Proportional Fair Resource Allocation on an Energy Harvesting Downlink -   Part I: Structure
  This paper considers the allocation of time slots in a frame, as well as power and rate to multiple receivers on an energy harvesting downlink. Energy arrival times that will occur within the frame are known at the beginning of the frame. The goal is to optimize throughput in a proportionally fair way, taking into account the inherent differences of channel quality among users. Analysis of structural characteristics of the problem reveals that it can be formulated as a biconvex optimization problem, and that it has multiple optima. Due to the biconvex nature of the problem, a Block Coordinate Descent (BCD) based optimization algorithm that converges to an optimal solution is presented. Numerical and simulation results show that the power-time allocations found by BCD achieve a good balance between total throughput and fairness. 
Neyre Tekbiyik, Tolga Girici, Elif Uysal-Biyikoglu, and Kemal   Leblebicioglu
cs.NI