Lyapunov Optimized Cooperative Communications With Stochastic Energy Harvesting Relay

Energy harvesting (EH) wireless communications have become more and more popular due to its capability of effectively reducing the battery replacement time. In this paper, we focus on decode-and-forward-based cooperative wireless communications with an EH relay. The stochastic characteristics of the harvestable energy and the wireless channel make it difficult to optimally manage the energy harvested at the relay for better communication performance. We formulate such a problem as an optimization by minimizing the long-term average symbol error rate (SER) subject to a battery constraint. Based on the Lyapunov optimization theory, we utilize the virtual queue technique and transform the optimization problem into a drift-plus-penalty minimization. Then, we conduct theoretic analysis of the optimal energy strategy derived by the proposed scheme. Specifically, we show the convexity of the drift-plus-penalty minimization problem, and prove that the virtual queue is bounded and the battery constraint is always satisfied. We also show that the proposed optimal energy management strategy is limited by an upper bound that is independent of the operation time index, derive the closed-form expression for the asymptotical average SER, and analyze the corresponding diversity order and EH gain. Finally, simulation results using the real solar irradiance data show that the proposed algorithm can achieve much better performance in terms of both average SER and diversity order, compared with the Markov decision process-based method.