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The calculation of the SIR distribution at the typical receiver (or,equivalently, the success probability of transmissions over the typical link)in Poisson bipolar and cellular networks with Rayleigh fading is relativelystraightforward, but it only provides limited information on the successprobabilities of the individual links. This paper introduces the notion of themeta distribution of the SIR, which is the distribution of the conditionalsuccess probability $P$ given the point process, and provides bounds, an exactanalytical expression, and a simple approximation for it. The meta distributionprovides fine-grained information on the SIR and answers questions such as"What fraction of users in a Poisson cellular network achieve 90% linkreliability if the required SIR is 5 dB?". Interestingly, in the bipolar model,if the transmit probability $p$ is reduced while increasing the network density$\lambda$ such that the density of concurrent transmitters $\lambda p$ staysconstant as $p\to 0$, $P$ degenerates to a constant, i.e., all links haveexactly the same success probability in the limit, which is the one of thetypical link. In contrast, in the cellular case, if the interfering basestations are active independently with probability $p$, the variance of $P$approaches a non-zero constant when $p$ is reduced to $0$ while keeping themean success probability constant.

The Meta Distribution of the SIR in Poisson Bipolar and Cellular Networks