Coverage Probability and Ergodic Capacity of Cell-Free Massive MIMO System

This letter studies the performance of an uplink cell-free massive multiple-input multiple-output (MIMO) system with maximum-ratio combining receiver over Rayleigh fading channel, in which many distributed access points configured with multiple antennas provide services to multiple single-antenna users. For such a system, we derive an exact expression for probability density function (PDF) of individual signal-to-interference-plus-noise ratio (SINR). Due to its complexity for performance evaluation purposes, this PDF of SINR is approximated as a gamma distribution, and the resulting expression is used to obtain the approximate expressions of the coverage probability and the ergodic capacity, respectively. Besides, in order to ensure uniformly good coverage probability and ergodic capacity, a max-min power control algorithm is proposed, which can be formed by solving a geometric programming problem. Numerical results verify the correctness of the theoretical analysis and confirm the effectiveness of the proposed algorithm.