  In this work, we consider an energy harvesting device (EHD) served by an
access point with a single antenna that is used for both wireless power
transfer (WPT) and data transfer. The objective is to maximize the expected
throughput of the EHD over a finite horizon when the channel state information
is only available causally. The EHD is energized by WPT for a certain duration,
which is subject to optimization, and then, EHD transmits its information bits
to the AP until the end of the time horizon by employing optimal dynamic power
allocation. The joint optimization problem is modeled as a dynamic programming
problem. Based on the characteristic of the problem, we prove that a time
dependent threshold type structure exists for the optimal WPT duration, and we
obtain closed form solution to the dynamic power allocation in the uplink
period.
