  This paper considers a nonlinear multi-hop multi-user multiple-input
multiple-output (MU-MIMO) relay channel, in which multiple users send
information symbols to a multi-antenna base station (BS) with one-bit
analog-to-digital converters via intermediate relays, each with one-bit
transceiver. To understand the fundamental limit of the detection performance,
the optimal maximum-likelihood (ML) detector is proposed with the assumption of
perfect and global channel state information (CSI) at the BS. This multi-user
detector, however, is not practical due to the unrealistic CSI assumption and
the overwhelming detection complexity. These limitations are addressed by
presenting a novel detection framework inspired by supervised-learning. The key
idea is to model the complicated multihop MU-MIMO channel as a simplified
channel with much fewer and learnable parameters. One major finding is that,
even using the simplified channel model, a near ML detection performance is
achievable with a reasonable amount of pilot overheads in a certain condition.
In addition, an online supervised-learning detector is proposed, which
adaptively tracks channel variations. The idea is to update the model
parameters with a reliably detected data symbol by treating it as a new
training (labelled) data. Lastly, a multi-user detector using a deep neural
network is proposed. Unlike the model-based approaches, this model-free
approach enables to remove the errors in the simplified channel model, while
increasing the computational complexity for parameter learning. Via
simulations, the detection performances of classical, model-based, and
model-free detectors are thoroughly compared to demonstrate the effectiveness
of the supervised-learning approaches in this channel.
