  In this paper, we study wireless powered communication networks that employ
the slotted ALOHA protocol, which is the preferred protocol for simple and
uncoordinated networks. In the energy harvesting (EH) phase, the base station
broadcasts radio frequency energy to the EH users (EHUs). The EHUs harvest the
broadcasted energy and use it to transmit information back to the base station
by contending for access to the uplink channel in the random access (RA) phase.
In order to ensure fairness among the users, we propose a proportionally fair
resource allocation scheme that exploits the RA nature of slotted ALOHA.
Specifically, assuming statistical channel state information, we determine the
optimal transmit power at the base station, the optimal durations of the EH and
RA phases, the channel access probability, and the rate of each EHU.
