High-SNR analysis of optimum multiuser detection with an unknown number of users

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. 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 fixed-point equation whose solutions yield the multiuser efficiency of the optimal detector. Special attention is paid to the large signal-to-noise ratio, which yields tight closed-form bounds on the minimum mean-squared error. These bounds analytically illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. By identifying the region of computationally feasible solutions, we study the maximum load that the detector can support for a given SNR and quality of service, specified by the multiuser efficiency.