Large-System Analysis of Multiuser Detection with an Unknown Number of Users: A High-SNR Approach

TL;DR

This paper investigates the performance of multiuser detection in large systems when the number of active users is unknown, using high-SNR analysis and statistical physics methods to derive bounds and system load limits.

Contribution

It introduces a high-SNR analysis framework for multiuser detection with unknown user activity, providing closed-form bounds and insights into system load capacity.

Findings

Derived approximate bounds for minimum mean-squared error at high SNR.

Analyzed the fixed-point equations for multiuser efficiency.

Identified maximum system load for given error probability.

Abstract

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).