  New communication standards need to deal with machine-to-machine
communications, in which users may start or stop transmitting at any time in an
asynchronous manner. Thus, the number of users is an unknown and time-varying
parameter that needs to be accurately estimated in order to properly recover
the symbols transmitted by all users in the system. In this paper, we address
the problem of joint channel parameter and data estimation in a multiuser
communication channel in which the number of transmitters is not known. For
that purpose, we develop the infinite factorial finite state machine model, a
Bayesian nonparametric model based on the Markov Indian buffet that allows for
an unbounded number of transmitters with arbitrary channel length. We propose
an inference algorithm that makes use of slice sampling and particle Gibbs with
ancestor sampling. Our approach is fully blind as it does not require a prior
channel estimation step, prior knowledge of the number of transmitters, or any
signaling information. Our experimental results, loosely based on the LTE
random access channel, show that the proposed approach can effectively recover
the data-generating process for a wide range of scenarios, with varying number
of transmitters, number of receivers, constellation order, channel length, and
signal-to-noise ratio.
