Uplink Coverage of User-Centric Cell-Free Networks Under Pilot Contamination and Spatial Correlation: A Tractable Stochastic Geometry Analysis

Abstract

Cell-free massive multiple-input multiple-output (MIMO) has been recognized as a key technology of sixth-generation mobile systems. However, its performance is limited by pilot contamination, spatial antenna correlation, and path loss. This paper studies the uplink coverage probability of a user-centric cell-free network in which access points (APs) and users are distributed as independent Poisson point processes. In this model, each user is served by all APs within a fixed cluster radius. The combined channel gain is factorized into a geometric factor, which collects the estimation qualities of the serving APs, and a fading factor. Both are driven by the same co-pilot users, so the desired signal and the coherent interference cannot be treated as independent. A two-point Laplace functional of the co-pilot field is therefore derived to capture the correlation between the estimation qualities of two APs, and the remaining dependence is modeled by a Gaussian copula, which yields the coverage probability in a semi-closed form. Numerical results show that under light load the antenna correlation costs 3% of the coverage probability at <inline-formula> <tex-math notation="LaTeX">$\rho =0.3$ </tex-math></inline-formula> and 16% at <inline-formula> <tex-math notation="LaTeX">$\rho =0.6$ </tex-math></inline-formula> relative to uncorrelated antennas. The same impairment is far more critical under heavy load, where the coverage probability declines by more than 96% as <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> rises to 0.9. In addition, the effective throughput admits an interior optimum in both the pilot length and the cluster radius.