  We propose a novel soft-output joint channel estimation and data detection
(JED) algorithm for multiuser (MU) multiple-input multiple-output (MIMO)
wireless communication systems. Our algorithm approximately solves a maximum
a-posteriori JED optimization problem using deep unfolding and generates
soft-output information for the transmitted bits in every iteration. The
parameters of the unfolded algorithm are computed by a hyper-network that is
trained with a binary cross entropy (BCE) loss. We evaluate the performance of
our algorithm in a coded MU-MIMO system with 8 basestation antennas and 4 user
equipments and compare it to state-of-the-art algorithms separate channel
estimation from soft-output data detection. Our results demonstrate that our
JED algorithm outperforms such data detectors with as few as 10 iterations.
