Decoupling of CDMA multiuser detection via the replica method
Dongning Guo, Sergio Verdú · 2003
In CDMA, the optimal multiuser detector in mean square sense is the conditional mean estimator (CME) regardless of the input distribution, which outputs the expected value of the transmitted symbols conditioned on the received signal and the channel state (spreading sequences, fading, etc). In this paper, we first note that every multiuser detector can be reformulated as the CME for a certain postulated CDMA channel with a postulated input distribution which may be different from the actual channel and inputs. Using the replica method developed in statistical physics, a class of generalized CME front end applied to randomly spread CDMA is studied in a unified framework in the large-system limit. It is found that for any input distribution, the single-user channel seen at the generalized CME output for each user is equivalent to a Gaussian channel followed by a monotonic decision function. The degradation factor in the effective SNR of the equivalent channel due to multiple access interference is the multiuser efficiency, which is found to satisfy a fixed-point equation. The spectral efficiency of such a system under both joint and separate decoding are derived. Based on a general linear vector channel model, our results are also applicable to MIMO channels such as those arising in multiantenna systems. 1