Multiuser detection using random-set theory

Ezio Biglieri¹ and Marco Lops²

¹Universitat Pompeu Fabra, Barcelona, Spain (e-mail: ezio.biglieri@upf.edu)

²Università di Cassino, Cassino, Italy (email: lops@unicas.it)

Abstract

In mobile multiple-access communications, not only the location of active users, but also their number varies with time. In typical analyses, multiuser detection theory assumes 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. In several situations, this assumption is overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of a number of users larger than the real one impairs performance.

This paper takes a different, more general approach to the problem of identifying (and possibly estimating the parameters of) active users in a dynamic environment where users are continuously entering and leaving the system. Our goal here is to lay the foundation of multiuser detection theory in an environment where the number of active users is unknown at the receiver, and in addition may change from one observation time to the next following a dynamic model. The tool of choice for our analysis is a probability theory developed over finite sets whose randomness is both in the number of their elements and in the values they take on.