TY - JOUR

T1 - Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models

AU - Miyoshi, Naoto

AU - Shirai, Tomoyuki

N1 - Funding Information:
∗ Research supported by JSPS Grant-in-Aid for Scientific Research (C) 16K00030. ∗∗ Research supported by JSPS Grant-in-Aid for Scientific Research (B) 26287019.

PY - 2017

Y1 - 2017

N2 - We consider a spatial stochastic model of wireless cellular networks, where the base stations (BSs) are deployed according to a simple and stationary point process on Rd, d ≥ 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio (SIR), which is a key quantity in wireless communications. In the case where the pathloss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and α-Ginibrebased models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.

AB - We consider a spatial stochastic model of wireless cellular networks, where the base stations (BSs) are deployed according to a simple and stationary point process on Rd, d ≥ 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio (SIR), which is a key quantity in wireless communications. In the case where the pathloss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and α-Ginibrebased models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.

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U2 - 10.19195/0208-4147.37.2.12

DO - 10.19195/0208-4147.37.2.12

M3 - Article

AN - SCOPUS:85039783334

VL - 37

SP - 431

EP - 453

JO - Probability and Mathematical Statistics

JF - Probability and Mathematical Statistics

SN - 0208-4147

IS - 2

ER -