On the Distribution of SINR for Cell-Free Massive MIMO Systems

Cell-free (CF) massive multiple-input multiple-output (mMIMO) has been considered as a potential technology for Beyond 5G. However, the performance of CF mMIMO systems has not been thoroughly studied. Most existing analytical studies on CF mMIMO systems rely on deriving average performance metrics. The statistical characteristics of the signal-to-interference-plus-noise ratio (SINR), which capture the tail behavior of SINR, are crucial for metrics such as outage probability and for emerging mission-critical applications that emphasize extreme and rare events, but have not been thoroughly investigated. In this paper, we aim to obtain the distribution of SINR in CF mMIMO systems. Considering a downlink CF mMIMO system with pilot contamination, we first give the closed-form expression of the SINR. Based on our analytical work on the two components of the SINR, i.e., desired signal and interference-plus-noise, we then derive the probability density function and cumulative distribution function of the SINR under maximum ratio transmission (MRT) and full-pilot zero-forcing (FZF) precoding, respectively. Subsequently, the closed-form expressions for two more sophisticated performance metrics, i.e., ergodic rate and outage probability, are obtained. Finally, we perform Monte Carlo simulations to validate our analytical work. Numerous numerical results demonstrate the effectiveness of the derived SINR distribution, ergodic rate, and outage probability.