The meta distribution (MD) of the signal to interference ratio (SIR) extends stochastic geometry analysis from spatial averages to reveals find-grained information about the network performance. There have been several efforts to establish the MD framework for the Poisson point process (PPP) and other ergodic point processes. However, the MD analysis for finite point processes is overlooked. In this letter, we develop the MD of the binomial point process (BPP), which is practical for cases with a priori knowledge about the number of devices as well as their geographical spatial existence. For such finite models, we define the MD as a location-dependent likelihood of a receiver to achieve a required SIR with a probability more than a predefined threshold. This letter also extends the MD of the BPP to find the MD of finite PPP and verifies the convergence of the newly derived MD to the ergodic PPP's MD. The obtained analytical derivations are validated using Monte-Carlo simulations.

中文翻译：

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二项式点过程下行链路 SIR 的元分布


信号干扰比 (SIR) 的元分布 (MD) 将随机几何分析从空间平均值扩展到揭示有关网络性能的细粒度信息。为了建立泊松点过程 (PPP) 和其他遍历点过程的 MD 框架，人们做出了一些努力。然而，有限点过程的 MD 分析却被忽视了。在这封信中，我们开发了二项式点过程（BPP）的MD，这对于具有有关设备数量及其地理空间存在的先验知识的情况是实用的。对于此类有限模型，我们将 MD 定义为接收器以大于预定义阈值的概率实现所需 SIR 的位置相关可能性。这封信还扩展了 BPP 的 MD，以找到有限 PPP 的 MD，并验证了新导出的 MD 与遍历 PPP 的 MD 的收敛性。使用蒙特卡罗模拟验证所获得的分析推导。