  This paper considers a wireless powered communication network (WPCN), where
multiple users harvest energy from a dedicated power station and then
communicate with an information receiving station. Our goal is to investigate
the maximum achievable energy efficiency (EE) of the network via joint time
allocation and power control while taking into account the initial battery
energy of each user. We first study the EE maximization problem in the WPCN
without any system throughput requirement. We show that the EE maximization
problem for the WPCN can be cast into EE maximization problems for two
simplified networks via exploiting its special structure. For each problem, we
derive the optimal solution and provide the corresponding physical
interpretation, despite the non-convexity of the problems. Subsequently, we
study the EE maximization problem under a minimum system throughput constraint.
Exploiting fractional programming theory, we transform the resulting non-convex
problem into a standard convex optimization problem. This allows us to
characterize the optimal solution structure of joint time allocation and power
control and to derive an efficient iterative algorithm for obtaining the
optimal solution. Simulation results verify our theoretical findings and
demonstrate the effectiveness of the proposed joint time and power
optimization.
