Large-System Analysis of Static Multiuser Detection with an Unknown Number of Users

We present a study of large multiple-access communication systems in which multiuser detection is performed without knowledge of the number of interferers. When the number of users increases without bound, optimum detectors can be analyzed asymptotically. A statistical physics approach based on spin glass theory provides analytical tools to deal with large systems in which the performance parameters to be analyzed (error probabilities, etc) are self-averaging in the limit. Of particular interest is the replica method that is used as a key technique to compute the free-energy function and the macroscopic parameters that determine the multiuser efficiency and the bit error probability in the large system limit.