Wireless networks appear Poissonian due to strong shadowing

Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently high variance, the statistics of the propagation loss of a single user with respect to different network stations are invariant with respect to their geographic positioning, whether regular or not, for a wide class of empirically homogeneous networks. Even in perfectly hexagonal case they appear as though they were realized in a Poisson network model, i.e., form an inhomogeneous Poisson point process on the positive half-line with a power-law density characterized by the path-loss exponent. At the same time, the conditional distances to the corresponding base stations, given their observed propagation losses, become independent and log-normally distributed, which can be seen as a decoupling between the real and model geometry. The result applies also to Suzuki (Rayleigh-log-normal) propagation model. We use Kolmogorov-Smirnov test to empirically study the quality of the Poisson approximation and use it to build a linear-regression method for the statistical estimation of the value of the path-loss exponent

Stronger wireless signals appear more Poisson

Keeler, Ross and Xia (2016) recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation model can be modelled by an inhomogeneous Poisson point process on the positive real line. The basic requirement for the results to apply is that there must be a large number of transmitters with different locations and random propagation effects.The aim of this note is to apply some of the main results of Keeler, Ross and Xia (2016) in a less general but more easily applicable form to illustrate how the results can be applied in practice. New results are derived that show that it is the strongest signals, after being weakened by random propagation effects, that behave like a Poisson process, which supports recent experimental work.Comment: 7 pages with 1.5 line spacin

Stronger wireless signals appear more Poisson

Keeler, Ross and Xia [1] recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation model can be modelled by an inhomogeneous Poisson point process on the positive real line. The basic requirement for the results to apply is that there must be a large number of transmitters with different locations and random propagation effects. The aim of this note is to apply some of the main results of [1] in a less general but more easily applicable form to illustrate how the results can be applied in practice. New results are derived that show that it is the strongest signals, after being weakened by random propagation effects, that behave like a Poisson process, which supports recent experimental work. [1] P. Keeler, N. Ross, and A. Xia:``When do wireless network signals appear Poisson?? '

Characterizing The SINR in Poisson Network Using Factorial Moment

Usually, cellular networks are modeled by placingeach tier (e.g macro, pico and relay nodes) deterministicallyon a grid. When calculating the metric performances suchas coverage probability, these networks are idealized for notconsidering the interference. Overcoming such limitation byrealistic models is much appreciated. This paper considered two-tier two-hop cellular network, each tier is consisting of two-hoprelay transmission, relay nodes are relaying the message to theusers that are in the cell edge. In addition, the locations of therelays, base stations (BSs), and users nodes are modeled as a pointprocess on the plane to study the two hop downlink performance.Then, we obtain a tractable model for the k-coverage probabilityfor the heterogeneous network consisting of the two-tier network.Stochastic geometry and point process theory have deployed toinvestigate the proposed two-hop scheme. The obtained resultsdemonstrate the effectiveness and analytical tractability to studythe heterogeneous performance

Characterizing The SINR in Poisson Network Using Factorial Moment

Usually, cellular networks are modeled by placingeach tier (e.g macro, pico and relay nodes) deterministicallyon a grid. When calculating the metric performances suchas coverage probability, these networks are idealized for notconsidering the interference. Overcoming such limitation byrealistic models is much appreciated. This paper considered two-tier two-hop cellular network, each tier is consisting of two-hoprelay transmission, relay nodes are relaying the message to theusers that are in the cell edge. In addition, the locations of therelays, base stations (BSs), and users nodes are modeled as a pointprocess on the plane to study the two hop downlink performance.Then, we obtain a tractable model for the k-coverage probabilityfor the heterogeneous network consisting of the two-tier network.Stochastic geometry and point process theory have deployed toinvestigate the proposed two-hop scheme. The obtained resultsdemonstrate the effectiveness and analytical tractability to studythe heterogeneous performance

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

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 $\mathbb{R}^d$, $d\ge2$. 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 path-loss 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 $\alpha$-Ginibre-based models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.Comment: Dedicated to Tomasz Rolski on the occasion of his 70th birthda