  Cell-free Massive multiple-input multiple-output (MIMO) is considered, where
distributed access points (APs) multiply the received signal by the conjugate
of the estimated channel, and send back a quantized version of this weighted
signal to a central processing unit (CPU). For the first time, we present a
performance comparison between the case of perfect fronthaul links, the case
when the quantized version of the estimated channel and the quantized signal
are available at the CPU, and the case when only the quantized weighted signal
is available at the CPU. The Bussgang decomposition is used to model the effect
of quantization. The max-min problem is studied, where the minimum rate is
maximized with the power and fronthaul capacity constraints. To deal with the
non-convex problem, the original problem is decomposed into two sub-problems
(referred to as receiver filter design and power allocation). Geometric
programming (GP) is exploited to solve the power allocation problem whereas a
generalized eigenvalue problem is solved to design the receiver filter. An
iterative scheme is developed and the optimality of the proposed algorithm is
proved through uplink-downlink duality. A user assignment algorithm is proposed
which significantly improves the performance. Numerical results demonstrate the
superiority of the proposed schemes.
