Replica analysis of large-system CDMA

We present some new results on large-system CDMA obtained through the replica method developed in statistical physics. We find the spectral efficiency of randomly spread CDMA subject to Gaussian noise and flat fading in the large-system limit under arbitrary input distributions. Both joint decoding and single-user decoding are considered. In the latter case, a conditional mean estimator is first applied to separate the users and it is found that the resulting single-user channel for every user is equivalent to a Gaussian channel. The multiuser efficiency of that Gaussian channel is the same for all users and satisfies a fixed-point equilibrium equation. The additive decomposition by Shamai-Verdu of optimum capacity in terms of single-user capacity is shown to hold for arbitrary input distributions.