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Antennas and Wireless Propagation Letters
1
Cluster-Based Non-Stationary Channel Modeling
for Vehicle-to-Vehicle Communications
Yan Li, Student Member, IEEE, Ruisi He
∗
, Member, IEEE, Siyu Lin, Member, IEEE, Ke Guan, Member, IEEE,
Danping He, Member, IEEE, Qi Wang, Student Member, IEEE , and Zhangdui Zhong, Senior Member, IEEE,
Abstract—In this paper, a three-dimensional (3-D) cluster-
based non-stationary channel model is proposed for vehicle-
to-vehicle (V2V) communications. To efficiently describe the
scattering environment and reflect the non-stationarity of V2V
channels, the proposed model considers the single- and double-
bounced clusters in 3-D space, and includes the effect of activity of
clusters by introducing visibility regions. Furthermore, based on
the geometrical relationships in the model, the channel impulse
response is derived as a sum of the line-of-sight, single- and
double-bounced rays, and the space-time-frequency correlation
properties are analyzed. Finally, the accuracy of the proposed
model is validated by realistic V2V channel measurements.
Index Terms—Cluster-based model, non-stationary channel,
vehicle-to-vehicle channel model.
I. INTRODUCTION
R
ESEARCH into vehicle-to-vehicle (V2V) wireless com-
munications has attracted much interest due to its wide
application in the field of intelligent transportation systems.
It is well-known that the design of vehicular communication
system requires a deep understanding of V2V channels.
Conventional V2V channel models have been widely stud-
ied in the literature. Regular shape geometry-based stochastic
models (GBSMs) such as two-ring and two-cylinder models
can be found in [1]. The GBSMs assume that the scatterers
are distributed on regular shapes, which may not represent the
practical V2V scattering environments due to the randomly
distributed buildings, trees, and road signs. The cluster-level
COST 2100 model defines a large quantity of clusters with
consistent stochastic parameters throughout the simulation
environment [2] [3], however, the COST 2100 model is not
mathematically tractable for space-time-frequency correlation
analysis. A twin-cluster model is proposed based on the
geometrical relationships in [4], it is designed for massive
multiple-input multiple-output (MIMO) cellular communica-
tions and only considers the twin-clusters in the environment.
Even though many V2V channel models have been proposed
over the past few years, there are still pressing needs to model
The work is supported by National 863 Key Project under Grant
2014AA01A706, Key Project from Beijing science and Technology Commis-
sion under Grant D151100000115004, Natural Science Base Research Plan in
Shanxi Province of China under Grant 2015JM6320, Natural Science Foun-
dation of China under Grant U1334202, U1534201, 61501020, 61501021,
and 61501023, State Key Lab of Rail Traffic Control and Safety Project
under Grant RCS2015K011, RCS2016ZJ005, and RCS2016ZT021, China
Postdoctoral Science Foundation under Grant 2016M591355, and Fundamen-
tal Research Funds for the Central Universities under Grant 2016YJS022.
Y. Li, R. He
∗
(corresponding author, e-mail: ruisi.he@ieee.org), S. Lin, K.
Guan, D. He, Q. Wang, and Z. Zhong are with the State Key Laboratory of
Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China.
the V2V channels considering both the effect of randomly
distributed scatterers and non-stationary property.
This paper proposes a V2V channel model which takes
the advantages of geometry-based models and cluster-based
models. First, we model the scattering environments with
single-bounced clusters (SBCs) and double-bounced clusters
(DBCs), both of which follow a Poisson distribution in three-
dimensional (3-D) space. Second, the visibility region (VR)
is considered in the cluster-based model, which represents
the activity of clusters to reflect the non-stationarity of V2V
channels. Third, we derive the channel impulse response as
a sum of the line-of-sight (LoS), single- and double-bounced
rays and further analyze the space-time-frequency correlation
characteristics. Finally, the channel properties are validated by
using the V2V channel measurements in [5] [6].
The remainder of this paper is organized as follows: Section
II proposes the cluster-based non-stationary V2V channel
model and analyzes the space-time-frequency correlation. Nu-
merical analysis and measurement validation are presented in
Section III, followed by the concluding remarks in Section IV.
II. CLUSTER-BASED NON-STATIONARY CHANNEL MODEL
A. Model Description
We consider a wideband MIMO V2V communication sys-
tem with multiple clusters in 3-D space, as illustrated in Fig. 1.
It is assumed that both the transmitter (Tx) and receiver (Rx)
are in motion, and equipped with L
t
omnidirectional transmit
and L
r
receive antennas. The SBCs and DBCs are distributed
in 3-D space to represent the scattering environment, and the
activities of clusters are taken into account to describe the non-
stationary V2V channels. The details are presented as follows:
1) Cluster Model:
In practical propagation environments, the multipath com-
ponents usually distribute in terms of clusters, where they have
similar delays and angles. We define two types of clusters in
the proposed model: the SBCs (the solid red square in Fig.
1) and the DBCs (the solid blue triangle in Fig. 1). Both
clusters are distributed in 3-D space, with an average density
following a Poisson distribution [2]. The distance vectors from
the cluster to Tx and Rx are D
T
m/s
and D
R
n/s
, respectively,
where s = 1, 2, ...S, m = 1, 2, ...M, and n = 1, 2, ...N
represent the SBCs, DBCs at the Tx side, and DBCs at the
Rx side, respectively. The azimuth and elevation angles of the
clusters in 3-D space are also considered, as listed in Table I. It
can be seen from Fig. 1 that some waves from the Tx antenna
elements may traverse directly to the Rx antenna elements