  In this paper we study the expectation maximization (EM) technique for
one-bit MIMO-OFDM detection (OMOD). Arising from the recent interest in massive
MIMO with one-bit analog-to-digital converters, OMOD is a massive-scale
problem. EM is an iterative method that can exploit the OFDM structure to
process the problem in a per-iteration efficient fashion. In this study we
analyze the convergence rate of EM for a class of approximate
maximum-likelihood OMOD formulations, or, in a broader sense, a class of
problems involving regression from quantized data. We show how the SNR and
channel conditions can have an impact on the convergence rate. We do so by
making a connection between the EM and the proximal gradient methods in the
context of OMOD. This connection also gives us insight to build new accelerated
and/or inexact EM schemes. The accelerated scheme has faster convergence in
theory, and the inexact scheme provides us with the flexibility to implement EM
more efficiently, with convergence guarantee. Furthermore we develop a deep EM
algorithm, wherein we take the structure of our inexact EM algorithm and apply
deep unfolding to train an efficient structured deep net. Simulation results
show that our accelerated exact/inexact EM algorithms run much faster than
their standard EM counterparts, and that the deep EM algorithm gives promising
detection and runtime performances.
