  In this paper, we consider a wireless powered communication network where
multiple users with RF energy harvesting capabilities communicate to a hybrid
energy and information access point (HAP) in full-duplex mode. Each user has to
transmit a certain amount of data with a transmission rate from a finite set of
discrete rate levels, using the energy initially available in its battery and
the energy it can harvest until the end of its transmission. Considering this
model, we propose a novel discrete rate based minimum length scheduling problem
to determine the optimal power control, rate adaptation and transmission
schedule subject to data, energy causality and maximum transmit power
constraints. The proposed optimization problem is proven to be NP-hard which
requires exponential-time algorithms to solve for the global optimum. As a
solution strategy, first, we demonstrate that the power control and rate
adaptation, and scheduling problems can be solved separately in the optimal
solution. For the power control and rate adaptation problem, we derive the
optimal solution based on the proposed minimum length scheduling slot
definition. For the scheduling, we classify the problem based on the
distribution of minimum length scheduling slots of the users over time. For the
non-overlapping slots scenario, we present the optimal scheduling algorithm.
For the overlapping scenario, we propose a polynomial-time heuristic scheduling
algorithm.
