  We propose a joint channel estimation and data detection (JED) algorithm for
densely-populated cell-free massive multiuser (MU) multiple-input
multiple-output (MIMO) systems, which reduces the channel training overhead
caused by the presence of hundreds of simultaneously transmitting user
equipments (UEs). Our algorithm iteratively solves a relaxed version of a
maximum a-posteriori JED problem and simultaneously exploits the sparsity of
cell-free massive MU-MIMO channels as well as the boundedness of QAM
constellations. In order to improve the performance and convergence of the
algorithm, we propose methods that permute the access point and UE indices to
form so-called virtual cells, which leads to better initial solutions. We
assess the performance of our algorithm in terms of root-mean-squared-symbol
error, bit error rate, and mutual information, and we demonstrate that JED
significantly reduces the pilot overhead compared to orthogonal training, which
enables reliable communication with short packets to a large number of UEs.
