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

By Martin Haenggi. 2015

293 citations recorded by the source corpus.

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 relatively straightforward, but it only provides limited information on the success probabilities of the individual links. This paper focuses on the meta distribution of the SIR, which is the distribution of the conditional success probability Ps given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as “What fraction of users in a Poisson cellular network achieve 90% link reliability if the required SIR is 5 dB?” Interestingly, in the bipolar model, if the transmit probability p is reduced while increasing the network density λ such that the density of concurrent transmitters λp stays constant as p → 0, Ps degenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability p, the variance of Ps approaches a non-zero constant when p is reduced to 0 while keeping the mean success probability constant.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

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Citations in the corpus

The Meta Distribution of SINR for Small Cell Networks with Temporal Traffic (2019, background): “We first condition the SINR on the realization of point process Φ , Φb ∪ Φu, which is the dominant factor for a general communication link, and define the conditional SINR coverage probability as follows [11], [14].”
Wireless Access in Ultra-Reliable Low-Latency Communication (URLLC) (2018, background): “…another, more restrictive reliability constraint that effectively controls the higher order moments of the outage probability via the concept of meta-probability [46]; namely, we require: In other words, we limit the probability that the outage probability given X n is larger than (cid:15) .”
Spatio-Temporal Analysis for SINR Coverage in Small Cell Networks (2019, methodology): “, the UEs in the bottom 5th percentile in terms of coverage performance, and is particularly interested to operators [15], [27].”
Channel Hardening and Favorable Propagation in Cell-Free Massive MIMO With Stochastic Geometry (2017, result): “The separation of the randomness caused by small-scale fading and by the spatial locations of APs is similar to the concept of meta distribution proposed in [25], where the difference mainly lies in the definition of the studied performance metrics.”
Ultrareliable and Low-Latency Wireless Communication: Tail, Risk, and Scale (2018, background): “4) Meta Distribution: The meta distribution is a finegrained key performance metric of wireless systems, first introduced in [68] which provides a mathematical foundation for questions of network densification under strict reliability constraints.”
Delay Analysis of Random Scheduling and Round Robin in Small Cell Networks (2018, background): “Moreover, as a generic UE may see common interferencing SAPs in consecutive time slots, the system service rate is temporally correlated [9], [14], [15].”
A Statistical Learning Approach to Ultra-Reliable Low Latency Communication (2018, methodology): “We rely on the concept of meta-probability [15] and introduce e pF = P [P[R(X) > log2(1 + Y )jX] > ] (15) = P[pF (R(X)) > ] ; (16)”