Online Power Control Based on Lyapunov Optimization Framework for Decode-and-Forward Relay Systems With Energy Harvesting

This paper studies the power control in a two-hop decode-and-forward relay system over fading channel. The relay node is an energy harvesting node and is equipped with a data buffer and a rechargeable battery with finite capacity. Under the condition that any prior and statistical knowledge about the harvested energy and channel fading is unknown, based on the Lyapunov optimization framework, an online power control strategy for the source node and the relay node is proposed to maximize the average transmission rate and minimize the average energy consumption of the source node. First, the optimization problem is decomposed into two sub-problems: minimizing the average energy consumption of the source node and maximizing the average transmission rate of the relay node. Then, we use the Lyapunov optimization framework to transform the minimization and maximization problems to the minimization of the upper bounds of two “drift-plus-penalty”s and solve them. The solution of the optimization problem only relies on the current channel coefficient, the state of the data buffer, the energy level of the battery in the current time slot, and the average transmission rate of the past time slots. Only a few calculations are needed to get the optimal power of the source node and the relay node. Finally, simulation is done to verify the performance of the proposed algorithm. The simulation results show that the transmission rate difference between the proposed algorithm and the ideal offline water filling algorithm is small, which has full knowledge of energy and channels in advance and is without the constraints of the causality of energy and data, and the overflow of the battery and data buffer. The proposed algorithm is greatly superior to the online greedy algorithm and the semi-greedy algorithm.