  In this paper, we consider the uplink of cell-free massive MIMO systems,
where a large number of distributed single antenna access points (APs) serve a
much smaller number of users simultaneously via limited backhaul. For the first
time, we investigate the performance of compute-and-forward (C&F) in such an
ultra dense network with a realistic channel model (including fading, pathloss
and shadowing). By utilising the characteristic of pathloss, a low complexity
coefficient selection algorithm for C\&F is proposed. We also give a greedy AP
selection method for message recovery. Additionally, we compare the performance
of C&F to some other promising linear strategies for distributed massive MIMO,
such as small cells (SC) and maximum ratio combining (MRC). Numerical results
reveal that C&F not only reduces the backhaul load, but also significantly
increases the system throughput for the symmetric scenario.
