On the Time Scales of Energy Arrival and Channel Fading in Energy Harvesting Communications

In wireless communication systems powered by harvested energy, besides the channel fading, there exists another dimension of dynamics, i.e., energy arrival variation. In this paper, we propose a framework for analyzing the energy harvesting powered wireless transmissions where the energy arrival variations and the channel fading are of different timescales. The energy arrival rate changes every N(N ≥ 1) time slots, and the channel state changes every M(M ≥ 1) slots. We consider a power allocation problem among the time slots, which can be formulated as a Markov decision process and solved by dynamic programming (DP) algorithm. For the special case that M = 1, a low-complexity two-stage DP algorithm is proposed, which decouples the original problem into inner and outer 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 when the energy arrival rate changes. Numerical simulations show that the average data rate decreases as N or M increases, and the two-stage DP algorithm can perform close to the DP optimal algorithm.