Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs

We investigate the application of the factor graph
framework for blind joint channel estimation and symbol detec-
tion on time-variant linear inter-symbol interference channels.
In particular, we consider the expectation maximization (EM)
algorithm for maximum likelihood estimation, which typically
suffers from high complexity as it requires the computation of the
symbol-wise posterior distributions in every iteration. We address
this issue by efficiently approximating the posteriors using the
belief propagation (BP) algorithm on a suitable factor graph. By
interweaving the iterations of BP and EM, the detection complex-
ity can be further reduced to a single BP iteration per EM step. In
addition, we propose a data-driven version of our algorithm that
introduces momentum in the BP updates and learns a suitable
EM parameter update schedule, thereby significantly improving
the performance-complexity tradeoff with a few offline training
samples. Our numerical experiments demonstrate the excellent
performance of the proposed blind detector and show that it
even outperforms coherent BP detection in high signal-to-noise
scenarios.