Multiuser detection using Random-Set Theory

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 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 a number of users larger than the real one may impair performance. This paper assumes a dynamic environment where users are continuously entering and leaving the system, and undertakes a general approach to the problem of identifying active users and estimating their parameters and data. Our goal is to lay the foundation of multiuser detection theory in an environment where the number and the parameters of active users are unknown at the receiver, and in addition may change from one observation time to the next following a known dynamic model. Using Random-Set Theory, we develop the tools that are needed for data detection in addition to parameter estimation, whereby a dynamic model for the evolution of parameters has been selected. Application of this theory allows Bayesian-filter equations to be written, which describe the evolution with time of the optimum causal multiuser detector. We illustrate this theory through a simple example of application, consisting of the detection of the number and identity of active interferers and of the data they carry.