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 (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 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 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.