Optimized Energy Harvesting in Cell-Free Massive MIMO Using Markov Process Evolution

This paper investigates a discrete energy state transition model for energy harvesting (EH) in cell-free massive multiple-input-multiple-output (CF-mMIMO) networks. A Markov chain-based stochastic process is conceived to characterize the temporal evolution of the user equipment (UE) energy level by leveraging state transition probabilities (STP) based on the energy differential ($\Delta E$) between the EH and consumed energy within each coherence interval. Tractable mathematical relationships are derived for the STP cases using a new stochastic model of non-linear EH, approximated using a Gamma distribution. This derivation leverages closed-form expressions for the mean and variance of the harvested energy. To improve the positive STP of the minimum energy UE among all network UEs, we aim to maximize the $\Delta E$ for this UE using two power allocation (PA) schemes. The first scheme is a heuristic PA using the relative channel characteristics to this UE from all access points (APs). The second scheme is the optimized PA based on the solution of a second-order conic problem to maximize the $\Delta E$ using a responsive primal-dual interior point method (PD-IPM) algorithm with modified backtracking line-search, iterating over multiple PA periods. Our simulation results illustrate that both the proposed PA schemes enhance the dynamic minimum UE energy level by around four-fold over full power control, along with the performance improvement attributed to spatial resource diversification of CF-mMIMO systems.