Multiuser detection based on random-set theory

In mobile multiple-access communications, not only the location of active users, but also their number varies with time. In typical analysis, multiuser detection theory has been developed under the assumption that the number of active users is constant and known at the receiver, and coincides with the maximum number of users entitled to access the system. This assumption is often overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of the number of users larger than the real one may impair performance. The main goal of this paper is to introduce a general approach to the problem of identifying active users and estimating their parameters and data in a random-access system where users are continuously entering and leaving the system. The tool we advocate is random-set theory (RST): applying this, we derive optimum receivers in an environment where the set of transmitters comprises an unknown number of elements. In this paper we restrict ourselves to active user identification and data detection.