Optimal Energy Efficiency in Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

The increasing demand for green wireless communications and the benefits of the promising cell-free (CF) massive multiple-input-multiple-output (mMIMO) systems towards their optimal energy efficiency (EE) are the focal points of this work. Specifically, despite previous works assuming a uniform placement for the access points (APs), we consider that their locations follow a Poisson point process (PPP) which approaches their opportunistic spatial randomness. Based on stochastic geometry, we derive a lower bound on the average spectral efficiency, and under a realistic power consumption model for CF mMIMO systems, we formulate an EE maximization problem achieving to obtain in closed form the optimal EE per unit area in terms of the pilot reuse factor and the AP density. Note that we have defined the EE per unit area and not just the EE to characterize the energy in systems with multi-point transmission. Thus, we provide important design insights for energy-efficient CF mMIMO systems.