  We consider the achievable average rates of a multiple-access system, which
consists of N energy-harvesting users (EHUs) that transmit information over a
block fading multiple-access channel (MAC) and a base station (BS) that
broadcasts radio frequency (RF) energy to the EHUs for wireless power transfer.
The information (over the uplink) and power (over the downlink) can be
transmitted either in time division duplex or frequency division duplex. For
the case when the EHUs battery capacities and the number of transmission slots
are both infinite, we determine the optimal power allocation for the BS and the
optimal rates and power allocations for the EHUs that maximize the achievable
rate region of the MAC. The resulting online solution is asymptotically
optimal, and also applicable for a finite number of transmission slots and
finite battery capacities.
