  This paper considers cell-free massive multiple-input multiple-output systems
where the multiple-antenna access points (APs) assist the single-antenna user
equipments (UEs) by wireless power transfer. The UEs utilize the energy
harvested in the downlink to transmit uplink pilot and information signals to
the APs. We consider practical Rician fading with the line-of-sight components
of the channels being phase-shifted in each coherence block. The uplink
spectral efficiency (SE) is derived for this model and the max-min fairness
problem is considered where the optimization variables are the AP and UE power
control coefficients together with the large-scale fading decoding vectors. The
objective is to maximize the minimum SE of the users under APs' and UEs'
transmission power constraints. An alternating optimization algorithm is
proposed for the solution of the highly-coupled non-convex problem.
