Spectral Efficiency of Large-system CDMA via Statistical Physics

The channel capacity of randomly spread CDMA subject to Gaussian noise and flat fading is studied in the large-system limit under arbitrary input distributions. Using the replica method originally developed in statistical physics, we find the spectral efficiencies under both joint decoding and single-user decoding. We show that under single-user decoding, where a conditional mean estimator is first applied to separate the users, each user is as if transmitting through a degraded Gaussian channel where the ratio of the effective energy to the true energy is the same multiuser efficiency to everyone. It is found that the multiuser efficiency is the solution to a fixed-point equilibrium equation. The spectral efficiency under both joint and separate decoding are expressed explicitly in the multiuser efficiency, the input distribution and the fading characteristics.