This paper proposes a novel approach for computing the meta distribution of the signal-to-interference-plus-noise ratio (SINR) for the downlink transmission in a wireless network with Rayleigh fading. The novel approach relies on an approximation mix of exact and mean-field analysis of interference (dominant interferer-based approximation) to reduce the complexity of analysis and enhance tractability. In particular, the proposed approximation omits the need to compute the first or the second moment of the SINR that is used in the beta approximation typically adopted in the literature but requires of computing the joint distance distributions. We first derive the proposed approximation based on a Poisson point process (PPP) network with a standard path-loss and Rayleigh fading and then illustrate its accuracy and operability in another four widely used point processes: Poisson bipolar network, Mat\'{e}rn cluster process (MCP), $K$-tier PPP and Poisson line Cox process (PLCP). Specifically, we obtain the SINR meta distribution for PLCP networks for the first time. Even though the proposed approximation looks simple but it shows good matching in comparison to the popular beta approximation as well as the Monte-Carlo simulations, which opens the door to adopting this approximation in more advanced network architectures.

翻译：本文提出了一种新颖的方法，用于计算瑞利衰落无线网络下行传输中信号与干扰加噪声比（SINR）的元分布。该方法融合了精确分析与均场干扰分析的混合近似（基于主导干扰的近似），以降低分析复杂度并提升可处理性。具体而言，所提出的近似避免了文献中常用β近似时所需的SINR一阶或二阶矩计算，但需要联合距离分布的求解。我们首先基于标准路径损耗与瑞利衰落的泊松点过程（PPP）网络推导了该近似，随后在另外四种广泛使用的点过程中验证了其准确性与可操作性：泊松双极网络、马特恩聚类过程（MCP）、K层PPP及泊松线考克斯过程（PLCP）。特别地，我们首次获得了PLCP网络的SINR元分布。尽管所提出的近似形式简洁，但与流行的β近似及蒙特卡洛模拟结果相比，其匹配性良好，这为该近似在更复杂网络架构中的应用敞开了大门。