  In random-access communication systems, the number of active users varies
with time, and has considerable bearing on receiver's performance. Thus,
techniques aimed at identifying not only the information transmitted, but also
that number, play a central role in those systems. An example of application of
these techniques can be found in multiuser detection (MUD). In typical MUD
analyses, receivers are based on 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.
  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 whose use we advocate is Random-Set Theory: applying this, we
derive optimum receivers in an environment where the set of transmitters
comprises an unknown number of elements. In addition, we can derive
Bayesian-filter equations which describe the evolution with time of the a
posteriori probability density of the unknown user parameters, and use this
density to derive optimum detectors. In this paper we restrict ourselves to
interferer identification and data detection, while in a companion paper we
shall examine the more complex problem of estimating users' parameters.
