  Limited-backhaul cell-free Massive multiple-input multiple-output (MIMO), in
which the fog radio access network (F-RAN) is implemented to exchange the
information between access points (APs) and the central processing unit (CPU),
is investigated. We introduce a novel approach where the APs estimate the
channel and send back the quantized version of the estimated channel and the
quantized version of the received signal to the central processing unit. The
Max algorithm and the Bussgang theorem are exploited to model the optimum
uniform quantization. The ergodic achievable rates are derived. We show that
exploiting microwave wireless backhaul links and using a small number of bits
to quantize the estimated channel and the received signal, the performance of
limited-backhaul cell-free Massive MIMO closely approaches the performance of
cell-free Massive MIMO with perfect backhaul links.
