In wireless communication systems powered by harvested energy, besides the channel fading, there is another dimension of dynamics induced by energy arrival variations, which makes the design of wireless transmission policies nontrivial. In this paper, we propose a framework for analyzing the energy harvesting powered wireless transmissions where the channel fading and the energy arrival variations are of different timescales. We define the duration between two consecutive changes of energy arrival rate as an energy harvesting frame, which consists of N channel fading slots. The power allocation problem can be formulated as an Markov decision process (MDP), and can be decoupled into two sub-problems. The inner problem deals with the power allocation in channel fading timescale in every N slots where the energy arrival rate keeps constant, and the outer problem deals with the energy management in energy harvesting timescale among frames. The two sub-problems can be solved by finite horizon dynamic programming (DP) and infinite horizon DP, respectively. Numerical simulations show that the average rate decreases slightly as N increases, and the rate under i.i.d. channel is higher than that under Markov channel.
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