Secrecy Performance Evaluation of Scalable Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

This paper presents the first performance analysis of physical layer downlink secure transmissions in a scalable cell-free massive MIMO (SCF-mMIMO) system. A stochastic geometry approach is used to model the locations of the access points (APs), user equipments (UEs), and eavesdroppers (Eves) as independent homogeneous Poisson point processes (HPPPs). In addition to applying maximum ratio transmission (MRT) to send the confidential messages, null-space artificial noise is also injected for secrecy enhancement. We analytically characterize the secrecy performance in terms of both the outage-based secrecy transmission rate (STR) and the ergodic secrecy rate (ESR), appropriate for slow quasi-static fading channels and fast block-fading channels, respectively. By utilizing moment matching and Gil-Pelaez inversion theorem, we are able to obtain mathematically tractable approximations for the performance metrics. These approximations are shown to have high accuracy as compared to simulation results. Our numerical results reveal useful design insights that cannot be inferred from existing studies. These insights answer important questions such as whether it is best to deploy as many APs each with fewer antennas and to what extent the artificial noise insertion is beneficial.