Gaussian Random Fields as a Model for Spatially Correlated Log-Normal Fading

Abstract

Slow fading or shadowing on a wireless channel is commonly modeled by stochastically independent, log-normally distributed random variables. However, as slow fading is caused by buildings and large size obstacles, spatial correlations occur. In this paper, Gaussian random fields are used as a model for correlated slow fading in urban environments. An exponential correlation function is employed. The according parameters are estimated from path gain predictions by an accurate rayoptical propagation algorithm, named CORLA. Furthermore, a multidimensional model is suggested to describe correlated shadowing of the path gains from different base stations to a single receiver.

On the Feasibility of Wireless Shadowing Correlation Models

“…The positive semidefiniteness of this model is dependent on ν: for 0 < ν ≤ 2, it is proved to be psd with the aid of Theorem 3 in [66, p. 364]. This of course includes models (19) and (21), as well as the choice of ν = 0.9682 in [91]. For ν > 2, however, the model is in non-psd [66, p. 137].…”

Efficient modeling of correlated shadow fading in dense wireless multi-hop networks

“…This lack of correlation does not happen in the real world since nearby MSs have similar shadowing environment, thus experiencing correlated shadow fading. To overcome this limitation, a twodimensional shadow fading model has been proposed to generate correlated shadowing values for neighboring MSs [6]. A unique shadow fading map is generated for each BS to represent shadowing losses for geographic locations.…”

Efficient Simulation using Shadowing Fields of Many Wireless Interferers with Correlated Shadowing

“…The idea of generating shadowing fields has already been explored [9], [12]- [14] with correlation functions of the form h(⃗ r i , ⃗ r j ) = f (∥⃗ r i − ⃗ r j ∥). We have argued in [10] that such models may not reflect true shadowing spatial correlation characteristics.…”

“…and S i 's will have the same correlation matrix as in (9). For numerical purposes,M can be approximated by a discrete-parameter matrix M DΘ×DR , with a regularly-spaced quantisation grid along θ and R. Correlation of the form (6), triangular in both dimensions, can be obtained by using a uniform square filter F FΘ×FR , ideally choosing F Θ and F R so that we have exactly…”

“…[5]- [7], [9], [10] 2) The total interference power is the sum of the individual interference powers, as explained by incoherent signal addition. [5], [7], [9], [11] …”