Wireless Networks Appear Poissonian Due to Strong Shadowing

Abstract

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 a 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 the Suzuki (Rayleigh-log-normal) propagation model. We use the 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.

Massive MIMO Forward Link Analysis for Cellular Networks

“…The BS positions form a stationary and ergodic point process Φ b ⊂ R 2 of density λ b , or a realization thereof, say a lattice network. As a result, the density of BSs within any region converges to λ b > 0 as this region's area grows [25]. In turn, the user positions conform to an independent point process Φ u ⊂ R 2 of density λ u , also stationary and ergodic.…”

What is the Best Spatial Distribution to Model Base Station Density? A Deep Dive into Two European Mobile Networks

“…However, the Poisson distribution has the main advantage of being tractable, e.g., it is possible to compute different system performance metrics in a closed-form. Moreover, recent works by [20] and then later by [6] show that random shadowing and fading models render networks to appear Poisson to the user, even if the BSs do not form a PPP. In contrast to these works, here we are more focused on highlighting the spatial distribution of BSs.…”

Multitier heterogeneous network using stochastic geometry and factorial moment approaches

“…2 It has recently been shown that, under a homogeneity condition, the BS positions are agnostic to the radio propagation waves, which mimics the BSs PPP distribution. 12,13 The performance of small cell networks is evaluated by fractional coverage characteristic to analyze the coverage probability, which captures the anisotropy of a single path-loss model. 2 The study concluded that the coverage probability with anisotropic path-loss models has been overestimated in low SIR regimes and has been underestimated in high SIR regimes.…”

“…The PPP model is constituted of BS, relay, and user parameters (eg, transmit power and path‐loss exponent) . It has recently been shown that, under a homogeneity condition, the BS positions are agnostic to the radio propagation waves, which mimics the BSs PPP distribution . The performance of small cell networks is evaluated by fractional coverage characteristic to analyze the coverage probability, which captures the anisotropy of a single path‐loss model .…”