Replica Analysis of Large-system CDMA

We present some new results on largesystem 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-Verdú of optimum capacity in terms of single-user capacity is shown to hold for arbitrary input distributions.