—In this letter, we consider a cloud radio access networks (C-RANs) in which base stations (BSs) are uniformly distributed inside a disk. The outage probability and the ergodic rate achieved by this C-RANs are analysed, where stochastic geometry is used to capture the randomness of BS locations. Compared to existing studies to C-RANs, more accurate analytical results are developed by applying the Gaussian-Chebyshev integration, as confirmed by our simulation results. Keywords—Cloud radio access networks, randomly deployed base stations, Gauss-Chebyshev integration, distributed beamforming.