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Communications Letters
1
A 3-D GBSM Based on Isotropic and Non-Isotropic
Scattering for HAP-MIMO Channel
Zhuxian Lian, Lingge Jiang, and Chen He
Abstract—A three-dimensional (3-D) geometry-based stochas-
tic model (GBSM) based on two cylinders is proposed for high
altitude platform (HAP) communication systems. The proposed
3-D GBSM uses the volume of inner cylinder to model isotropic
scattering environment, and that between the inner cylinder and
the outer cylinder to model non-isotropic scattering environment.
In this letter, the time-variant parameters including distances
between the scatterers and receiver, azimuth angle of departure
(AAOD), and elevation angle of departure (EAOD) are investigat-
ed for HAP multiple-input multiple-output (MIMO) channel. The
proposed model is validated by the spatial correlation function of
measurement results, and the numerical results also demonstrate
that the proposed 3-D GBSM with time-varying parameters is
applicable to describe the 3-D HAP-MIMO channel.
Index Terms—Geometry-based stochastic model (GBSM), high
altitude platform (HAP), isotropic scattering, non-isotropic scat-
tering.
I. INTRODUCTION
T
HE fourth generation (4G) and prospective fifth gen-
eration (5G) communication services demand increased
bandwidth and high data rates, and high altitude platform
(HAP) is a possible antenative way to deliver wireless com-
munications services. Multiple-input multiple-output (MIMO)
technology could offer high data rates for radio propagation
environments by exploiting spatial multiplexing [1].
The system performance of MIMO channel is significantly
effected by the spatial or temporal correlation of subchannels
[2]. In HAP-based communication systems, the surrounding
scatterers, which are often located higher than the terrestrial
mobile station (TMS), have high elevation angles, and the
waves trave not only in horizontal plane, but in vertical
plane [1]. A correlation-based three-dimensional (3-D) model
is necessary to HAP-MIMO communication systems. In [3]-
[4], two-dimensional (2-D) geometry-based stochastic models
(GBSMs) based on non-isotropic scattering are proposed for
vehicle-to-vehicle (V2V) Ricean fading channel. In [5]-[6],
3-D GBSMs based on non-isotropic scattering are proposed
for unmanned aerial vehicle (UAV) MIMO and HAP-MIMO
This work is supported by the National High Technology Research and
Development Program of China (863 Program) (No.2014AA01A704), the
National Natural Science Foundation of China (No.91438113, No.61771308,
and No.61371086), and the open research fund of National Mobile Commu-
nications Research Laboratory, Southeast University (No.2017D11). (Corre-
sponding author: Lingge Jiang)
Z. Lian and C. He are with the Department of Electronic Engineering,
Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: lianzhuxi-
an@sjtu.edu.cn; chenhe@sjtu.edu.cn).
L. Jiang is with the Department of Electronic Engineering, Shanghai
Jiao Tong University, Shanghai 200240, China and also with National
Mobile Communications Research Laboratory, Southeast University (e-mail:
lgjiang@sjtu.edu.cn).
communication systems, respectively, and they both assume
that the scatterers are distributed on the surface of a cylinder.
The COST 2100 model including isotropic scattering and non-
isotropic scattering is investigated in [7], and the measurement
result shows that the isotropic scattering is always visible in
GBSM. In [1], a 3-D GBSM for the scatterers inside a cylinder
is proposed for HAP-MIMO channel, and the hyperbolic
probability density function (PDF) is used to describe the
distances between the scatterers and TMS, which is only
suitable for isotropic scattering environment [8]. In [3]-[6],
the isotropic scattering is ignored and the models are not
sufficient to accurately describe the statistical properties of
the real propagation scenarios.
Measurement results on a spatial channel model (SCM)
in [9] show that the proposed model based on time variant
distances between the last bounce scatterers and the TMS,
angle of arrival (AOA), and angle of departure (AOD) could
capture the variation observed in real situations. In HAP-based
communication systems, the scatterers around the receiver
have high elevation angles and the distances between the re-
ceiver and the scatterers should be considered as time variation
[1]. So, the time-variant parameters should be investigated in
the HAP-MIMO channel.
In this letter, a 3-D GBSM based on isotropic scattering
and non-isotropic scattering is proposed for HAP-MIMO
communication systems. It is assumed that the local scatterers
around the TMS are distributed within two cylinders, and the
HAP is free of local scatterers. The volume of inner cylinder
is used to model isotropic scattering environment, and the
volume between the inner cylinder and the outer cylinder is
used to model non-isotropic scattering environment. In [10],
time-varying distances between the scatterers and TMS are
considered for HAP-MIMO model, but time-varying azimuth
angle of departure (AAOD) and elevation angle of departure
(EAOD) are ignored. In order to accurately describe statistical
properties of the proposed 3-D GBSM, the time-variant pa-
rameters including distances between the scatterers and TMS,
AAOD, and EAOD are investigated in this letter. Numerical
results of statistical properties demonstrate that the proposed 3-
D GBSM is applicable to describe the characteristics of HAP-
MIMO channel.
II. 3-D GBSM FOR NARROW-BAND HAP-MIMO
CHANNEL
A. Description of 3-D GBSM for Narrow-Band HAP-MIMO
Channel
A 3-D GBSM based on isotropic scattering and non-
isotropic scattering is proposed in this section. Let us con-