Beam Tracking for UAV Mounted SatCom
on-the-Move with Massive Antenna Array

arXiv:1709.07989v1 [] 23 Sep 2017

Jianwei Zhao, Feifei Gao, Qihui Wu, Shi Jin, Yi Wu, Weimin Jia

Abstract—Unmanned aerial vehicle (UAV)-satellite communication has drawn dramatic attention for its potential to build the
integrated space-air-ground network and the seamless wide-area
coverage. The key challenge to UAV-satellite communication is
its unstable beam pointing due to the UAV navigation, which
is a typical SatCom on-the-move scenario. In this paper, we
propose a blind beam tracking approach for Ka-band UAVsatellite communication system, where UAV is equipped with
a large-scale antenna array. The effects of UAV navigation are
firstly released through the mechanical adjustment, which could
approximately point the beam towards the target satellite through
beam stabilization and dynamic isolation. Specially, the attitude
information can be realtimely derived from data fusion of lowcost sensors. Then, the precision of the beam pointing is blindly
refined through electrically adjusting the weight of the massive
antennas, where an array structure based simultaneous perturbation algorithm is designed. Simulation results are provided to
demonstrate the superiority of the proposed method over the
existing ones.
Index Terms—UAV, SatCom on-the-move, beam tracking,
mechanical adjustment, electrical adjustment, massive antenna
array.

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Fig. 1. The integrated space-air-ground network.

I. I NTRODUCTION
Satellite communication has become a promising solution
to realize high data rates anywhere, anytime, and towards the
seamless wide-area coverage , in which unmanned aerial vehicle (UAV)-satellite communication1 is a key part for building
the integrated space-air-ground network [1], [2]. As is shown
in Fig. 1, UAV communication could be adopted to serve users
without infrastructure coverage such as disaster areas after
earthquake, where the ground communication infrastructure is
destroyed, or could assist the existing communications, e.g.,
the rapid service recovery and the base station (BS) offloading
of the extremely crowded areas. In these circumstances, UAV
acts as a relay, connecting to terrestrial networks via a satellite
link, and serves user terminals via a ground link [3].
On the other side, spectrum crowding and increased data
rates encourage the migration to millimeter wave (mmWave)
J. Zhao and F. Gao are with Tsinghua National Laboratory for Information
Science and Technology (TNList) Beijing 100084, P. R. China (e-mail:
zhaojw15@mails.tsinghua.edu.cn, feifeigao@ieee.org). J. Zhao is also with
High-Tech Institute of Xian, Xian, Shaanxi 710025, China.
Q. Wu is with the Department of Electronics and Information Engineering,
Nanjing University of Aeronautics and Astronautics, Nanjing 210007, China
(email: wuqihui2014@sina.com).
S. Jin is with the National Communications Research Laboratory, Southeast
University, Nanjing 210096, P. R. China (email: jinshi@seu.edu.cn).
Yi Wu is with College of Photonic and Electronic Engineering, Fujian
Normal University, Fuzhou, 350117, China (e-mail: wuyi@fjnu.edu.cn).
W. Jia is with High-Tech Institute of Xian, Xian, Shaanxi 710025, China
(e-mail: jwm602@163.com).
1 Geosynchronous satellite is usually used for UAV-satellite communication
since its location relative to earth keeps invariant.

band, typically Ka-band [4]–[8]. Though the heavy path loss
of Ka-band seemingly blocks it from practical usage, the
micro wavelength of Ka-band permits the employment of large
amount of antennas onto a small area to achieve adequate
spatial gains and combat such propagation losses [9]–[14].
Meanwhile, multiple-antennas with small size would be specifically suitable for UAV mounted transmission, which also
removes the requirement of the expensive high-gain directional
antenna in satellite communication and thus greatly reduces
the overall system cost.
In general, the performances of the communication systems
critically rely on the channel state information (CSI), which
brings a large number of CSI estimation works [15]–[22].
Different from the conventional wireless communications systems, UAV based one would encounter new challenges. Due
to the continuous navigation of UAV, the channel would vary
constantly for both the UAV-satellite link and the UAV-ground
link. Furthermore, because of the constraints of the overall
system cost and the power consumption, the available radio
frequency (RF) chains are limited for UAV-satellite communication systems. A beam sweeping method was adopted in [20]
for beam tracking, which spends significant resources to train
the beam in all directions. A priori knowledge aided channel
tracking method was proposed in [21] for Teraherz massive
MIMO system, where a linear motion is adopted to derive
angles of the incident signals and then the complex gains are
estimated by pilots. However, the linear movement model re-

2

Albeit most methods [15]–[22] can be extended to the UAVground link, the channel tracking for UAV-satellite link still
needs to be investigated due to its distinct properties. For UAVsatellite link, the premise of establishing a successful link is
the alignment of the spatial beam from UAV to satellite, i.e.,
the spatial beam should keep “locking” the direction of the
target satellite during UAV navigation [23]–[26], which is a
typical SatCom on-the-move. However, the attitude variation
of UAV (including yaw angle, pitch angle and roll angle)
would constantly affect the beam pointing. Therefore, UAV
needs to overcome the effects of its navigation, and persistently adjusts the spatial beam towards the target satellite. An
electrical tracking method for phased-array antenna system
was developed in [26], which adopts the electrical feedback
to track the beam pointing variation. However, for UAVsatellite link, it is always preferred that the steered spatial beam
should be pointed from the normal of the array antenna plane
since the array antenna gain is proportional to the projected
area of the antenna aperture in the direction of the target
satellite [23], which demands for the mechanical adjustment
as did in conventional SatCom on-the-move [25].
In this paper, we propose a blind hybrid beam tracking
method for the UAV-satellite communication with a massive
uniform plane array (UPA). The mechanical adjustment is
firstly adopted to alleviate the effects of UAV navigations,
where the spatial beam can be pointed towards the target
satellite through the beam stabilization algorithm and dynamic
isolation algorithm. However, due to the limited precision of
low cost attitude sensors, the system error, and measurement
error, the mechanical adjustment could only roughly points the
spatial beam of UAV to the target satellite. We then design an
electrical adjustment to further calibrate beam pointing, where
the spatial beam is steered to DOA of the incident signals in
a more accurate manner with an array structure based simultaneous perturbation algorithm. Finally, simulation results are
provided to verify the effectiveness of the proposed method
and demonstrate its superiority over the existing candidates.
The rest of the paper is organized as follows. The system
model is described in section II. Beam tracking with mechanical adjustment is presented in section III, while beam
tracking with electrical adjustment is presented in section
IV. The simulations are then displayed in section V. Finally,
conclusions are drawn in section VI.
Notations: Vectors and matrices are denoted by boldface
small and capital letters; the transpose, complex conjugate,
Hermitian, inverse, and pseudo-inverse of the matrix A are
denoted by AT , A∗ , AH , A−1 and A† , respectively.

1
0.8
Amplitude

stricts its application for practical nonlinear movement scenes.
An angle division multiple access (ADMA) based channel
tracking scheme was proposed in [22] for massive MIMO
systems, where channel tracking is transmitted to estimating
the direction of arrival (DOA) information of the incoming
signals and the time-varying complex gain information, which
greatly reduces the complexity of channel tracking.

0.6
0.4
0.2
0
1.5
1.5

1
1
0.5
β(rad)

0.5
0

0

α(rad)

Fig. 2. The characteristic of Ka-band massive array antenna.

II. P ROBLEM F ORMULATION
A. Channel Model
Let us consider a UAV-satellite communication system,
where UAV is equipped with UPA of M × N antennas with
M ≫ 1, N ≫ 1, while a single antenna is installed on the
geosynchronous satellite [27], [28]. Due to the constraints
of system cost and power consumption, the available radio
frequency (RF) chains are limited for UAV-satellite communication system. In this paper, it is assumed that UAV has
only one dedicated RF chain, i.e., single channel receiver
mode [29], [30].
Define A(αl , βl ) ∈ CM×N as the array response matrix,
whose (m, n)-th element can be expressed as
A(αl , βl ) = ej

2πd
λc [(m−1) sin αl

cos βl +(n−1) sin αl sin βl ]

,

(1)

where αl and βl are the azimuth angle and elevation angle
of the l-th path from the target satellite. Then, the M × N
channel matrix H between the target satellite and UAV can
be expressed as [19], [24]
H=

L
X
al e−j2πdl /λc
√
A(αl , βl ),
MN
l=1

(2)

where L represents the number of the incident pathes, dl is the
distance between antenna 1 of UAV and the satellite along path
l, and λc is the carrier wavelength. Moreover, al is the complex
channel attenuation of the l-th path due to gaseous, cloud,
rain, and scintillation attenuation. A combination method
considering the above effects can be seen in [24].
For UAV-satellite link, there are limited scatters in the
propagation surroundings and thus the number of the incident
paths meets L ≪ N and L ≪ M . Propagation measurement
says that the overwhelming majority of the total energy arrives
at the receiver from the direct path in satellite communication [23]. Meanwhile, fixed satellite communication systems
above 10 GHz have been verified to operate under loss of
sight (LOS) only [24]. Therefore, LOS ray is the dominant

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Fig. 3. The error analysis of UAV beam pointing, where the beam direction
should be stabilized at the vicinity of the plane normal for high quality of
communication.

one while the other Non-LOS (NLOS) components can be
ignored for the Ka-band UAV-satellite communication link.
Define the spatial domain channel matrix as the 2-dimension
discrete Fourier transform (2D-DFT) of H, i.e.,
H̃ = FM HFN ,

(3)

where FM and FN are the normalized DFT matrices with
dimension M × M and N × N . According to the analysis
in [19], the significant values of the spatial channel H̃ are
centered around DOA α and β of the impinging signal, as
shown in Fig. 2. Besides, the massive number of antennas
could form narrow beam with high spatial gain, and thus is
very suitable for UAV-satellite communication.
B. Problem Formulation
For UAV-satellite link, the beam pointing error would
severely degrade the communication quality, which should be
kept as small as possible. In addition, it has been verified
that the optimal working range of UPA is in the vicinity of its
normal, and the array gain is proportional to the projected area
of the antenna aperture in the direction of the target satellite,
which declines by sine of the elevation angle [23]. For example
in Fig. 3, the spatial beam would be distorted if it deviates far
from the direction of the plane normal.
In general, there are two main factors affecting beam
pointing: satellite perturbation and UAV navigation. In order
to overcome the influence of the satellite perturbation, the
position-keeping technique is usually adopted so that the
latitude and longitude errors of the satellite position are kept
within the allowable range. A good example of positionkeeping technique is [31], where satellite perturbation has
little effect on beam pointing within one hour and can be
neglected. On the other side, the UAV navigation, including
the carrier’s heading, pitching and rolling motion, are very
detrimental. Unfortunately, there is no corresponding method
to overcome the effects of UAV navigation for UAV-satellite
communication systems.

Fig. 4. The structure of the UAV communication system, where a mechanical
adjustment subsystem is installed at BS and each antenna is equipped with a
analog shifters instead of a dedicated RF chain.

To remedy the effects of UAV navigation, we propose a
new beam tracking method based on the joint mechanical
adjustment and electrical adjustment. The structure of the
designed beam tracking system is depicted in Fig. 4, which
consists of three segments: (1) the perception part contains
the measurement sensors and is responsible to sense the UAV
attitude variations as well as to measure the corresponding
angular rate; (2) the decision part, i.e., the arithmetic and
control unit (ACU), provides control commands to stabilize
beam pointing according to the outputs of the perception
part; (3) the operative part contains the control motors (the
azimuth angle control monitor, the polarization angle control
monitor, and the elevation angle control monitor) and phase
shifters, etc., which implements the directives of the decision
part.
Traditionally, the high precision inertial navigation system [25] is used to obtain the attitude information in UAV
military applications. However, the cost is not affordable
for the civil applications. Recently, with the development of
the micro electro mechanical system (MEMS), there appear
many low-cost attitude sensors, such as MEMS gyros, MEMS
accelerator, global position system (GPS). Therefore, we propose to utilize these low-cost sensors to derive the attitude
information and reduce the total system cost. The attitude
determination principles of these low-cost sensors can be
found in Appendix A.
III. C OARSE B EAM A LIGNMENT WITH M ECHANICAL
A DJUSTMENT
Due to small wavelength of Ka-band, the size of massive
array antenna is not large, which makes the mechanical
adjustment based beam tracking applicable [25]. In general,
the mechanical adjustment for beam tracking consists of two
steps: the beam stabilization and the dynamic isolation, which
is shown in Fig. 5.

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Fig. 5. Mechanical adjustment with beam stabilization and dynamic isolation.

Communication
satellite

x
y
z

t

f
a
UAV

b

o
n

Fig. 6. The definition of different reference frames, including n-frame, bframe, a-frame, f -frame and t-frame.

A. Beam Stabilization
The proposed beam stabilization jointly utilizes the UAV
attitude information and satellite location information to track
the spatial beam. To represent UAV attitude information, we
need to explain the reference frames first, which describe
the relationships between UAV attitude and beam pointing.
Different reference frames are also shown in Fig. 6.
1) The geodetic coordinate frame (n-frame): Its origin is
chosen as the UAV center of gravity (UAVCG), and its
three axes xn , yn , zn are separately aligned with the
direction of north, east, and geocentric.
2) The UAV-fixed coordinate frame (b-frame): Its origin is
UAVCG, and its three axes xb , yb , zb , i.e., roll axis, pitch
axis, and yaw axis, are aligned with its longitudinal (forward), lateral (right), and vertical (downward) direction.
3) The azimuth-rotary coordinate frame (a-frame): Its origin
is the array antenna center of gravity (AACG). Its axis
za is parallel to zb , while axis ya is identical with
the direction of UPA elevation axis. The axis xa is
perpendicular to the plane spanned by the axis ya and za .
According to the relationship of b-frame and a-frame, the
b-frame would be consistent with the a-frame when we
rotate the azimuth angle α around the axis zb .
4) The UPA coordinate frame (f -frame): Its origin is AACG.
Besides, its axis yf is parallel to ya , while its xf axis
points to the satellite. The axis zf is perpendicular to

the plane spanned by the axis xf and yf . On the basis
of the relationship of f -frame and a-frame, the a-frame
would be consistent with the f -frame when we rotate the
elevation angle β around the axis ya .
5) The spatial beam coordinate frame (t-frame): Its origin
is also AACG, and axis yt is identical with the direction
of electric field, while xt is parallel to xf . The axis zt
is perpendicular to the plane spanned by the axis xt and
yt . Based on the relationship between the f -frame and tframe, the f -frame would be consistent with the t-frame
when we rotate the polarization angle γ around the axis
xt .
The UAV attitude relative to the n-frame is determined by
the yaw angle Ψ, the pitch angle θ, and the roll angle φ, while
the beam attitude of UAV array antenna relative to the b-frame
is dependent on the azimuth angle α, the elevation angle β,
and the polarization angle γ. Moreover, the beam attitude of
UAV array antenna relative to the n-frame can be expressed
by the Euler angles o, e, and v. The relationships between
different frames are shown in Fig. 7, and the transformation
between different frames can be realized by the coordinate
transformation matrix [25].
Denote Ctb as the coordinates transformation matrix between the b-frame and the t-frame, which can be realized
by three continuous spatial rotation: rotating α around the

cos α sin α 0
axis zb that is represented by T1 (α)= − sin α cos α 0 ,
0
0
1
rotating
β around the

 axis ya that is represented by T2 (β)=
cos β 0 − sin β
 0
1
0 , and rotating γ around the axis xt that
sin β 0 cos β


1
0
0
sin γ .
is represented by T3 (γ)= 0 cos γ
0 − sin γ cos γ

Each of the three rotations are illustrated in Fig. 8. Thus,
Ctb can be mathematically expressed as (4), shown on the top
of the next page.
According to the position relationships of UAV and satellite,
we can obtain the Euler angles o, e, v of the spatial beam

5



cos α cos β
Ctb = T3 (γ) T2 (β) T1 (α) =  cos α sin β sin γ − sin α cos γ
sin α sin γ + cos α sin β cos γ
ωut =Ctb ωub = T3 (γ) T2 (β) T1 (α) ωub


1
0
0
cos β 0
sin γ   0
1
=  0 cos γ
0 − sin γ cos γ
sin β 0

zb za

zf

sin α cos β
sin α sin β sin γ + cos α cos γ
sin α sin β cos γ − cos α sin γ


− sin β
cos α
  − sin α
0
cos β
0

E


− sin β
cos β sin γ  .
cos β cos γ



sin α 0
ωubx
cos α 0   ωuby  .
0
1
ωubz

za
zW

J

(4)

(10)

zf

yf

xb

D
xa

Ob OT

D

OT

ya

yb

ya

xa x f



E

OT

xf

J

xt

y f yW





Fig. 8. The transformation from the b-frame to t-frame.

relative to the n-frame as



−1 tan(λ−λs )
◦

o
=
180
+
tan
,

sin ϑ





RE
cos
ϕ
cos(λ−λ
)−
s
RE +hE
e = tan−1 √
,
ϕ cos(λ−λs )]2


 1−[cos 


 v = tan−1 sin(λ−λs ) ,
tan ϑ

(5)

where ϑ is the UAV latitude, λ is UAV longitude, λs is
longitude of target satellite, RE and hE are the earth radius
and the UAV altitude.
Similarly, we can derive the coordinates transformation
matrix between the n-frame and the t-frame Ctn as
Ctn = T3 (v) T2 (e) T1 (o) .

(6)

Furthermore, when the UAV attitude information (ψ, θ, φ)
is obtained (the derivation is presented in Appendix B), the
coordinates transformation matrix between the n-frame and
the b-frame Cbn can be expressed as
Cbn = T3 (φ) T2 (θ) T1 (ψ) .

(7)

As shown in Fig. 7, the coordinates transformation from the
n-frame to the t-frame can be decomposed into the transformation from n-frame to the b-frame and the transformation
from the b-frame to the t-frame, namely,
Ctn = Cbn Ctb ,

or Ctb = (Cbn )−1 Ctn .

(8)

From (8), the final angle in the b-frame for aligning the
spatial beam of UAV to the target satellite can be derived as

T12
,
 α = arctan T11
β = − arcsin T13 ,
(9)

γ = arctan TT23
,
33

where Tm,n is the (m, n)-th element in Ctb .
B. Dynamic Isolation

When UAV navigates, its attitude will change and would
affect beam pointing. The corresponding angular rate in the
b-frame, denoted as ωub , is coupled with the direction of
the spatial beam through geometric constraints and friction
constraints, and could be measured by gyros. Let us further
denote the coupled angular rate of the spatial beam due to
UAV navigation in the t-frame as ωut . Then, it can be derived
as (10), shown on the top of the page. Moreover, in (10), ωubx ,
ωuby and ωubz are the elements of ωub .
Next, we propose the dynamic isolation algorithm to compensate ωut as well as release the effects of UAV navigation,
and the detailed scheme is shown in Fig. 9. Specially, the
control monitors of the azimuth angle, the polarization angle,
and the elevation angle are jointly utilized to make the spatial
beam point to the target satellite.

6

Å
Å
Fig. 9. The procedure of dynamic isolation.

Denote ωαa , ωβf and ωγt as the control monitor
outputs
඀ḷ㌫
of the azimuth angle, the polarization angle, and the elevation
angle respectively. According to the inter-relations of the aframe, the f -frame, and the t-frame, the azimuth angular rate
in the t-frame, denoted as ωαt , can be obtained from azimuth
angle control monitor as
ωαt = T3 (γ) T2 (β) ωαa


1
0
0
cos β
sin γ  0
= 0 cos γ
0 − sin γ cos γ
sin β

0
1
0

 
− sin β
0
 0  , (11)
0
cos β
ωα

while the elevation angular rate in the t-frame, denoted as ωβt ,
can be obtained from the elevation control monitor as

 
1
0
0
0
sin γ  ωβ  . (12)
ωβt = T3 (γ) ωβf =  0 cos γ
0 − sin γ cos γ
0

Moreover, the polarization angular rate in the t-frame can be
T
directly obtained by ωγt = [ωγ 0 0] .
Then, the total beam pointing angular rates from the control
monitors in the t-frame, denoted as ωmt , are the sum of ωαt ,
ωjtβ , and ωγt , i.e.,
ωmt = ωγt + T3 (γ) ωβf + T3 (γ) T2 (β) ωαa .

(13)

Take the t-frame as the reference, the eventual physical
angular rate of beam pointing, denoted as ω, is the result of
a combination of the UAV’s own navigation and the control
monitor’s outputs, namely,
ω = ωmt + ωut .

IV.඀ḷ㌫
F INE B EAM A LIGNMENT WITH E LECTRICAL
A DJUSTMENT
඀ḷ㌫

Due to the system error and the measurement error, purely
counting on mechanical adjustment is not sufficient to yield
an accurate beam pointing. To further improve the precision of
beam pointing, we propose an electrical adjustment method.
඀ḷ㌫

A. Electrical Adjustment with Simultaneous Perturbation
As mentioned earlier, we consider the hybrid scheme to
decrease the system cost and power consumption. Therefore,
the received signal at UAV can be expressed as
y = wH hs + wH n,

(16)

where h = vec(H), w is the M N × 1 receive beamforming
vector with |wi | = 1, s is the transmitted signal of the satellite,
and n is the M N × 1 noise vector.
Then, the instant power of the received signal at UAV can
be expressed as
P = |y|2 = wH Rs w + wH Rn w,

(17)

(14)

To overcome the effect of UAV attitude variation, it is required that ω = 0 such that the spatial beam is always pointing
to the target satellite. After some tedious computations, the
angular rates of the control monitors can be obtained from (14)
as

 ωα=− cos α · tan β · ωubx −sin α · tan β · ωuby −ωubz ,
ωβ = sin α · ωubx − cos α · ωuby ,

ωγ = (− cos α · ωubx − sin α · ωuby ) sec β.
(15)
Remark 1: The mechanical adjustment is performed according to the attitude information rather than the training symbols,
which is a blind way for beam tracking.

where Rs = hsshH and Rn = nnH are the temporal
covariance matrices of the signal and the noise respectively.
Let [α, β] be the relative location of the target satellite after
mechanical adjustment. Since mechanical adjustment could
approximately stabilize the beam direction near the normal
of UPA, the value of α and β would be small. To achieve
a superior quality of service in UAV-satellite communication,
the power of the received signal at UAV should be made as
high as possible to guarantee the beam pointing in a precise
direction [26].
It has been demonstrated in [19] that P can be maximized
by aligning the beam direction with the desired signal source
direction, i.e., w = vec (A(α, β)). In this scheme, the phase

7

of the (m, n)-th element of A(α, β), denoted as p(m,n) can
be expressed as
2πd sin α
[(m − 1) cos β + (n − 1) sin β]
λc
2πd sin α p
(m − 1)2 + (n − 1)2
=
" λc
#

p(m,n) =

m−1
. sin β + arcsin p
.
(m − 1)2 + (n − 1)2

(18)

From (18), the DOA information is required for receive
beamforming. However, the single RF chain at UAV restricts
the application of many advanced DOA estimation algorithms,
such as MUSIC, ESPRIT, and Capon [34]–[37]. For single RF
chain receiver, a zero-knowledge beamforming method was
suggested in [38], but this method is time-consuming due to
sequential perturbation of the phase shifters. Besides, the convergence speed would become much slower with the increase
of the massive array antennas. A simultaneous perturbation
method was proposed in [39] to accelerate the convergence
speed. However, the method is fully isotropic and still requires
many iterations for convergence. Here, we propose to utilize
the array structure to further accelerate the converge speed for
UAV with massive array antennas.
Note from (18) that the values of the phase shifters for beam
alignment are related to the antenna locations (m, n). Hence,
we could utilize the array antenna structure to accelerate the
convergence speed. Specially, the instant power of the received
signals are utilized for the electrical adjustment instead of the
training symbols, which is also a blind way.
Denote ĝk (wk ) as the estimation of the gradient
∂P (wk )/∂wk , which can be derived from two noisy measurements of the received signal power as (19), shown on the
top of the page.
Moreover, in (19), ξk and the elements of ∆k are random perturbation parameter at the k-th iteration following a
Bernoulli ±1 distribution with probability 1/2. Meanwhile, b,
c as well as Ω are all the small perturbation parameters, and
D can be expressed as


d11 · · · d1N

..  ,
..
(20)
D =  ...
.
. 
dM1

· · · dMN

p
where dmn = (m − 1)2 + (n − 1)2 .
Then, the received beamforming vector can be adjusted
according to the following formula
wk+1 = wk − ηk ĝk (wk ),
ξ

(21)

where ηk = a/(ζ + k) is the step size for the adjustment at
the k-th iteration, and ξ, ζ are step perturbation parameters.
The perturbation parameters in (19) and (21) can be obtained
by the guide lines in [40].
The detailed steps of the proposed method are shown in
Algorithm 1. Since the proposed electrical adjustment utilizes
the array structure, it can be named as array structure based
simultaneous perturbation (ASSP).
Remark 2: Since the value of α and β are small, the time for
convergence would not be large. Besides, by utilizing the array

Algorithm 1 : Electrical adjustment
• Step 1: Initialization: initialize the spatial beam direction
of the array antenna as w = 1MN ×1 , and obtain the UAV
latitude ϑ, the UAV longitude λ and the satellite longitude
λs ;
• Step 2: Beam coarse alignment: adopt beam stabilization
(9) and dynamic isolation (12) to realize the rough
alignment of the spatial beam;
• Step 3: Beam fine alignment: perform the array structure
aided DOA tracking. Set k = 0, and pick parameters
a, b, c, ζ, Ω, ξ according to the guide lines [40];
• Step 4: Simultaneous perturbation: generate the perturbation scalar ξk and ∆k , and derive two instant power
measurements of the UAV received signals P (w+ ) and
P (w− ), where w+ = wk + b/(k + 1)Ω Dξk + c/(k +
1)Ω ∆k and w− = wk −b/(k +1)Ω Dξk −c/(k +1)Ω ∆k ;
• Step 5: The beam pointing updating: estimate the gradient ĝt (wk ) using (19) and update the beam direction
wk+1 by (21);
• Step 6: Decision: terminate algorithm when the power
of the received signal increases little, or else return to
Step 3.

structure, the convergence speed of the proposed algorithm is
not relevant to the number of the phase shifter or equivalently
the number of the array antennas, and would be much faster
than the traditional techniques in [38], [39].
B. Complex Gains Estimation
Through the joint mechanical adjustment and electrical
adjustment, the spatial beam can be pointed to the target
satellite without training, i.e., a blind way. With the tracked
beam, we can further derive the gain information by sending
training symbols towards the target satellite as did in [19].
Since there is only one dominant beam for transmission, the
minimum size of the training sequence is 1 for both uplink
and downlink channel.
V. S IMULATIONS

AND

R ESULTS

In this section, numerical results are provided to demonstrate the effectiveness of the proposed method. We set M =
128, N = 64 and d = λ2 , and the channel vector between
UAV and target satellite can be produced according to (2).
The experimental platform, which consists of the outdoor
part and the indoor part, is installed at the three-axis flight
simulation turntable to imitate the navigation of UAV. The
outdoor part are composed of XW-ADU3601, XW-IMU5220
and XW-ADU7612 [41]–[43]. Specifically, XW-ADU3601 is
a two-antenna GPS outputting the measurement of ψm ; XWIMU5220 is an MEMS inertial measurement unit that can
output the attitude angular rates ωub and the measurements
of θm and φm ; XW-ADU7612 is an attitude and heading
reference system, which can provide the attitude to an accuracy
of 0.1◦ as comparison. The DSP processor runs in the indoor
parts with the frequency 400 MHz, which is ACU of the
platform. Note that the platform can provide measurements

8

ĝt (wk ) =

P (wk +

bDξk
(k+1)Ω

+

bDξk
− P (wk − (k+1)
Ω −
h
i
bDξk
c∆k
2 (k+1)Ω + (k+1)Ω
c∆k
(k+1)Ω /)

c∆k
(k+1)Ω /)

.

(19)

181
1.5
α
β

ψ/°

180
179

1

Reference
0

0

10

Data fusion
20

30

40

50

θ/°

−1
−2
−3
1.5

0.5

Angle error/°

178

0

10

20

30

40

50

0

−0.5

1

φ/°

−1

0.5
0

−1.5

0

10

20

t/s

30

40

50

Fig. 10. The performance of attitude determination.

10

20

30

40

50

t/s

Fig. 12. The errors of the beam pointing from mechanical adjustment.

1

0.5

δψ/°

0

0.995

0
0.99

−0.5
0
0.5

10

20

30

40

0.985

50
NRSP

δθ/°

0.98

0

0.975
0.97

−0.5
0
0.5

10

20

30

40

50

0.965

δφ/°

0.96

0
−0.5

The proposed method
Method in [39]
Method in [38]

0.955
0.95

0

10

20

30
t/s

40

50

1

2

3

4

5
6
7
8
Number of the iterations

9

10

11

12

Fig. 11. The error of the estimated attitude.

Fig. 13. The performance of the electrical adjustment, where SNR= 20dB.

of the attitude information, and it can be used to verify the
validity of the mechanical adjustment. The target satellite is
set as AsiaSat-3S [44] with longitude 105.5◦ , while the testing
location is Xi’an shaanxi with latitude 34.27◦ and longitude
108.95◦. According to (5), the Euler angles of the beam
alignment is a = 6.11◦ , e = 50.1◦ , and v = −5.05◦.
Fig. 10 shows the attitude from Kalman filter based data
fusion, where the attitude from the XW-ADU7612 is also displayed as comparison, while Fig. 11 shows the corresponding
attitude error. It can be seen from Fig. 10 that the regulation
of attitude variation from data fusion coincides with the
practical attitude value, which verifies that the data fusion can
effectively integrate the measurements from different sensors
and provide relatively precise attitude information. However,

we can see clearly from Fig. 11 that there are still attitude
errors from data fusion, and the maximum error of the attitude
reaches 0.5◦ , which is consistent with the result in (42)-(44).
With the tracked attitude, we then derive the beam pointing
through mechanical adjustment, and the beam pointing errors
of the azimuth angle α and the elevation angle β are shown in
Fig. 12. It can be seen that the pointing errors of both α and β
are within 0.5◦ in most time, and mechanical adjustment can
only approximately make the beam point to the target satellite.
The reason is that the attitude error from data fusion cannot
be neglected, which would be coupled into beam pointing and
make the beam deviate from the target satellite.
Next, we show the performance of electrical adjustment
in Fig. 13 and Fig. 14 with SNR=10 dB and SNR=20 dB

9



 





0
0
ωubx (τ )
φ̇(τ )
 ωuby (τ )  =  0  + T3 [φ(τ − 1)]  θ̇(τ )  + T3 [φ(τ − 1)] T2 [θ(τ − 1)]  0 
ωubz (τ )
0
0
ψ̇(τ )



1 sin φ(τ − 1) tan θ(τ − 1) cos φ(τ − 1) tan θ(τ − 1)
ωubx (τ )
  ωuby (τ )  .
cos φ(τ − 1)
− sin φ(τ − 1)
= 0
0 sin φ(τ − 1)/ cos θ(τ − 1) cos φ(τ − 1)/ cos θ(τ − 1)
ωubz (τ )

1
0.995
0.99
0.985

NRSP

0.98
0.975
0.97
0.965
0.96
The proposed method
Method in [39]
Method in [38]

0.955
0.95

1

2

3

4

5
6
7
8
Number of the iterations

9

10

11

12

Fig. 14. The performance of the electrical adjustment, where SNR=10dB.

0.5

0.4

Angle error/deg

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

2

4

6
8
Number of the iterations

10

much faster speed than other two methods, since the array
structure is utilized for beam tracking. Besides, we can find
that the number of iteration is increasing with the decrease of
SNR for all the displayed methods. The number of iteration
for convergence is 4 for SNR=20dB, while it increases to
7 at SNR=10 dB for the proposed method. However, the
convergence of the methods in [38] and [39] is much worse
compared to their higher SNR case. This is because for
low SNR case, the noise is dominant and would affect the
convergence speed of the electrical adjustment.
In the last example, we show the final angle error of
the proposed simultaneous perturbation with SNR=10 dB in
Fig. 15. We see that with the increase of the iteration number,
the angle errors of both α and β become smaller, and the
eventual angle errors stay in the magnitude of 10−2 , which is
consistent with the result in Fig. 13. Hence, through the joint
mechanical and electrical adjustment, the spatial beam can be
precisely pointed to the target satellite.
VI. C ONCLUSIONS

α
β

0.45

(22)

12

In this paper, we proposed a blind beam tracking method
for Ka-band UAV-satellite communication system with hybrid
massive antennas. The proposed method mainly consists of
two procedures: mechanical adjustment and electrical adjustment. The former one, including the beam stabilization and
dynamic isolation, is used to overcome the effect of UAV
navigation and realize the coarse alignment, while the latter
one is used to further improve the tracking precision and
realize the fine alignment. Moreover, tracking the spatial beam
can be simplified to tracking the DOA information of the
satellite, which greatly decreases the training overhead and
improves the system efficiency. Various examples are provided
to verify the efficiency of the proposed method.

Fig. 15. The angle error of the electrical adjustment, where SNR=10dB.

respectively, where the method in [38] and [39] are also
displayed as comparison. According to the guide lines in [40],
the step parameters are set as a = 0.7, b = 0.02, c =
0.01, ζ = 0.1, τ = 0.1, ξ = 0.602. The performance metric
is the normalized received signal power (NRSP). The prior
NRSP is 0.952, which further verifies that the mechanical
adjustment could approximately point the spatial beam to
the target satellite. It can be seen that all the perturbation
methods can converge to the maximum received power, i.e.,
the spatial beam of UAV is pointed to the practical DOA of
the incident signals. The proposed method can converge with

A PPENDIX A
ATTITUDE D ETERMINATION P RINCIPLES
L OW-C OST S ENSORS

OF

T HE

(1) MEMS Gyros: The three MEMS gyros (roll gyro, pitch
gyro and yaw gyro) are installed near the UAVCG in the
three directions of the b-frame, which can measure the attitude
variation of UAV. Denote the angular rate outputs of the
T
gyros as ωub = [ωubx (τ ) ωuby (τ h) ωubz (τ )] , andidenote the
variation of the UAV attitudes as φ̇(τ ) θ̇(τ ) ψ̇(τ ) . Denote τ
as the time index. According to the definitions
h of the reference
i
frames, the relationship between ωub and φ̇(τ ) θ̇(τ ) ψ̇(τ )
can be expressed as (22), shown on the top of the page.

10

Then, we can obtain a rough measurement of the threedimension attitude angles, denoted as φm (τ ), θm (τ ), and
ψm (τ ), from the gyro integration as

 
 

φ̇(τ )
φm (τ )
φm (τ − 1)
 θm (τ )  =  θm (τ − 1)  +  θ̇(τ )  .
(23)
ψm (τ )
ψm (τ − 1)
ψ̇(τ )
(2) Accelerator: The accelerator is also installed at UAVCG,
which can derive the attitude of the UAV by measuring the local gravity acceleration directly. Denote f (τ ) =
T
[fx (τ ), fy (τ ), fz (τ )] as the measurement of the accelerator,
and the relationship between the output of accelerator and the
attitude of UAV can be expressed as




fx (τ )
− sin θ(τ )
f (τ ) =  fy (τ )  ≈ −g  sin φ(τ ) cos θ(τ )  ,
(24)
fz (τ )
cos φ(τ ) cos θ(τ )

where g is the gravitational acceleration.
Then, the measured pitch angle and the roll angle can be
obtained by


fx (τ )
,
(25)
θm (τ ) = arcsin
g


fy (τ )
.
(26)
φm (τ ) = arctan
fz (τ )

(3) GPS: When two GPS antennas are installed at the front
and back of UAV, they can provide measured yaw angle by
using carrier-phase differential technology. When the baseline
length between the two GPS antennas is d, the coordinate of
baseline can be expressed as [d 0 0] in the b-frame. Meanwhile,
we can derive the coordinate of baseline in the n-frame as
[x(τ ) y(τ ) z(τ )]. Then, the coordinates of the same baseline
in the b-frame and the n-frame can be transformed by Cbn as




x(τ )
d
 0  = Cbn  y(τ )  .
(27)
z(τ )
0
Then, we can acquire the measured yaw angle from (27) as


z(τ )
.
(28)
ψm (τ ) = − arctan
x(τ )
A PPENDIX B
L OW C OST ATTITUDE D ETERMINATION WITH DATA
F USION
The low cost attitude sensors can measure the attitude
information. However, there would exist large error due to
the imprecision of the low-cost gyros, e.g., the drift error and
sideslip angle. Therefore, we try to utilize the Kalman filter
based data fusion to derive an accurate UAV attitude.
Direction cosine matrix, quaternion and Euler angle are
the most commonly used methods for attitude description,
among which the quaternion method not only has low computation complexity, but can also be realtimely updated with
high accuracy. Hence, we adopt the quaternion for attitude
representation.

The quaternion uses four parameters, denoted as q1 , q2 , q3 ,
and q4 , to represent the three dimension attitude of the UAV,
which is defined as

T
q = q1 ρ
,
(29)
T

.
where ρ = q2 q3 q4
With the quaternion, the attitude updating equation can be
represented by
Ts T
Ξ [q(τ − 1)]ωub (τ ),
(30)
2
where Ts is the sampling interval. Moreover, Ξ[q(τ − 1)] can
be derived as (31), shown on the top of the page.
After some tedious transformations of (30), we can further
derive that
q(τ ) = q(τ − 1) +

q(τ ) = Γq(τ − 1) = q(τ − 1),
where 

(32)


−ωubx −ωuby −ωubz



0
ωubz −ωuby 
Ts  ωubx
.
Γ=

I4×4 + 2  ωuby −ωubz

0
ωubx
ωubz ωuby −ωubx
0
Therefore, the system equation can be expressed as


0

q(τ ) = Γq(τ − 1) + χ,

(33)

where χ is the system noise vector, and each element belongs
to CN (0, Qχ ).
When the quaternion is used for attitude updating, it should
meet the normalized condition:
q1 2 + q2 2 + q3 2 + q4 2 = 1.
Then, the normalized quaternion can be expressed as
q
q′ = p
.
qT q

(34)

(35)

Since we can directly obtain coarse values of the attitude
from the low-cost sensors, the measurement of the quaternion
can be obtained from
θm
φm
ψm
θm
φm
ψm
cos cos
+ sin
sin sin
, (36)
q0m = cos
2
2
2
2
2
2
ψm
θm
φm
ψm
θm
φm
q1m = cos
cos sin
− sin
sin cos
, (37)
2
2
2
2
2
2
ψm
θm
φm
ψm
θm
φm
q2m = cos
sin cos
+ sin
cos sin
, (38)
2
2
2
2
2
2
ψm
θm
φm
ψm θm
φm
q3m = sin
cos cos
+ cos
sin sin
. (39)
2
2
2
2
2
2
Note that in the above equations, we omit the time index τ
for simplicity.
Therefore, the measurement equation can be expressed as
z(τ ) = [q0m q1m q2m q3m ]T + u,

(40)

where u is the measurement noise vector, and each element
meets CN (0, Qωk ).
According to the system equation (33) and the measurement
equation (40), the UAV attitude can be tracked by Kalman filter
based data fusion [32], [33], which integrates the outputs of
the low-cost sensors to provide a precise attitude information.
The detailed steps are shown in Algorithm 2.

11





 
0
−q3 (τ − 1) q2 (τ − 1)
 q4 (τ − 1)I3×3 +  q3 (τ − 1)
0
−q1 (τ − 1)  
.
Ξ[q(τ − 1)] = 


−q2 (τ − 1) q1 (τ − 1)
0
−ρT
Algorithm 2 : Attitude determination by Kalman filter
• Step 1: Initialization: ;
• Step 2: Prediction: q(τ |τ − 1) = Γq(τ − 1);
• Step 3: Minimum prediction MSE: κ(τ |τ − 1) = Γ(τ −
1)κ(τ − 1)Γ(τ − 1)H + Qχ ;
• Step 4: Kalman gain matricx: Υ(τ ) = κ(τ |τ −
1)[κ(τ |τ − 1) + Qu ]−1 ;
• Step
5: Updation and normalization: q̂(τ )
=
q(τ |τ−1)+Υ(τ )[z(τ )−q(τ |τ−1)]
;
{q(τ |τ−1)+Υ(τ )[z(τ )−q(τ |τ−1)]}T{q(τ |τ−1)+Υ(τ )[z(τ )−q(τ |τ−1)]}
• Step 6: MMSE: κ(τ ) = [I − ̟k (τ )]κ(τ |τ − 1);
• Step 7: Go to next time instant τ + 1.

For attitude adjustment, we need to further transform the
quaternion to the attitude angle. Since Cnb can be derived from
the tracked quaternion as


 
0
−q̂3 q̂2
 q̂4 I3×3 −  q̂3
0
−q̂1  

Cnb (q̂) = ΞT (q̂) 


−q̂2 q̂1
0
T
−ρ̂


C11 C12 C13
=  C21 C22 C23  ,
(41)
C31 C32 C33
the attitude can be obtained from the definition of Cnb (q̂) as


C21
= ψ(τ ) + δψ(τ ),
(42)
ψ̂(τ ) = arctan
C11
θ̂(τ ) = arcsin (−C31 ) = θ(τ ) + δθ(τ ),


C32
φ̂(τ ) = arctan
= φ(τ ) + δφ(τ ),
C33

(43)

(44)

where δψ(τ ), δθ(τ ), δφ(τ ) are the attitude errors due to the
system error and measurement error, while ψ(τ ), θ(τ ), φ(τ )
are the true values of the UAV attitudes.
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