Energy Harvesting Characterization in Cell-Free Massive MIMO Using Markov Chains

Abstract

This paper explores a discrete energy state transition model for energy harvesting (EH) in cell-free massive multiple-input multiple-output (CF-mMIMO) networks. Multiple-antenna access points (APs) provide wireless power and information to single-antenna UE equipment (UEs). The harvested energy at the UEs is used for both uplink (UL) training and data transmission. We investigate the energy transition probabilities based on the energy differential achieved in each coherence interval. A Markov chain-based stochastic process is introduced to characterize the evolving UE energy status. A detailed statistical model is developed for a non-linear EH circuit at the UEs, using the derived closed-form expressions for the mean and variance of the harvested energy. More specifically, simulation results confirm that the proposed Gamma distribution approximation can accurately capture the statistical behavior of the harvested energy. Furthermore, the energy state transitions are evaluated using the proposed Markov chain-based framework, while mathematical expressions for the self, positive and negative transition probabilities of the discrete energy states are also presented. Our numerical results depict that increasing the number of APs with a constant number of service antennas provides significant improvement in the positive energy state transition and reduces the negative transition probabilities of the overall network.