estimation and interference cancellation is assumed. The channel is mismatched and provided by a linear estimator whose initial pilot-based decisions are iteratively refined by using a feedback from the single-user decoders. By an application of the replica method, a tool from statistical physics, and density evolution with Gaussian approximation, we show that the performance metrics of the considered multiuser system converge in distribution at the large system limit to that of a simple single-user system operating over a flat fading channel. We also give the exact result of the hard decision feedback based channel estimator analyzed approximately by Li et al. (2007).