Using Poisson processes to model lattice cellular networks

Abstract

Abstract-An almost ubiquitous assumption made in the stochastic-analytic approach to study of the quality of user-service in cellular networks is Poisson distribution of base stations, often completed by some specific assumption regarding the distribution of the fading (e.g. Rayleigh). The former (Poisson) assumption is usually (vaguely) justified in the context of cellular networks, by various irregularities in the real placement of base stations, which ideally should form a lattice (e.g. hexagonal) pattern. In the first part of this paper we provide a different and rigorous argument justifying the Poisson assumption under sufficiently strong lognormal shadowing observed in the network, in the evaluation of a natural class of the typical-user service-characteristics (including path-loss, interference, signal-to-interference ratio, spectral efficiency). Namely, we present a Poisson-convergence result for a broad range of stationary (including lattice) networks subject to log-normal shadowing of increasing variance. We show also for the Poisson model that the distribution of all these typical-user service characteristics does not depend on the particular form of the additional fading distribution. Our approach involves a mapping of 2D network model to 1D image of it "perceived" by the typical user. For this image we prove our Poisson convergence result and the invariance of the Poisson limit with respect to the distribution of the additional shadowing or fading. Moreover, in the second part of the paper we present some new results for Poisson model allowing one to calculate the distribution function of the SINR in its whole domain. We use them to study and optimize the mean energy efficiency in cellular networks.

Dense Small Cell Networks: From Noise-Limited to Dense Interference-Limited

“…In [34], a similar theorem which was also extended from Blaszczyszyn's work [11], [35] was proposed to analyze a ndimensional network, in which NLoS and LoS transmissions are not considered. By utilizing the Equivalence theorem above, the transformed cellular network has the exactly same performance for the typical MU with respect to the coverage probability and the ASE compared with the original network, which is proved in Appendix A and validated by Monte Carlo simulations in Section VI.…”

“…(39), (a) is due to the reason that when λ → ∞, the network is interference-limited and noise can be ignored compared with the aggregate interference, which is also validated by results in Section VI. The proof of (b) can be found in [11,Remark 9] and [14,Theorem 4] and are omitted here.…”

“…By using displacement theorem [11], [33], the point process Φ NL n is Poisson with intensity measure…”

Maximizing the Energy Efficiency of Virtualized C-RAN via Optimizing the Number of Virtual Machines

“…The reason of adapting PPP at each iteration, rather than treating uniformly, is to contemplate the practical deployment and real life scenarios during the distribution of RRHs and UEs [36]. The Poison distribution measures the probability that a certain number of events occur within a certain period of time.…”

In-Band Full-Duplex Communications for Cellular Networks with Partial Uplink/Downlink Overlap

“…The PPP assumption for cellular networks is justified by experimental studies in [9], [10] and a theoretical study in [11]. The locations of the UEs are modeled via an independent PPP Ψ u with intensity λ u λ such that each BS will always have a user to serve.…”