  The performance of simultaneous wireless information and power transfer
(SWIPT) in downlink (DL) cell-free massive multiple-input multiple-output
(MIMO) is investigated. Tight approximations to the DL harvested energy and the
DL/uplink (UL) achievable rates are derived for two practical channel state
information (CSI) cases by using a non-linear energy harvesting model for
time-switching and power-splitting protocols. Max-min fairness-based transmit
power control policies are employed to mitigate the deleterious near-far
effects caused by distributed transmissions/receptions in cell-free massive
MIMO. The achievable common DL energy-rate trade-off is derived, and thereby,
it is shown that the proposed max-min power control guarantees user-fairness
regardless of near-far effects in terms of both harvested energy and achievable
rate. The benefits of user estimated DL CSI to boost the SWIPT performance are
explored. These performance metrics are compared against those of the
conventional co-located massive MIMO, and thereby, it is revealed that the
reduction of path-losses and lower average transmit powers offered by cell-free
massive MIMO can be exploited to boost the energy-rate trade-off of SWIPT at
the expense of increased backhaul requirements.
