Meta Distribution of Downlink SIR for Binomial Point Processes

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.