Cell-free (CF) massive multiple-input multiple-output (mMIMO) has been considered as a potential technology for Beyond 5G communication systems. However, the performance of CF mMIMO systems has not been well studied. Most existing analytical work on CF mMIMO systems is based on the expected signal-to-interference-plus-noise ratio (SINR). The statistical characteristics of the SINR, which is critical for emerging applications that focus on extreme events, have not been investigated. To address this issue, in this paper, we attempt 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., achievable rate and outage probability, can be obtained. Finally, we perform Monte Carlo simulations to validate our analytical work. The results demonstrate the effectiveness of the derived SINR distribution, achievable rate, and outage probability.

翻译：无蜂窝大规模多输入多输出（CF mMIMO）已被视为超5G通信系统的潜在技术。然而，CF mMIMO系统的性能尚未得到充分研究。现有大多数关于CF mMIMO系统的分析工作基于期望信干噪比（SINR）。对于关注极端事件的新兴应用至关重要的SINR统计特性，尚未得到研究。为解决这一问题，本文尝试获取CF mMIMO系统中SINR的分布。考虑存在导频污染的下行CF mMIMO系统，我们首先给出SINR的闭式表达式。基于对SINR两个分量（即期望信号与干扰加噪声）的分析工作，我们分别推导了最大比传输（MRT）和全导频迫零（FZF）预编码下SINR的概率密度函数和累积分布函数。随后，可得到两个更复杂性能指标（即可达速率和中断概率）的闭式表达式。最后，我们通过蒙特卡洛仿真验证分析结果，验证了所推导的SINR分布、可达速率和中断概率的有效性。