We analyze multiuser detection under the assumption that the number of users
accessing the channel is unknown by the receiver. In this environment, users'
activity must be estimated along with any other parameters such as data, power,
and location. Our main goal is to determine the performance loss caused by the
need for estimating the identities of active users, which are not known a
priori. To prevent a loss of optimality, we assume that identities and data are
estimated jointly, rather than in two separate steps. We examine the
performance of multiuser detectors when the number of potential users is large.
Statistical-physics methodologies are used to determine the macroscopic
performance of the detector in terms of its multiuser efficiency. Special
attention is paid to the fixed-point equation whose solution yields the
multiuser efficiency of the optimal (maximum a posteriori) detector in the
large signal-to-noise ratio regime. Our analysis yields closed-form approximate
bounds to the minimum mean-squared error in this regime. These illustrate the
set of solutions of the fixed-point equation, and their relationship with the
maximum system load. Next, we study the maximum load that the detector can
support for a given quality of service (specified by error probability).Comment: to appear in IEEE Transactions on Information Theor