A Three-Dimensional Geometry-based Stochastic Model for Air-to-Air UAV Channels

Full text

A Three-Dimensional Geometry-based Stochastic
Model for Air-to-Air UAV Channels
Yan Zhang∗, Yuxuan Zhou†, Zijie Ji∗, Kun Lin∗, and Zunwen He∗
∗School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081 P.R.China
†Electrical and Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA
Emails:{zhangy (Corresponding author), jizijie, linkun bit, hezunwen}@bit.edu.cn, yuxuanz2@andrew.cmu.edu
Abstract—Recently, the utilization of unmanned aerial vehicles
(UAVs) has been increasingly popular in various fields. As a brand
new scenario of wireless communication, establishing feasible
UAV channel models is necessary for the design and deployment
of UAV-aided communication systems. In this paper, a three-
dimensional (3D) geometry-based stochastic model (GBSM) is
proposed for UAV air-to-air (A2A) channels. Based on this model,
we derive the space-time correlation function (STCF), through
which the impacts of some key parameters have been analyzed.
Finally, the better universality of the proposed model is verified
and some useful conclusions giving references for practical design
are provided.
Index Terms—Air-to-air (A2A), channel model, geometry-
based stochastic model (GBSM), space-time correlation function
(STCF), unmanned aerial vehicles (UAVs).
I. INT ROD UC TI ON
Unmanned aerial vehicles (UAVs) have been widely applied
in many fields including cargo transport, agriculture, commu-
nication relay, and emergency rescue. Though originally used
for military purpose, UAVs now possess great potential to play
an important role in more areas with reduced cost and excel-
lent convenience. Among the concerned applications, UAVs
working as wireless communication relays have been a hot
topic in recent years. Due to the differences from traditional
channel characteristics, UAV-multi-input multi-output (UAV-
MIMO) channel models are worthy of further investigation to
meet specific application requirements [1].
As a new scenario, UAV-aided communication has attracted
extensive research interest, but the related research is still on
the primary stage. Some preliminary measurements of UAV
channels [2]–[4] have been carried out to provide references
for channel modeling. Generally, the existing models can be
classified into deterministic models and stochastic ones. Based
on computational electromagnetics, deterministic models can
provide the channel responses for UAV scenarios and achieve
high modeling accuracy. However, the high computational
complexity and site-specificity restrict the applications of these
models. In contrast, stochastic models with low complexity
and configuration flexility can be extended to various UAV
scenarios well with relatively high precision, including the
statistical models [5], the curved-earth two-ray (CE2R) model
[6], and geometry-based stochastic models (GBSMs) [7]. The
statistical models based on Rayleigh or Ricean distribution
were popular in terrestrial wireless communications but failed
to capture the characteristics of three-dimensional (3D) UAV
communication systems, e.g., mobility and altitude. The CE2R
model was designed for big UAVs mainly considering the
large-scale channel characteristics from the line-of-sight (LoS)
path and ground reflection, which is unsuitable for commonly
used small UAV scenarios. Unlike the two methods mentioned
above, GBSMs retain the insight of ray-tracing and character-
ize the channels by analyzing the geometrical relationships in
randomly distributed scatterers. The GBSMs have been widely
used in the cellular or vehicular channel modeling for their low
complexity and high accuracy [7]–[12].
In terms of air-to-ground (A2G) scenarios, cylinder model
[10], single-sphere model [11], and single-hemisphere model
[12] have been proposed and obtain favorable results. How-
ever, those models are based on the assumption that the
UAV side is free of scattering, which may be invalid in
the dense urban/suburban scenarios. Meanwhile, the existing
works mainly focus on the A2G communications. In practical
applications, communication links can also be built between
two UAVs to provide relays, groups, networks, etc. Therefore,
the channel models in air-to-air (A2A) scenarios [13]–[15] are
urgently required.
In this paper, a two-sphere GBSM for A2A UAV-MIMO
channels is proposed, where the scatterers around both the
transmitter and the receiver are considered. At the same time,
the LoS path is considered together with the single-bounce and
double-bounce components. Based on this model, the space-
time correlation function (STCF) is derived and the impacts of
different parameters on the STCF are analyzed, which provide
useful guidance to the deployment of UAV communications.
II. 3D GBSM FO R A2A UAV-MIMO CH AN NE LS
The considered A2A system includes two UAVs employed
as the base station (BS)-UAV and the relay station (RS)-
UAV. Both of them can move in arbitrary directions. Here,
we consider a downlink transmission. The BS-UAV served as
the transmitter (Tx) and the RS-UAV as the receiver (Rx) are
equipped with nTtransmit and nRreceive antenna elements,
numbered as 1≤p≤nTand 1≤l≤nR, respectively.
In view of the noticeable height UAVs working at, some
3D characteristics like elevation angles of electromagnetic
waves and movements should be taken into account. The
proposed 3D two-sphere GBSM for A2A UAV channels is
978-1-7281-9484-4/20/$31.00 ©2020 IEEE
2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall) | 978-1-7281-9484-4/20/$31.00 ©2020 IEEE | DOI: 10.1109/VTC2020-Fall49728.2020.9348433
Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on May 18,2021 at 04:17:57 UTC from IEEE Xplore. Restrictions apply.

1
p
1
l
( 2)n
R
D
R
O
2
l
O
ܵ(௡ଵ)
( 2)n
S
T
v
R
v
0
E
( 1)n
T
E
T
T
R
T
( 2)n
T
D
( 1)n
R
E
( 2)n
T
E
T
[
( 2)n
R
E
'O
R
[
T
O
2
p
Fig. 1. Schematic diagram of the 3D GBSM for A2A UAV channels.
illustrated in Fig. 1. In this model, three kinds of paths are
considered, including the LoS, single-bounce, and double-
bounce components.
Compared with other A2G GBSMs [10], [11] in which only
non-line-of-sight (NLoS) components are considered, the LoS
component is also taken into account in this model for the
reason that the UAVs can fly at a high altitude and the LoS path
may exist in the A2A scenarios. The effective scatterers around
the UAVs at both sides are both non-uniformly distributed on
two spherical surfaces (with height HTand radius R1centered
at the Tx, and height HRand radius R2centered at the
Rx). With the scatterers following a specific joint probability
density function (PDF), the single-bounce and double-bounce
components can be modeled.
Without losing generality, uniform linear arrays with two
antenna elements spacing of δTand δRare employed at Tx
and Rx sides, respectively. Note the configuration of antenna
arrays can be easily extended to any number of elements. As
shown in Fig. 1, the two transmit antenna elements p1and
p2locates at a height of HThigher than the origin Owith a
central point denoted by OT, while the receive ones l1and l2
are set around ORwith a height of HRabove O′. To simplify
the description, we use d(A, B)to denote the distance between
two points Aand B. In this way, we have d(O, O′) = D,
d(O, OT) = HTand d(O′, OR) = HR. The expression of the
elevation angle between Tx and Rx β0can be given as β0=
arctan (HT−HR)/D. Assumptions δT, δR≪R1, R2≪D
are exploited in the following derivations.
Assuming there are N1effective scatterers around Tx lying
on the spherical surface of radius R1and the n1-th one is
denoted by S(n1), where 1≤n1≤N1. Similarly, the n2-th
scatterer around Rx at a distance of R2is indicated as S(n2),
where 1≤n2≤N2. The azimuth and elevation angles of OT
relative to S(n1)are defined as the angles of departure (AoD).
The angles of arrival (AoA) denote the azimuth and elevation
angles of S(n2)relative to OR. Other important parameters are
listed in Table I.
Now, we begin to derive the channel impulse response (CIR)
TABLE I
NOTATIO NS OF KE Y PARAMETERS IN THE CHAN NEL MO DE L
Symbol Definition
DThe projection distance between Tx and Rx
R1,R2The radius of the two effective scatterer spheres
HT,HRThe height of Tx and Rx, respectively
β0The elevation angle between Tx and Rx
θT,θRThe orientation of antenna arrays at Tx and Rx
δT,δRThe antenna element spacings at Tx and Rx
vT,vRThe velocity of Tx and Rx, respectively
fT,fRThe maximum Doppler shift at Tx and Rx
γT,γRThe azimuth angle of movement direction at Tx and Rx
ξT,ξRThe elevation angle of movement direction at Tx and Rx
α(n1)
T,β(n1)
TThe azimuth and elevation AoD at S(n1)
α(n2)
R,β(n2)
RThe azimuth and elevation AoA from S(n2)
α(n1)
T0,β(n1)
T0The mean azimuth and elevation AoD in von Mises-Fisher PDF
α(n2)
R0,β(n2)
R0The mean azimuth and elevation AoA in von Mises-Fisher PDF
k1,k2The distribution parameter in PDF of AoD and AoA
of this model and their STCF. Firstly, the CIR of the LoS
component between antenna elements pand lis
hLoS
pl (t)=√K
K+1 e−j2π
λd(p,l)ej2πfTtcos(αLoS
T−γT)cosβLoS
T
ej2πfRtcos(αLoS
R−γR)cosβLoS
R,
(1)
where j2=−1,λis the carrier wavelength, fT=vT/λ and
fR=vR/λ are maximum Doppler shifts. Kdesignates the
Ricean factor.
As for NLoS paths, the CIR of single-bounced rays can be
expressed as
hSBi
pl (t)=√1
K+1 lim
Ni→∞
1
√Ni
Ni
∑
ni=1
ejϕ(ni)
e−j2π
λ[d(p,S(ni))+d(S(ni),l)]
ej2πfTt[cos(α(ni)
T−γT)cosβ(ni)
TcosξT+sinβ(ni)
TsinξT]
ej2πfRt[cos(α(ni)
R−γR)cosβ(ni)
RcosξR+sinβ(ni)
RsinξR]g(ni),
(2)
where i∈ {1,2},ϕ(ni)and g(ni)are the random phase
and amplitude gain of the ni-th scattered wave, respectively.
Similarly, the CIR of double-bounced rays is given as
hDB
pl (t)=√1
K+1 lim
N1,N2→∞
1
√N1N2
N1
∑
n1=1
N2
∑
n2=1
ejϕ(n1,n2)
e−j2π
λ[d(p,S(n1))+d(S(n1),S(n2))+d(S(n2),l)]
ej2πfTt[cos(α(n1)
T−γT)cosβ(n1)
TcosξT+sinβ(n1)
TsinξT]
ej2πfRt[cos(α(n2)
R−γR)cosβ(n2)
RcosξR+sinβ(n2)
RsinξR]g(n1, n2),
(3)
where ϕ(n1, n2)and g(n1, n2)are the random phase and
amplitude gain of the double-bounced path. We suppose that
lim
Ni→∞ ∑Ni
ni=1 E[|g(ni)|2] + E[|g(n1, n2)|2]=1, where Niis
the number of scatterers.
The STCF of two complex sub-channels p1l1and p2l2,
which depicts both the spatial and temporal correlations be-
tween them, is defined as
Rp1l1,p2l2(δT, δR, τ, t) = E[h∗
p1l1(t)hp2l2(t+τ)],(4)
where hp1l1(t)and hp2l2(t)denote the CIRs of subchannels
p1l1and p2l2, respectively. Hence, the STCF of LoS compo-
Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on May 18,2021 at 04:17:57 UTC from IEEE Xplore. Restrictions apply.

nent can be written as
RLoS
p1l1,p2l2(δT, δR, τ ) = K
K+1 e−j2π
λ[d(p1,l1)−d(p2,l2)]
ej2πτ (fTcos(αLoS
T−γT)cosβLoS
T−fRcos(αLoS
R−γR)cosβLoS
R).
(5)
Based on the geometrical relationships of the single-bounce,
the dependence between angles α(n1)
T,β(n1)
Tand α(n1)
R,β(n1)
R
can be obtained. Since R1, R2≪D, the angle α(n1)
Rtends to
be 0. By using the sine theorems for triangles, the simplified
angel expressions are
cosα(n1)
R= 1,sinα(n1)
R=R1sinα(n1)
Tcosβ(n1)
T
D−R1cosα(n1)
Tcosβ(n1)
T
.(6)
Along the z-axis, it can be acquired that
Dtanβ0+R1sinβ(n1)
T=tanβ(n1)
R(D−R1cosα(n1)
Tcosβ(n1)
T)
(7)
i.e.,
tan β(n1)
R=Dtanβ0+R1sinβ(n1)
T
D−R1cosα(n1)
Tcosβ(n1)
T
.(8)
Considering some approximations, e.g., √1 + x≈1 + 1
2x, if
x≪1, the approximate expressions are
cosβ(n1)
R= cosβ0[1 −R1
Dcosβ0sin2β0(sinβ(n1)
T
sinβ0
+cosα(n1)
Tcosβ(n1)
T
cosβ0)],
sinβ(n1)
R= sinβ0[1 + R1
Dcosβ0cos2β0(sinβ(n1)
T
sinβ0
+cosα(n1)
Tcosβ(n1)
T
cosβ0)].
(9)
Apply the same process to angles α(n2)
T,β(n2)
Tand α(n2)
R,
β(n2)
Rand the dependence can be written as
cos α(n2)
T= 1,sinα(n2)
T=R2sinα(n2)
Rcosβ(n2)
R
D+R2cosα(n2)
Rcosβ(n2)
R
,
cos β(n2)
T= cosβ0[1 + R2
Dcosβ0sin2β0(sinβ(n2)
R
sinβ0
+cosα(n2)
Rcosβ(n2)
R
cosβ0)],
sinβ(n2)
T= sinβ0[1 −R2
Dcosβ0cos2β0(sinβ(n2)
R
sinβ0
+cosα(n2)
Rcosβ(n2)
R
cosβ0)].
(10)
Assuming the number of scattering is infinite, thus discrete
random variables α(n1)
T,β(n1)
Tand α(n2)
R,β(n2)
Rcan be replaced
by continuous variables α(1)
T, β(1)
Tand α(2)
R,β(2)
R. They both
conform a joint PDF f(α, β)respectively. Hence, the correla-
tion functions of NLoS components become
RSBi
p1l1,p2l2(δT, δR, τ ) = 1
K+1
∫π
−π∫π
2
−π
2e−j2π
λ[d(p1,S(ni))+d(S(ni),l1)−d(p2,S(ni))−d(S(ni),l2)]
ej2πfTτ[cos(α(i)
T−γT)cos(β(i)
T)cosξT+sin(β(i)
T)sinξT]
ej2πfRτ[cos(α(i)
R−γR)cos(β(i)
R)cosξR+sin(β(i)
R)sinξR]
f(α(i)
R/T, β(i)
R/T)dα(i)
R/Tdβ(i)
R/T,
(11)
RDB
p1l1,p2l2(δT, δR, τ )= 1
K+1
∫π
−π∫π
−π∫π
2
−π
2∫π
2
−π
2e−j2π
λ[d(p1,S(n1))+d(S(n1),S(n2))+d(S(n2),l1)]
ej2π
λ[d(p2,S(n1))+d(S(n1),S(n2))+d(S(n2),l2)]
ej2πfTτ[cos(α(1)
T−γT)cos(β(1)
T)cosξT+sin(β(1)
T)sinξT]
ej2πfRτ[cos(α(2)
R−γR)cos(β(2)
R)cosξR+sin(β(2)
R)sinξR]
f(α(1)
T, β(1)
T)f(α(2)
R, β(2)
R)dα(1)
Tdβ(1)
Tdα(2)
Rdβ(2)
R.
(12)
Consequently, the STCF of the whole channels is defined
as [9]
Rp1l1,p2l2(δT, δR, τ ) = RLoS
p1l1,p2l2(δT, δR, τ )+
2
∑
i=1
ηSBiRSBi
p1l1,p2l2(δT, δR, τ )+ηDBRDB
p1l1,p2l2(δT, δR, τ ),
(13)
where ∑2
i=1 ηSBi+ηDB = 1 and the single-bounced rays are
composed of two parts, SB1bouncing on the Tx sphere and
SB2on the Rx sphere. The amount of power that the single-
and double-bounced rays contribute to the total scattered
power is 1/(K+1). Since the BS-UAV locates higher than the
RS-UAV, less effective scattering is distributed at that altitude
and scattering is more likely to happen when rays arrive at
the Rx sphere. Therefore, we choose relatively small power
related parameters ηSB1and ηDB in comparison with ηSB2.
Like [8], von Mises-Fisher PDF is used to characterize the
azimuth angle αand the elevation angle β. The von Mises-
Fisher PDF is defined as
f(α, β) = kcosβ
4πsinhkek[cosβ0cosβcos(α−α0)+sinβsinβ0],(14)
where α∈[−π, π],β∈[−π
2,π
2]and α0,β0refer to the
mean value of the azimuth angle αand the elevation angle
β. The parameter kshows the spread extent around the mean
angle. When krises from 0, the scattering becomes more and
more concentrated and the environment turns more and more
non-isotropic. Assuming the BS-UAV locates higher than the
RS-UAV and there is less local scattering, the parameter k1
for the BS-UAV is set to be higher than k2for the RS-UAV
in the following analysis.
III. SIM UL ATIO N RES ULTS AND ANALYS IS
In this section, the numerical simulation results of STCFs
with different model parameter values and corresponding anal-
ysis are presented. Without loss of generality, the initialized
parameters are nT=nR= 2,D=400 m, R1=R2= 20 m,
λ= 0.1m, β0=π/3,vT= 0 m/s, vR= 10 m/s, ξT= 0,
ξR=π/3,γT= 0,γR= 0,α(n1)
T0= 0,β(n1)
T0=−π/6,
α(n2)
R0=π,β(n2)
R0=π/6,θT=θR=π/2,K= 1,k1= 3.6,
k2= 1.2,ηSB1= 1/12,ηSB2= 5/6,ηDB = 1/12. Unless
otherwise stated, the values of the above parameters remain
the same.
A. Temporal Correlation
1) The Impact of Different Moving Angles ξR,γR:Fig. 2
represents the temporal correlations Rp1l1(τ)for different
moving directions of the RS-UAV when vT= 1 m/s and BS-
UAV moves towards the receiver, i.e., ξT=π/3,γT= 0. As
Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on May 18,2021 at 04:17:57 UTC from IEEE Xplore. Restrictions apply.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
/s
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized temporal correlation
R=/6, R=0
R=/6, R=
R=/3, R=0
R=/3, R=
R=/2, R=N/A
Fig. 2. Impact on temporal correlations for different moving directions.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
/s
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized temporal correlation
vR=0m/s
vR=1m/s
vR=10m/s
Fig. 3. Impact on temporal correlations for different moving velocities of
the RS-UAV.
we can see, the strongest temporal correlation appears when
the two UAVs are moving directly towards each other, i.e.,
ξR=π/3,γR=π. In this case, the environment changes
least and therefore leading to the greatest temporal correlation.
Moreover, the temporal correlations show oscillations when
τ > 0.004 s due to the existence of LoS components. The
same is true for the oscillations in the remaining figures.
2) The Impact of Different Velocities of the RS-UAV vR:
Fig. 3 depicts the temporal correlations Rp1l1(τ)for various
moving velocities of the RS-UAV. It can be observed that the
faster the RS-UAV moves, the quicker the temporal correlation
drops. When the transmitter and receiver are in a relatively
stationary state, the temporal correlation remains constant as
the time delay increases. Therefore, the design of the A2A
communication systems has to pay much attention to the rapid
changes in channel responses caused by the fast movements
of the UAVs.
0 10 20 30 40 50 60 70 80 90 100
T/
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized spatial correlation
k=0.01
k=3
k=6
Fig. 4. Impact on spatial correlations for different distributions of local
scattering of the RS-UAV.
0.4
0
0.5
0.6
0.7
Normalized Spatial correlation
0
0.8
R/
0.5 20
0.9
1
40
T/
60
80
1100
Fig. 5. Impact on spatial correlations for different antenna spacings under a
non-isotropic environment.
B. Spatial Correlation
1) The Impact of Different Distribution Parameters k:
Fig. 4 shows the transmit spatial correlations Rp1l1,p2l2(δT)
for different angle spreads of local scattering around the RS-
UAV. It is clear that the larger k, which makes local scattering
more concentrated in the spatial distribution, results in the
higher spatial correlation.
2) The Impact of Antenna Spacings δT,δR:Fig. 5 illus-
trates the spatial correlation Rp1l1,p2l2(δT, δR)under the scene
we set before. It is shown that the spatial correlation reduces
with the increase in either the transmit or receive antenna
spacing. Additionally, the receive spatial correlation is smaller
than the transmit spatial correlation. This is because that
there are usually fewer scatterers at higher heights, so more
scattering is assumed to be distributed around the receiver.
Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on May 18,2021 at 04:17:57 UTC from IEEE Xplore. Restrictions apply.

C. Degrading to A2G Single-sphere GBSM
Since the two-sphere GBSM is an expanded form of the
single-sphere GBSM, it can degrade back to the single-sphere
GBSM in specific conditions. In order to match well with
the work in [11], the values of some relevant parameters are
changed as K= 0,vT= 10 m/s, vR= 0 m/s, ξT=π/3,
ξR= 0,k= 10,ηSB1= 0,ηSB2= 1,ηDB = 0. When Ricean
factor K= 0, LoS component is excluded. As for NLoS, only
SB2is considered when ηSB2= 1. After numerical analysis
with MATLAB, the degraded version of our model obtained
similar results with those in [11]. It proves that the proposed
model have better generality than the single-sphere model.
IV. CONCLUSION
In this paper, a 3D two-sphere GBSM for A2A UAV-MIMO
channels has been proposed. The theoretical expression of the
STCF has been derived based on the geometrical relationship.
Moreover, through numerical simulation, it is demonstrated
that some important parameters, such as moving directions, ve-
locities of UAVs, scattering distribution, and antenna spacings,
have great impacts on the temporal and spatial correlation.
Finally, we show that the proposed two-sphere model has good
generalization performance and it can degrade to the single-
sphere model.
ACKNOWLEDGMENT
This work was supported by the National Key R&D Pro-
gram of China under Grant 2020YFB1804901, the National
Natural Science Foundation of China under Grant 61871035,
and Ericsson company.
REF ER EN CE S
[1] W. Khawaja, I. Guvenc, D. W. Matolak, U. Fiebig and N. Schneck-
enberger, “A survey of air-to-ground propagation channel modeling for
unmanned aerial vehicles,” IEEE Commun. Surveys Tuts., vol. 21, no. 3,
pp. 2361–2391, 3rd Quart., 2019.
[2] T. J. Willink, C. C. Squires, G. W. K. Colman and M. T. Muccio,
“Measurement and characterization of low-altitude air-to-ground MIMO
channels,” IEEE Trans. Veh. Technol., vol. 65, no. 4, pp. 2637–2648,
Apr. 2016.
[3] L. Zhou, Z. Yang, G. Zhao, S. Zhou, and C.-X. Wang, “Propagation
characteristics of air-to-air channels in urban environments,” in Proc.
IEEE Global Commun. Conf. (GLOBECOM), Abu Dhabi, United Arab
Emirates, 2018, pp. 1–6.
[4] Z. Cui, C. Briso-Rodr´
ıguez, K. Guan, C. Calvo-Ram´
ırez, B. Ai, and
Z. Zhong, “Measurement-based modeling and analysis of UAV air-
ground channels at 1 and 4 GHz,” IEEE Antennas Wireless Propag.
Lett., vol. 18, no. 9, pp. 1804–1808, Sep. 2019.
[5] M. Simunek, F. P. Font´
an, and P. Pechac, “The UAV low elevation
propagation channel in urban areas: Statistical analysis and time-series
generator,” IEEE Trans. on Antennas and Propag., vol. 61, no. 7,
pp. 3850–3858, Jul. 2013.
[6] D. W. Matolak and R. Sun, “Unmanned aircraft systems: Air-ground
channel characterization for future applications,” IEEE Veh. Technol.
Mag., vol. 10, no. 2, pp. 79–85, Jun. 2015.
[7] Z. Lian, L. Jiang, and C. H, “A 3-D GBSM based on isotropic and
non-isotropic scattering for HAP-MIMO channel,” IEEE Commun. Lett.,
vol. 22, no. 5, pp. 1090-1093, May 2018.
[8] X. Cheng, Q. Yao, M. Wen, C.-X. Wang, L. Y. Song, and B. L. Jiao,
“Wideband channel modeling and intercarrier interference cancellation
for vehicle-to-vehicle communication systems,” IEEE J. Sel. Areas
Commun., vol. 31, no. 9, pp. 434–448, Sep. 2013.
[9] Y. Yuan, C.-X. Wang, Y. He, M. M. Alwakeel, and H. Aggoune, “3D
wideband non-stationary geometry-based stochastic models for non-
isotropic MIMO vehicle-to-vehicle channels,” IEEE Trans. Wireless
Commun., vol. 14, no. 12, pp. 6883–6895, Dec. 2015.
[10] L. Zeng, X. Cheng, C.-X. Wang, and X. Yin, “A 3D geometry-based
stochastic channel model for UAV-MIMO channels,” in Proc. IEEE
Wireless Commun. and Networking Conf. (WCNC), San Francisco, CA,
USA, Mar. 2017, pp. 1–5.
[11] K. Jin, X. Cheng, X. Ge, and X. Yin, “Three dimensional modeling and
space-time correlation for UAV channels,” in Proc. IEEE Veh. Technol.
Conf. (VTC Spring), Sydney, NSW, Australia, Jun. 2017, pp. 1–5.
[12] Q. Zhu, K. Jiang, X. Chen, W. Zhong and Y. Yang, “A novel 3D
non-stationary UAV-MIMO channel model and its statistical properties,”
IEEE China Commun., vol. 15, no. 12, pp. 147–158, Dec. 2018.
[13] Z. Ma, B. Ai, R. He, G. Wang, Y. Niu, and Z. Zhong, “A wideband
non-stationary air-to-air channel model for UAV communications,” IEEE
Trans. Veh. Technol., vol. 69, no. 2, pp. 1214–1226, Feb. 2020.
[14] X. Zhang, J. Liu, F. Gu, D. Ma, and J. Wei, “An extended 3-D ellipsoid
model for characterization of UAV air-to-air channel,” in Proc. IEEE
Int’l Conf. Comm. (ICC), Shanghai, China, 2019, pp. 1–6.
[15] M. Walter, D. Shutin, D. W. Matolak, N. Schneckenburger, T. Wiede-
mann, and A. Dammann, “Analysis of non-stationary 3D air-to-air
channels using the theory of algebraic curves,” IEEE Trans. Wireless
Commun., vol. 18, no. 8, pp. 3767–3780, Aug. 2019.
Authorized licensed use limited to: BEIJING INSTITUTE OF TECHNOLOGY. Downloaded on May 18,2021 at 04:17:57 UTC from IEEE Xplore. Restrictions apply.