Statistical Mechanical Study of Code-Division Multiple-Access Multiuser Detectors —Analysis of Replica Symmetric and One-Step Replica Symmetry Breaking Solutions—

We study the problem of performance evaluation of code-division multiple-access (CDMA) multiuser detectors by means of statistical mechanics using the replica method. The replica symmetric solutions were analyzed previously. As is well known, the replica symmetric solution becomes unstable when the temperature (magnitude of noise) is lowered. In this paper, we investigate both the behavior and the stability of the replica symmetric solutions in the low temperature region. We find that the solutions have complicated bifurcation structures in the low temperature region where the solutions coexist. We also find that there are two types of replica symmetry breaking, Almeida–Thouless (AT)-instability and freezing. We obtain the one-step replica symmetry breaking solution in each case. Further, we compare the theoretical results with the results from the Monte-Carlo simulations. Consequently, we find that the theoretical results agree with the numerical simulations.