Two-Dimensional Shadow Fading
Modeling on System Level
Chen Zhang, Xiaohui Chen, Huarui Yin, and Guo Wei
Department of Electrical Engineering and Information Science
University of Science and Technology of China, HeFei, Anhui, 230027, P.R.China
Email: zhangzc@mail.ustc.edu.cn, {cxh, yhr, wei}@ustc.edu.cn
Abstract—In this paper, we propose a novel complete two-
dimensional shadow fading modeling on system level charac-
terized by both spatial auto-correlation and site-to-site cross-
correlation. Numerical results confirm that the proposed algo-
rithm based on two-dimensional filter to generate shadowing
auto-correlation is more approaching theoretical results com-
paring with the previous method, and the empirical cross-
correlation coefficient is embedded well in our proposed model.
Additionally, the linear interpolation scheme of the proposed
model significantly reduces the computational complexity on
system level simulation.
I. INTRODUCTION
The mobile wireless channel has been researched for a
long time based on measurement data. Typically it can be
modeled as a combination of three factors: path loss, shadow
fading and fast fading. As is well known, fast fading is
only influential to the link level simulation, and path loss is
mostly determined by the distance between transmitter and
receiver, therefore the random variability of mobile wireless
channel is almost affected by shadow fading on system level
simulation. Moreover, the correlation in shadow fading is a
significant step in obtaining more realistic and accurate chan-
nel propagation models. Neglecting the shadowing correlation
could lead to expressively compromising the performance of
techniques which have strong dependence on radio link quality
such as inter-cell handover, wireless localization, or neighbor
discovery applications. Specially, shadowing correlation would
have negative influence to the rank of the channel matrix,
therefore, affect the diversity gain and finally compromise
the realization of interference alignment which attracts lots
of attention of research recently.
Gudmundson [1] proposed a one-dimensional model for
auto-correlation of shadow fading which has been widely used
in wireless channel simulations. However, this model can not
be extended to two-dimensional scenarios and also ignores
existence of the shadowing cross-correlation. Recently, many
scholars and organizations have proposed different methods
and algorithms for the sake of complete shadowing model
such as [2], [3], [4], and [5]. Unfortunately, these works do
have several limitations as follows: the work in [2] is based
on the sums of sinusoids (SOS) method for shadowing auto-
correlation, nonetheless the SOS approach is naturally flawed
in aspect of spectral properties [6]; while a comparatively
complete shadow fading model is established in [3], however
whose simulated results are departed far from theoretical val-
ues for the auto-correlation; besides, [3], [4] and [8], arbitrarily
assume the cross-correlation as a constant value without any
proof or experimental supporting; and in the proposed models
of [5] and [7], every mobile station is provided a unique
shadow fading mapping, whose computational complexity will
be huge, due to the large quantity and random mobility of
the mobile stations, which is not suitable for system level
simulation.
In this paper, we develop a two-dimensional shadow fading
model, considering both the spatial auto-correlation and the
site-to-site cross-correlation, which is complete and accurate.
First, we propose a two-dimensional filter algorithm based
on Wiener-Khinchin theorem [9] to provide two-dimensional
auto-correlation for shadow fading, with the advantage of
avoiding defects brought by SOS method. Moreover we in-
troduce and analyze some essential cross-correlation models
based on experimental results and select the Saunders’ results
[10] which is more accurate and practical, as a part of our
system level simulation model. Additionally, different from
providing a unique shadow fading mapping for every mobile
station [5], we suggest a linear interpolation scheme which
significantly reduces the computational complexity on system
level simulation. Finally, the numerical results show that the
auto-correlation of our model is more approaching theoretical
results comparing with [3] and Saunders’ cross-correlation
sub-model is embedded well in our complete model.
II. M
ODEL AND ALGORITHM
A. Log-normal Model
A statistical model consisting of path loss, shadow fad-
ing and fast fading for the random attenuation is developed
through many experimental results. Fig. 1 [11] elucidates the
ratio of the received-to-transmit power in decibels (dB) versus
log distance for the influence of path loss, shadow fading and
fast fading. Considering the effect of the shadow fading only,
its statistical distribution follows a log-normal law, which has
been empirically confirmed to describe accurately the variation
in both outdoor and indoor radio propagation environments
[1].
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2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC)
978-1-4673-2569-1/12/$31.00 ©2012 IEEE 1671