Optimal power and rate allocation in the degraded Gaussian relay channel with energy harvesting nodes

Energy Harvesting (EH) is a novel technique to prolong the lifetime of the wireless networks such as wireless sensor networks or Ad-Hoc networks, by providing an unlimited source of energy for their nodes. In this sense, it has emerged as a promising technique for Green Communications, recently. On the other hand, cooperative communication with the help of relay nodes improves the performance of wireless communication networks by increasing the system throughput or the reliability as well as the range and efficient energy utilization. In order to investigate the cooperation in EH nodes, in this paper, we consider the problem of optimal power and rate allocation in the degraded full-duplex Gaussian relay channel in which source and relay can harvest energy from their environments. We consider the general stochastic energy arrivals at the source and the relay with known EH times and amounts at the transmitters before the start of transmission. This problem has a min-max optimization form that along with the constraints is not easy to solve. We propose a method based on a mathematical theorem proposed by Terkelsen [1] to transform it to a solvable convex optimization form. Also, we consider some special cases for the harvesting profile of the source and the relay nodes and find their solutions efficiently.