Position Optimization for Swarm-based UAV-to-UAV Communication
Systems
Mingzhi Xu, Kuan Wu
a
, Jianchao Chen
b
, Xiaojing Huang and Ming Jiang
∗ c
School of Electronics and Information Technology (School of Microelectronics),
Sun Yat-sen University, Guangzhou, China
∗
Keywords:
UAV-to-UAV Communication, UAV Swarm Communication, Relative Position Optimization (RPO),
Successive Convex Approximation (SCA), Energy Efficiency (EE).
Abstract:
Unmanned aerial vehicle (UAV) technologies have played an important role in the beyond-fifth-generation
(B5G) networks. To meet the increasing demand for UAV swarm communications, in this paper we propose
an intra-swarm UAV-to-UAV (IaS-U2U) communication mechanism for enabling data services in the so-called
out-of-coverage (OOC) scenario, where the conventional terrestrial cellular network infrastructure is not avail-
able, for example in the cases of mountains, oceans, deserts and forests. Specifically, an optimization problem
is formulated by jointly considering the single-pair transmission rate (STR) and the propulsion power (PP),
where the UAVs’ pairing and relative positioning are taken into account. To solve the complicated joint opti-
mization problem, we decompose it into the UAV pairing process and the relative position optimization (RPO)
process, where in the latter a successive convex approximation (SCA) based RPO algorithm is proposed. Sim-
ulation results show that the new scheme can provide notable gains in terms of energy efficiency (EE) over
selected benchmark methods under different conditions.
1 INTRODUCTION
Unmanned aerial vehicle (UAV) technologies have
played an important role in the beyond-fifth-
generation (B5G) networks. While a single UAV can
participate in the cellular network communication as
user equipment (UE), a group of autonomous UAVs
forming a swarm can provide a higher overall capabil-
ity and more flexibilities for data services. Thus, UAV
swarm technologies have recently attracted increasing
attention in the area of UAV communications, target-
ing the complicated and cooperative tasks such as col-
laborative surveillance/computing, natural disaster re-
covery, search and rescue operations and many more
applications.
Among the existing issues related to UAV commu-
nications, Liu et al. (Liu and Lau, 2019) formulated
a transmission rate maximization problem consider-
ing the interference of users to jointly optimize UAVs’
positions, user association, and wireless backhaul ca-
pacity allocation. However, the aspect of propulsion
energy is also worth considering due to the typically
a
https://orcid.org/0000-0003-2448-4604
b
https://orcid.org/0000-0002-0024-8618
c
https://orcid.org/0000-0001-9064-7307
limited airborne energy at UAVs (Zeng et al., 2019;
Ahmed et al., 2020). Zeng et al. (Zeng et al., 2019)
derived the expression of propulsion power (PP) for
rotary-wing UAVs and formulated an energy mini-
mization problem, targeting a joint optimization of
UAV trajectory, communication time allocation and
task completion latency. Ahmed et al. (Ahmed et al.,
2020) tried to maximize the throughput under the
constraint of energy consumption, involving aspects
like UAV trajectory, transmit power and user asso-
ciation. In addition, Ye et al. (Ye et al., 2021) in-
vestigated an energy-constrained system throughput
maximization problem in a scenario, where the UAV
charges the internet-of-things (IoT) sensors along its
trajectory, based on an energy consumption model for
rotary-wing UAVs considering the hovering, flying
and charging energy.
However, the aforementioned works only focus on
UAV-to-ground (U2G) scenario, which does not in-
volve UAV-to-UAV (U2U) technologies. In U2U sce-
narios, many technical challenges are foreseen. Ran-
jha et al. (Ranjha and Kaddoum, 2020) discussed the
applicability of different access, forward error correc-
tion and modulation schemes in multi-hop U2U com-
munication. Du et al. (Du et al., 2020) analyzed the
22
Xu, M., Wu, K., Chen, J., Huang, X. and Jiang, M.
Position Optimization for Swarm-based UAV-to-UAV Communication Systems.
DOI: 10.5220/0011319900003286
In Proceedings of the 19th International Conference on Wireless Networks and Mobile Systems (WINSYS 2022), pages 22-32
ISBN: 978-989-758-592-0; ISSN: 2184-948X
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

spectrum sensing and sharing problems between the
U2U pair and the cellular user. Zhang et al. (Zhang
et al., 2019) proposed a cooperative UAV sense-and-
send protocol for cellular UAVs, and formulated a
subchannel allocation and UAV speed optimization
problem to maximize the uplink sum-rate. Though,
the above schemes do not consider or optimize the
UAVs’ positions, which however constitute one of the
key issues in the context of swarm-based U2U com-
munication systems.
Then, other researchers start to consider U2U so-
lutions involving the UAV’s position or trajectory. For
example, Wang et al. (Wang et al., 2020) attempted
to minimize the U2U mission completion time by
jointly optimizing the UAVs’ trajectories and trans-
mit power using the successive convex approxima-
tion (SCA) algorithm. Nevertheless, their approach
ignores the quality-of-service (QoS) constraints. Fur-
thermore, note that the techniques of (Zhang et al.,
2019) and (Wang et al., 2020) rely on the comput-
ing facilities of ground base stations. Thus, they can-
not be applied to the so-called out-of-coverage (OOC)
scenario defined by the third generation partnership
project (3GPP), where terrestrial communication in-
frastructure is not available. Examples of the OOC
scenario can be the cases that when the UAV travels
through a humanless area, such as mountains, oceans,
deserts and forests.
Noting the representativeness and significance of
the OOC scenario for UAV-oriented applications,
Chen et al. (Chen, 2020) suggested that UAVs may
act as relay nodes to assist data communication be-
tween terrestrial UEs. They studied a few aspects, for
instance the UAVs’ positions, transmission power and
bandwidth allocation, such that the system transmis-
sion rate can be maximized. However, they only fo-
cused on the UAVs’ individual hovering positions and
ignored their interactions as a swarm, thus limiting
the potential applications to scenarios without intra-
swarm collaborations. Then, realizing the importance
of UAV swarming, Hong et al. (Hong et al., 2020)
proposed a proactive topology-aware routing scheme
for the OOC scenario, where the routing is dynami-
cally adjusted based on the swarm’s mobility. Nev-
ertheless, they assumed that the relative positions of
UAVs change only when the swarm travels close to
an obstacle. In other words, the impact on U2U com-
munication from the UAVs’ relative positions was ig-
nored (Hong et al., 2020). Moreover, all the afore-
mentioned schemes neglect the PP of UAVs. How-
ever, this is among the most critical issues of prac-
tical U2U systems, especially in many typical OOC
scenarios, where power charging stations are usually
unavailable. To address the PP issue in OOC scenar-
ios, it would be beneficial to design an efficient U2U
communication mechanism by taking into account the
UAVs’ energy aspect.
Under the above background, we propose a new
scheme for intra-swarm U2U (IaS-U2U) communica-
tion in the OOC scenario. The main contributions of
our work include:
• Different from many approaches (Zhang et al.,
2019; Wang et al., 2020; Chen, 2020) which ei-
ther assume the support from ground base sta-
tions or consider non-swarming UAVs only, we
propose a new swarm-based IaS-U2U communi-
cation mechanism particularly targeting the OOC
scenario.
• To our best knowledge, we appear to be the first
to investigate the joint optimization problem of
the single-pair transmission rate (STR) and the
PP of UAVs under QoS constraints in the OOC
scenario. This is different from many existing
schemes (Zhang et al., 2019; Hong et al., 2020),
where one of or both the STR and PP aspects
are not considered. Furthermore, while existing
methods such as (Hong et al., 2020) only focus on
the UAVs’ trajectory, we cast important insights
into the impact from the position optimization on
the system’s attainable performance under a given
swarm velocity.
• To solve the joint optimization problem, we first
decompose it and then construct an SCA-based
relative position optimization (RPO) algorithm,
which can provide an initial solution satisfying
the complicated QoS constraints, such that the de-
composed problem can be iteratively solved.
The rest of the paper is organized as follows. The
system model is presented in Section 2. In Section 3,
we introduce the proposed IaS-U2U communication
mechanism and formulate the joint optimization prob-
lem constrained by the QoS requirements. Then in
Section 4, the details of the proposed RPO algorithm
are provided for solving the target problem. Simula-
tion results and discussions are offered in Section 5,
and our conclusions are outlined in Section 6.
2 SYSTEM MODEL
In this work, we focus on the transmission issue be-
tween the UAVs in the same travelling swarm. Fig-
ure 1 shows a UAV swarm deployed in an OOC sce-
nario, where three types of UAVs co-exist. More
specifically, the central UAV (C-UAV) is located at
the virtual relative center of the swarm with a radius
Position Optimization for Swarm-based UAV-to-UAV Communication Systems
23

of r
sw
. It is responsible for coordinating and designat-
ing a moving trajectory that applies to all UAVs in the
swarm, including a total of M helper UAVs (H-UAV)
and N requester UAVs (R-UAV) besides the C-UAV.
We consider a general scenario, where some H-UAVs
transmit their stored data packets to specific R-UAVs
in the same swarm through selected U2U channel
links that satisfy the QoS requirement. In reality, this
can be for example the case of collaborative surveil-
lance and computing, where R-UAVs, which have a
more powerful computing capability, are responsible
for certain analysis or processing based on the input
surveillance information collected by H-UAVs with a
large cache space and specialized in data sensing.

 



Figure 1: The illustration of the intra-swarm U2U network
topology.
Note that the swarm basically is a moving in-
tranet, except that all UAVs have satellite naviga-
tion functions and thus know their own global posi-
tions. Thus, the C-UAV can broadcast its position in-
formation at the beginning of each time slot for co-
ordinating the swarm’s movement. Other UAVs in
the swarm can combine their own global coordinates
with the received global coordinates of the C-UAV, so
as to deduce their intra-swarm coordinates relative to
C-UAV through simple geometric calculations. Fur-
thermore, C-UAV may support satellite communica-
tion for exchanging crucial control signalling, such
as commands from a remote control center. From
the perspective of broadband access, Figure 1 may be
viewed as an OOC scenario with no support from con-
ventional terrestrial networks.
As any UAV may take the role of H-UAV or R-
UAV in different time depending on specific require-
ments and conditions, we assume that the H-UAVs
and R-UAVs are randomly distributed in the swarm
as a generalized example. Furthermore, the distance
between any two UAVs is no less than a predefined
safety distance d
min
to avoid collisions. Moreover,
without loss of generality, we assume that the dis-
tance between different swarms is relatively large,
such that the inter-swarm interference may be ne-
glected. Though, the intra-swarm interference exists
in the swarm under the full frequency reuse factor of
one. For simplicity, all UAVs are assumed to fly at the
same altitude, thus we may only focus on x,y direc-
tions of the two-dimensional trajectory plane.
Denote N =
{
1,··· , n,··· , N
}
and M =
{
N + 1,··· , N + m,··· ,N + M
}
as the sets of the
indices of R-UAVs and H-UAVs, respectively. Under
the high-altitude airborne environment, the signal
propagation between UAVs may be considered
following a line-of-sight (LOS) channel (Du et al.,
2020; Wang et al., 2020). The channel gain from
H-UAV m to R-UAV n can be formulated as
g
m
(w
n
) = β∥w
m
− w
n
∥
−α
, m ∈ M , n ∈ N , (1)
where w
i
, ∀i ∈ M ∪ N is the position of R-UAV i, α
is the path loss exponent, β is the channel coefficient
and ∥·∥ is the L2-norm operator. We also assume that
the Doppler effect can be reasonably compensated for
the swarm.
Compared with fixed-wing UAVs, rotary-wing
UAVs are lighter in weight and hence have more flex-
ibilities in practical applications (Zeng et al., 2019;
Ahmed et al., 2020; Ye et al., 2021). Thus, in the
sequel we formulate the target optimization problem
based on the PP model of the rotary-wing UAV, which
depends on the UAV’s velocity V (Zeng et al., 2019)
as
P
p
(V ) =P
bla
(1 +
3V
2
U
2
tip
) +
1
2
d
rat
ρs
rot
AV
3
+ P
ind
(

1 +
V
4
4v
4
rot
−
V
2
2v
2
rot
), (2)
where P
bla
is the blade profile power, U
tip
is the tip
speed of the rotor blade, P
ind
is the induced power,
v
rot
is the mean rotor induced velocity, d
rat
is fuselage
drag ratio, ρ is the air density, s
rot
is the rotor solidity,
and A is the rotor disc area (Zeng et al., 2019).
3 COMMUNICATION
MECHANISM AND PROBLEM
FORMULATION
3.1 The Proposed IaS-U2U
Communication Mechanism
For better understanding the rationale of our opti-
mization problem to be introduced in Section 3.2, let
WINSYS 2022 - 19th International Conference on Wireless Networks and Mobile Systems
24

us cast more insights into the mechanism of the IaS-
U2U system.
Note that in the OOC scenario of Figure 1, the
UAVs cannot be managed through the normal way
as in terrestrial networks. Thus, compared with
the schemes in (Zhang et al., 2019; Wang et al.,
2020) where ground base stations are responsible for
scheduling U2U transmissions, in our case the C-
UAV serves as the centralized node to control the
UAV initialization. Then, the proposed RPO algo-
rithm is distributedly executed by each of the R-UAVs
in a sequential order, such that their positions can be
optimized. In Figure 2, the IaS-U2U communica-
tion mechanism tailored for the OOC scenario is por-
trayed, which is outlined as follows:
1. First, each R-UAV broadcasts the U2U re-
quest (3GPP, 2020) and the content feature infor-
mation (CFI) associated with its targeted data to
all H-UAVs. Then, each H-UAV broadcasts the
CFI of its cached data. Each R-UAV performs dis-
tributed pairing trials with each H-UAV.
2. Every successfully paired R-UAV sends its pair-
ing result to C-UAV, which then combines all re-
ceived results to form a pairing list. Subsequently,
C-UAV initiates the RPO procedure at R-UAVs
through a polling strategy as follows:
(a) C-UAV sends a position information list con-
taining the coordinates of all H-UAVs and R-
UAVs, and the pairing list to the polled R-UAV
n, which then executes the RPO algorithm.
(b) R-UAV n reports the optimization result infor-
mation, which contains the pairing status (suc-
cess or failure) and the RPO solution, to C-UAV
and its paired H-UAV.
i. If the optimization fails, both H-UAV and R-
UAV will wait for the next round of pairing.
ii. Otherwise, R-UAV n moves to the new posi-
tion, and then reports a movement completion
message to its paired H-UAV and C-UAV.
(c) C-UAV initiates the RPO procedure at the next
available R-UAV in a random order, if there re-
mains any.
3. Finally, after all paired R-UAVs are polled, each
moved R-UAV establishes U2U connection with
its paired H-UAV.
Based on the mechanism of Figure 2 designed for
the OOC scenario, our main objective is then to de-
termine the UAV pairing, and to find out to which
optimized positions R-UAVs should move, such that
qualified U2U connections can be established for the
targeted H-UAV∼R-UAV pairs.
3.2 Problem Formulation
In this subsection, we first present the PP and STR
models, and then formulate the corresponding joint
optimization problem for the IaS-U2U communica-
tion system concerned. Define a binary matrix X =
[x
m,n
]
(N+M)×N
, where x
m,n
= 1 and x
m,n
= 0 denote
that H-UAV m pairs and does not pair with R-UAV n,
respectively. We assume that each H-UAV can serve
at most one R-UAV and each R-UAV can only be
served by at most one H-UAV, namely
(
C1 :
∑
n∈N
x
m,n
⩽ 1, ∀m ∈ M
C2 :
∑
m∈M
x
m,n
⩽ 1, ∀n ∈ N
. (3)
Different from (Hong et al., 2020) which only fo-
cuses on the UAV’s pairing without considering the
impact from their positions, in this work we try to ex-
plore the opportunity of exploiting the intra-swarm
movements of UAVs for potential performance en-
hancements. For R-UAV n, we denote w
start
n
and w
n
as
its initial position before time slot δ and the final posi-
tion after time slot δ, respectively. Since we focus on
the RPO process at R-UAVs, we assume that H-UAVs
and C-UAV fly at the same velocity, which is defined
as the swarm velocity v
sw
= [v
sw
x
,v
sw
y
]
T
, where v
sw
x
and
v
sw
y
denote the swarm velocity in x and y directions,
respectively. Thus, we may define the velocity vector
of R-UAV n as
v
n
=
w
n
− w
start
n
δ
+ v
sw
. (4)
Then, despite that many existing works (Wang et al.,
2020; Chen, 2020; Hong et al., 2020) ignore the PP
of UAVs in their designs, it is desirable to consider
its potential impact on the performance of the IaS-
U2U system, where the energy aspect is a critical con-
straint, especially in many OOC scenarios typically
without power charging facilities. According to (2),
the PP of R-UAV n can be expressed as
P
p
(w
n
) =P
bla
Ç
1 +
3∥v
n
∥
2
U
2
tip
å
+
1
2
d
rat
ρs
rot
A∥v
n
∥
3
+ P
ind
I
1
(v
n
),
(5)
where
I
1
(v
n
) =
Ç

1 +
∥v
n
∥
4
4v
4
rot
−
∥v
n
∥
2
2v
2
rot
å
1
2
. (6)
Furthermore, assuming a frequency reuse factor of
unity, we define the STR from H-UAV m to R-UAV
n in the IaS-U2U communication as
R(w
n
) = B log
2
ñ
1 +
p
m
g
m
(w
n
)
Bε +
∑
j∈M \m
p
j
g
j
(w
n
)
ô
, (7)
Position Optimization for Swarm-based UAV-to-UAV Communication Systems
25

%URDGFDVW&),
532SURFHGXUH
5HSRUWPRYHPHQWFRPSOHWLRQ
5HSRUWRSWLPL]DWLRQUHVXOWLQIRUPDWLRQ
6HQGSDLULQJUHVXOW
,IIDLOZDLWIRU
QH[WURXQG
6HQGSDLULQJDQGSRVLWLRQLQIRUPDWLRQOLVWV
(VWDEOLVK88FRQQFHWLRQ
%URDGFDVW88UHTXHVWDQG&),
,IIDLOZDLWIRU
QH[WURXQG
58$9
0RYHWRQHZSRVLWLRQ
+8$9
&8$9
8$9SDLULQJ
88FRPPXQLFDWLRQSURFHGXUH
Figure 2: The proposed IaS-U2U communication mechanism.
where we take into account the U2U interference,
∑
j∈M \m
p
j
g
j
(w
n
), which is often ignored in the ex-
isting literature (Wang et al., 2020; Chen, 2020; Hong
et al., 2020), while B, ε and p
m
denote the system
bandwidth, the noise power spectrum density and the
transmit power of H-UAV m, respectively. In addi-
tion, we define the total PP of R-UAVs, P
tot
p
, the to-
tal STR of H-UAVs, R
tot
, and the system energy effi-
ciency (EE), µ, as
P
tot
p
=
∑
n∈N
P
p
(w
n
), (8a)
R
tot
=
∑
m∈M
∑
n∈N
x
m,n
R(w
n
), (8b)
µ =
R
tot
P
tot
p
. (8c)
respectively, where µ is a metric used for performance
evaluation purpose.
Therefore, to reflect the aspects of both the PP and
the STR, we combine (5) and (7) to form a joint objec-
tive function for the IaS-U2U communication system,
formulated as
U(X,W
R-UAV
)
=
∑
m∈M
∑
n∈N
x
m,n
[R(w
n
)−θ
n
ϕP
p
(w
n
)]. (9)
Then, our target optimization problem can be repre-
sented by
P1 : max
{
X,W
R-UAV
}
U(X,W
R-UAV
) (10)
subjected to (3) and













C3 : ∥v
n
∥ ⩽ V
max
, ∀n ∈ N
C4 : ∥w
n
∥ ⩽ r
sw
, ∀n ∈ N
C5 : R(w
n
) ⩾ R
min
for x
m,n
=1, ∀m ∈ M , ∀n ∈ N
C6 : ∥w
i
− w
j
∥ ⩾ d
min
, ∀i, j ∈ M ∪N , i ̸= j
C7 : ∥w
n
∥ ⩾ d
min
, ∀n ∈ N
,
(11)
where W
R-UAV
= [w
1
,· ·· ,w
N
] denotes the position
matrix of R-UAVs, θ
n
∈ (0,1] represents the priority
factor of R-UAV n, which is used to adjust the impact
of the PP term in the joint optimization problem, and
ϕ is the calibration factor that ensures the PP to be
in the same order of magnitude as well as the same
unit as the STR. Moreover, C3 indicates the maxi-
mum R-UAV velocity V
max
, C4 requires that R-UAVs
are within the swarm area, C5 applies the QoS con-
straint of the minimum STR R
min
for the radio link
between the paired H-UAV and R-UAV, and C6/C7
are anti-collision constraints.
Note that P1 in (10) is a typical mixed-integer non-
linear programming (MINLP) problem, which is non-
convex because X is a discrete variable. To solve P1,
we propose to first decompose it into the UAV pairing
process and the RPO process, and then to solve it in a
distributed way.
4 THE PROPOSED SOLUTION
4.1 The UAV Pairing Process
Based on Figure 2, a UAV obtains other UAVs’ CFI
before invoking the UAV pairing process. To ensure
WINSYS 2022 - 19th International Conference on Wireless Networks and Mobile Systems
26

that C3 in (11) is satisfied after UAV pairing, it is nec-
essary to down-select the candidate H-UAVs, which
can be achieved as follows.
Intuitively, the higher similarity between the data
requested by R-UAV n and the data cached at H-
UAV m, the higher possibility of establishing a U2U
connection between R-UAV n and H-UAV m should
be. Thus, each UAV first calculates the packet con-
tent similarities associated with its candidate UAVs
based on the Jaccard coefficient, which is a popular
metric designed for measuring the similarity between
two entities (Niwattanakul et al., 2013), to generate
a pairing preference list. Then, R-UAV n measures
the signal-to-interference-plus-noise ratio (SINR) for
each H-UAV and removes those below the average
SINR from its pairing preference list. Subsequently,
during the pairing procedure described in Section 3.1,
the classic distributed pairing approach, namely the
Gale-Shapley (GS) algorithm (Gusfield and Irving,
1989), can be applied to achieve one-to-one pairing
between R-UAVs and H-UAVs, yielding the pairing
matrix solution X
∗
. After setting the transmit power
of unpaired H-UAVs to zero, each paired R-UAV can
invoke the RPO process below in a sequential order
and solves P1 in a distributed way.
4.2 The Proposed RPO Process
After the pairing matrix is determined, the success-
fully paired R-UAV n needs to solve the following
problem in the RPO process
P2 : max
w
n
U
n
(w
n
) = max
w
n
[R(w
n
) − θ
n
ϕP
p
(w
n
)], (12)
subjected to













C8 : ∥v
n
∥ ⩽ V
max
C9 : ∥w
n
∥ ⩽ r
sw
C10 : R(w
n
) ⩾ R
min
C11 : ∥w
n
− w
j
∥ ⩾ d
min
, ∀ j ∈ M ∪ N \n
C12 : ∥w
n
∥ ⩾ d
min
, (13)
where U
n
(w
n
) denotes the objective function of R-
UAV n, and C8-C12 are the constraints similar to
those in (11), but applying to this specific R-UAV
n. Note that P2 is non-concave and C10-C12 are
non-convex. To solve P2, the objective function and
its constraints may have to be slackened. Similar
to (Zeng et al., 2019), we introduce a slack variable
τ
C13 : τ ⩾ I
1
(v
n
), (14)
where I
1
(v
n
) is defined in (6). Then, by replacing
I
1
(v
n
) with its upper bound τ given in (14), P
p
(w
n
)
in (5) can be approximated by the convex function
˜
P
p
(w
n
,τ) =P
bla
Ç
1 +
3∥v
n
∥
2
U
2
tip
å
+
1
2
d
rat
ρs
rot
A∥v
n
∥
3
+ P
ind
τ. (15)
Hence, based on (15), P2 can be reformulated to
P3 : max
{
w
n
,τ
}
[R(w
n
) − θ
n
ϕ
˜
P
p
(w
n
,τ)], s.t. C8-C13, (16)
where the term −θ
n
ϕ
˜
P
p
(w
n
,τ) is concave (Zeng et al.,
2019). Then, we have:
Proposition 1. P3 is equivalent to P2.
Proof 1. When τ > I
1
(v
n
), to maximize P3, we may
decrease the value of τ in (14), such that the value of
˜
P
p
(w
n
,τ) in (16) can be reduced, until the equal sign
of (14) holds to yield P
p
(w
n
) =
˜
P
p
(w
n
,τ). Then, P3 is
equivalent to P2. The proof completes.
To tackle the non-convex C13, we may first
square (14) to get τ
2
⩾ I
2
1
(v
n
), which is then summed
up with its reciprocal to yield τ
2
+
∥v
n
∥
2
v
2
rot
⩾
1
τ
2
by ex-
ploiting I
1
(v
n
) defined in (6). Next, we perform the
first-order Taylor expansion on τ
2
and
∥v
n
∥
2
v
2
rot
at τ = τ
(k)
and v
n
= v
(k)
n
, respectively, such that C13 can be
slackened to the following convex constraint
C14 : T
1
(τ;τ
(k)
) + T
2
(v
n
;v
(k)
n
) ⩾
1
τ
2
, (17)
where
T
1
(τ;τ
(k)
) = (τ
(k)
)
2
+ 2τ
(k)
(τ − τ
(k)
)
T
2
(v
n
;v
(k)
n
) = −
∥v
(k)
n
∥
2
v
2
rot
+
2
v
2
rot
(v
(k)
n
) • v
n
(18)
with • being the vector inner product operator, and
(·)
(k)
denotes the variable obtained at the k-th (k =
0,· ·· ,K
max
) iteration with k = 0 being the index of the
initial solution and K
max
being the maximum number
of iterations. According to the definition of v
n
and the
slack variable value formula in (Zeng et al., 2019), for
a given w
(k)
n
, we may calculate τ
(k)
by
τ
(k)
= I
1
(v
(k)
n
), (19)
where
v
(k)
n
=
w
(k)
n
− w
start
n
δ
+ v
sw
. (20)
Furthermore, since ∥a∥∥b∥ ⩾ a • b, C11 and C12 can
be slackened to the convex constraints C15 and C16,
respectively







C15 : (w
(k)
n
− w
j
) • (w
n
− w
j
)
⩾ d
min
∥w
(k)
n
− w
j
∥, ∀ j ∈ M ∪ N \n
C16 : w
(k)
n
• w
n
⩾ d
min
∥w
(k)
n
∥
.
(21)
Position Optimization for Swarm-based UAV-to-UAV Communication Systems
27

In addition, note that P3 and C10 are non-convex
because the function R(w
n
) defined in (7) is non-
concave. Similar to the first-order Taylor expansion
on log(a+ y) at y = y
(k)
, R(w
n
) may be approximated
by
ˆ
R(w
n
;w
(k)
n
), due to
ˆ
R(w
n
;w
(k)
n
)=R(w
(k)
n
)+I
(k)
2

∑
l∈M
p
l
g
l
(w
n
)−g
(k)

− I
(k)
3

∑
j∈M \m
p
j
g
j
(w
n
) − g
(k)
−m

,
(22)
where I
(k)
2
=
Blog
2
e
Bε+g
(k)
, I
(k)
3
=
Blog
2
e
Bε+g
(k)
−m
, g
(k)
=
∑
l∈M
p
l
g
l
(w
(k)
n
) and g
(k)
−m
=
∑
j∈M \m
p
j
g
j
(w
(k)
n
).
To deal with the non-concavity of g
l
(w
n
) and g
j
(w
n
)
in (22), we follow (Liu and Lau, 2019) to perform
the first-order Taylor expansion on g
l
(w
n
) and
g
j
(w
n
) at ∥w
n
− w
l
∥
α
= ∥w
(k)
n
− w
l
∥
α
and w
n
= w
(k)
n
,
respectively, yielding

























g
l
(w
n
)≈ ˜g
′
l
(w
n
;w
(k)
n
)
=
2∥w
(k)
n
− w
l
∥
α
− ∥w
n
− w
l
∥
α
β
−1
∥w
(k)
n
− w
l
∥
α
g
j
(w
n
)≈ ˜g
′′
j
(w
n
;w
(k)
n
)
=
∥w
(k)
n
−w
j
∥
2
−α(w
(k)
n
−w
j
) • (w
n
−w
(k)
n
)
β
−1
∥w
(k)
n
−w
j
∥
α+2
,
(23)
where ˜g
′
l
(w
n
;w
(k)
n
) is a concave function and
˜g
′′
j
(w
n
;w
(k)
n
) is an affine function. According to (23),
ˆ
R(w
n
) may be further approximated by the following
convex function (Chi et al., 2017)
˜
R(w
n
;w
(k)
n
) ≈R(w
(k)
n
)
+ I
(k)
2

∑
l∈M
p
l
˜g
′
l
(w
n
;w
(k)
n
) − g
(k)

− I
(k)
3

∑
j∈M \m
p
j
˜g
′′
j
(w
n
;w
(k)
n
) − g
(k)
−m

.
(24)
Therefore, C10 may be slackened to the convex con-
straint
C17 :
˜
R(w
n
;w
(k)
n
) ⩾ R
min
. (25)
Thus, we may replace R(w
n
) in (16) by its approxi-
mated version
˜
R(w
n
;w
(k)
n
) in (24), as well as replace
constraints C10 and C11/C12 in (13) by their slack-
ened versions, C17 in (25) and C15/C16 in (21), re-
spectively. Then, P3 may be further reformulated to a
new convex problem
P4 : max
{
w
n
,τ
}
˜
U
n
(w
n
,τ; w
(k)
n
)
= max
{
w
n
,τ
}
[
˜
R(w
n
;w
(k)
n
) − θ
n
ϕ
˜
P
p
(w
n
,τ)], (26)
subjected to C8, C9 and C14-C17.
Next, we can apply the SCA algorithm (Chi et al.,
2017) to solve P3 by iteratively solving P4 until con-
vergence. In the first iteration of solving P4, we need
to provide an initial solution satisfying the constraints
of the original problem, namely P2. However, due to
C10, it is difficult to prove P2 is feasible and to find
the initial solution directly. Hence, we temporarily
ignore C10 and the PP term in P2 to construct a tran-
sitional STR maximization (STRM) problem as
P5 : max
{
w
n
}
R(w
n
), s.t. C8, C9, C11, C12. (27)
Note that P5 is a simplified version of P2 and hence
the aforementioned operations in (21) and (24) are
also applicable. Then, P5 can be transformed to a
convex problem
P6 : max
{
w
n
}
˜
R(w
n
;w
(k)
n
), s.t. C8, C9, C15, C16. (28)
Then, we use w
(0)
n
= w
start
n
as the initial solution to
solve P6 iteratively by the SCA algorithm, such that
the maximum STR, R
m,n
max
, and a local optimal solution
of P5, w
tmp
n
, can be obtained later. Thus, we have two
cases:
• If R
m,n
max
⩾ R
min
, P2 is feasible, implying that w
tmp
n
satisfies the QoS-related C10 of (13) and the
equivalent problem P3 also has a feasible solu-
tion according to Proposition 1. Then, w
tmp
n
can
be used to construct the initial solution of P4 as
{w
(0)
n
,τ
(0)
}, where w
(0)
n
= w
tmp
n
and τ
(0)
is cal-
culated by (19). P4 is then solved iteratively to
achieve a local optimal solution w
∗
n
of P2.
• If R
m,n
max
< R
min
, P2 is infeasible, indicating that the
RPO operation of R-UAV n fails. Then, R-UAV n
should stay at its initial position w
start
n
relative to
C-UAV and wait for the next round of RPO.
We summarize the above operations in Algo-
rithm 1, where ∆ denotes a predefined accuracy in-
dicator.
5 SIMULATION AND
COMPLEXITY ANALYSIS
5.1 Simulation Results
In this subsection, the performance results of the
proposed RPO scheme are provided, which were gen-
erated through MATLAB-based simulations and av-
eraged over a number of trails. Note that for the IaS-
U2U communication under the OOC scenario studied
WINSYS 2022 - 19th International Conference on Wireless Networks and Mobile Systems
28

Algorithm 1: The Proposed RPO Algorithm.
1: Input: w
start
n
, K
max
, R
min
, ∆
2: //Stage 1: STRM optimization
3: w
(0)
n
= w
start
n
, k = 0
4: repeat
5: Solve P6 to obtain the optimal solution w
tmp
n
6: w
(k+1)
n
= w
tmp
n
7: k = k + 1
8: until


R(w
(k)
n
)−R(w
(k−1)
n
)
R(w
(k)
n
)


< ∆ or k = K
max
9: Set R
m,n
max
= R(w
tmp
n
), where w
tmp
n
is a solution to
P5
10: if R
m,n
max
⩾ R
min
then
11: //Stage 2: Joint optimization
12: w
(0)
n
= w
tmp
n
13: Calculate τ
(0)
by (19)
14: k = 0
15: repeat
16: Solve P4 to obtain its optimal solution w
∗
n
17: w
(k+1)
n
= w
∗
n
18: Calculate τ
(k+1)
by (19)
19: k = k + 1
20: until


U
n
(w
(k)
n
)−U
n
(w
(k−1)
n
)
U
n
(w
(k)
n
)


< ∆ or k = K
max
21: else
22: Current RPO operation at R-UAV n fails ⇒
set w
∗
n
= w
start
n
23: end if
24: Output: w
∗
n
in this work, there exist few directly comparable ref-
erence schemes. Hence, we use the following adapted
benchmarkers:
1. The PP minimization (PPM) scheme: It is ob-
tained by adapting the STR model and constraints
of (Zeng et al., 2019) to fit into our scenario.
Specifically, we first use the STR model expressed
in (7), and then apply the slackening and approx-
imation processes similar to P4 under constraints
C8-C12.
2. The STRM scheme: It targets solving P5 in (27)
only, which does not consider the PP aspect.
Aiming for fair comparison, the UAV pairing pro-
cess proposed in Section 4.1 and Stage 1 of Algo-
rithm 1 are applied to all schemes. After Stage 1 of
Algorithm 1, the PPM scheme minimizes the PP of
R-UAVs, while the STRM scheme ignores the U2U
pairs not satisfying the QoS-related C10 of (13).
The default values of the main parameters used
in our simulations are as follows, unless otherwise
stated. The values of PP-related variables are cho-
sen similar to (Zeng et al., 2019) for fair comparison,
namely P
bla
= 79.865 W, U
tip
= 120 m/s, d
rat
= 0.6,
ρ = 1.225 kg/m
3
, s
rot
= 0.05 m
3
, A = 0.503 m
2
,
P
ind
= 88.628 W and v
rot
= 4.03 m/s. The channel pa-
rameters are referred to (Wang et al., 2020), namely
B = 5 Hz, β = −60 dB, α = 2 and ε = −170 dBm/Hz.
Others parameters are v
sw
= [0,20]
T
m/s, V
max
=
45 m/s (3GPP, 2017), p
m
= 0.2 W, ∀m ∈ M (3GPP,
2017), K
max
= 10, ∆ = 0.1, ϕ = 0.15 Mbit/s/W,
R
min
= 4 Mbit/s (3GPP, 2019), M = 5, N = 5, δ =
0.5 s, r
sw
= 25 m, d
min
= 2 m and θ
n
= 0.5, ∀n ∈
N (Zhu et al., 2019).
Note that the UAV swarms’ velocity has a large
impact on various aspects of the IaS-U2U communi-
cation, as seen in Figure 3. For example, when the
swarm velocity ∥v
sw
∥ increases, Figure 3a indicates
that the total PP of R-UAVs P
tot
p
first increases and
then reduces. The phenomenon is consistent with the
trend of PP with different velocities observed in (Zeng
et al., 2019). More specifically:
• On the one hand, Figure 3a shows that when the
swarm is at a low velocity, P
tot
p
reduces as the
safety distance d
min
increases. According to (7),
a higher d
min
may extend the distance between R-
UAVs and H-UAVs and hence decrease the STR.
This thus results in a growing proportional im-
pact from PP to the joint objective function given
by (9). Thus, the algorithm tends to mitigate the
PP for leveraging the maximization of (9) as re-
quired by (10).
• On the other hand, however, according to C3 and
C7 in (11), a higher swarm velocity with a larger
d
min
may make it more challenging for R-UAVs
to fulfil the QoS-related constraints, and hence
may reduce the number of qualified U2U pairs.
Then, while the algorithm tends to reduce PP to
exchange for a larger output of the joint objective
function, the fewer available U2U pairs, imply-
ing a reduced opportunity for R-UAVs’ position
optimization, could not provide sufficient contri-
butions to system improvement, thus significantly
offsetting the effect of PP reduction.
Therefore, from the two aspects above, a medium-
to-high swarm velocity results in a higher P
tot
p
, al-
though its increment rate against velocity could be
relatively lower under a greater d
min
. To maintain a
low PP, we may select a relative low swarm velocity
of around 10 m/s, as shown in Figure 3a.
Furthermore, Figure 3b shows that the total STR
of H-UAVs R
tot
reduces as the swarm velocity and/or
d
min
become higher. Similar to our analysis for Fig-
ure 3a above, the reason for this phenomenon is also
due to C3 and C7 in (11). Again, the increment of
swarm velocity and d
min
will reduce the number of
Position Optimization for Swarm-based UAV-to-UAV Communication Systems
29

Swarm velocity, ||v
sw
|| (m/s)
0 10 20 30 40
Total PP of R-UAVs, P
tot p
(KW)
0.5
1
1.5
2
2.5
3
3.5
d
min
=2 m
d
min
=6 m
d
min
=10 m
0 5 10 15
0.6
0.8
1
(a) PP performance of RPO
Swarm velocity, ||v
sw
|| (m/s)
0 10 20 30 40
Total STR of H-UAVs, R
tot
(Mbit/s)
20
30
40
50
60
70
80
d
min
=2 m
d
min
=6 m
d
min
=10 m
(b) STR performance of RPO
Swarm velocity, ||v
sw
|| (m/s)
0 10 20 30 40
System EE,  (Mbits
-1
KW
-1
)
0
20
40
60
80
100
d
min
=2 m
d
min
=6 m
d
min
=10 m
(c) EE performance of RPO
Swarm velocity, ||v
sw
|| (m/s)
0 10 20 30 40
System EE,  (Mbits
-1
KW
-1
)
0
20
40
60
80
100
RPO, 
n
=0.25
RPO, 
n
=0.5
RPO, 
n
=1
STRM
PPM
35 40 45
10
20
30
(d) EE performances of various schemes
Figure 3: Performances of the IaS-U2U system supported by various algorithms.
R-UAVs qualified for U2U pairing, and thus affects
the overall STR performance. Interestingly, Figure 3c
illustrates that the EE µ first increases and then re-
duces when the swarm velocity becomes larger, and
that the shortest safety distance of d
min
= 2 m helps to
achieve the highest R
tot
and EE at the cost of a moder-
ately increased PP compared with other larger values
of d
min
. Note that thanks to the rapid development of
UAV technologies, the safety distance has been grad-
ually reduced in recent years (Zhu et al., 2019), which
may therefore provide a beneficial condition for the
proposed RPO scheme.
From Figure 3a, Figure 3b and Figure 3c, we can
see that a performance tradeoff exists among P
tot
p
, R
tot
,
µ and ∥v
sw
∥, while RPO tends to balance these as-
pects of the IaS-U2U system. Last but not the least,
it is worth pointing out that RPO can achieve a higher
EE than the benchmarker schemes STRM and PPM,
as proved by Figure 3d under d
min
= 2 m, where use-
ful system design hints can be found. For example,
to achieve a higher EE, one may reduce (or increase)
the priority factor θ
n
of RPO, when ∥v
sw
∥ is lower (or
higher) than the threshold of 32.5 m/s at the intersect-
ing point of the various RPO curves associated with
different θ
n
.
5.2 Complexity Analysis
Note that the computational complexity of the pro-
posed RPO scheme in Algorithm 1 mainly depends
on the interior-point method (IPM) (Nesterov and
Nemirovskii, 1994), which yields a complexity of
K
iter
· log(1/ε) · O(n
3.5
var
)(Wang et al., 2020), where
K
iter
, ε and n
var
denote the number of SCA iterations,
the predefined accuracy of IPM and the number of
variables, respectively.
For Stage 1 and Stage 2 of RPO, we have n
var
= 2
and n
var
= 3, respectively. Naturally, if a higher RPO
accuracy, denoted by ς, of the algorithm is targeted,
a larger K
iter
is required. Table 1 shows the average
WINSYS 2022 - 19th International Conference on Wireless Networks and Mobile Systems
30

0 2 4 6 8 10
Number of iterations, k
8
10
12
14
16
18
20
22
Objective Function of Stage 1, (Mbit/s)
-40
-35
-30
-25
-20
-15
-10
-5
Objective Function of Stage 2,
RPO, Stage 1
RPO, Stage 2
Figure 4: The convergence of the RPO algorithm with K
max
= 10.
value of K
iter
required for achieving a given RPO ac-
curacy. In addition, recall that the objective functions
of Stage 1 and Stage 2 in RPO are
˜
R in (28) and
˜
U
n
in (26), respectively. Figure 4 shows that both of them
become saturated after only a few iterations, indicat-
ing a good convergence of the RPO algorithm.
Table 1: The average number of SCA iterations required for
achieving a given target RPO accuracy.
ς 10
−1
10
−2
10
−3
K
iter
Stage 1 3.6560 4.7625 8.6073
(average) Stage 2 2.5866 4.4713 7.7300
6 CONCLUSIONS
In this paper, an IaS-U2U communication mechanism
is proposed for the OOC scenario, where a joint op-
timization problem is formulated by taking into ac-
count the STR and the PP. After decomposing the
problem to the UAV pairing and the RPO processes,
we devise a new two-stage algorithm to solve it. Sim-
ulations show that good EE gains can be achieved
over selected benchmarker schemes under various
conditions. Our future research will extend this work
to the scenario with multiple swarms.
ACKNOWLEDGEMENTS
This work was supported by the Key-Area Research
and Development Program of Guangdong Province
under Grant 2019B010157002.
REFERENCES
3GPP (2017). 3rd generation partnership project; technical
specification group radio access network; study on en-
hanced LTE support for aerial vehicles; (release 15).
TR 36.777 V15.0.0.
3GPP (2019). 3rd generation partnership project; techni-
cal specification group service and system aspects; en-
hancement for unmanned aerial vehicles; stage 1 (re-
lease 17). TR 22.829 V17.1.0.
3GPP (2020). 3rd generation partnership project; techni-
cal specification group core network and terminals;
proximity-services (ProSe) user equipment (UE) to
ProSe; stage 3 (release 16). TS 24.334 V16.0.0.
Ahmed, S., Chowdhury, M. Z., and Jang, Y. M. (2020).
Energy-efficient UAV-to-user scheduling to maximize
throughput in wireless networks. IEEE Access,
8:21215–21225.
Chen, Q. (2020). Joint position and resource optimization
for multi-UAV-aided relaying systems. IEEE Access,
8:10403–10415.
Chi, C. Y., Li, W. C., and Lin, C. H. (2017). Convex Opti-
mization for Signal Processing and Communications.
CRC Press.
Du, B., Xue, R., Zhao, L., and Leung, V. C. (2020). Coali-
tional graph game for air-to-air and air-to-ground cog-
nitive spectrum sharing. IEEE Trans. Aerosp. Elec-
tron. Syst., 56(4):2959–2977.
Gusfield, D. and Irving, R. W. (1989). The Stable Marriage
Problem: Structure and Algorithm. MIT Press.
Hong, L., Guo, H., Liu, J., and Zhang, Y. (2020). To-
ward swarm coordination: topology-aware inter-UAV
routing optimization. IEEE Trans. Veh. Technol.,
69(9):10177–10187.
Liu, A. and Lau, V. K. N. (2019). Optimization of
multi-UAV-aided wireless networking over a ray-
Position Optimization for Swarm-based UAV-to-UAV Communication Systems
31

tracing channel model. IEEE Trans. Wirel. Commun.,
18(9):4518–4530.
Nesterov, Y. and Nemirovskii, A. (1994). Interior-
point Polynomial Algorithms in Convex Programming.
SIAM, Philadelphia, PA, USA.
Niwattanakul, S., Singthongchai, J., Naenudorn, E., and
Wanapu, S. (2013). Using of Jaccard coefficient for
keywords similarity. In Proc. Int. Multi Conf. Eng.
Comput. Sci., volume I, pages 380–384.
Ranjha, A. and Kaddoum, G. (2020). Quasi-optimization
of distance and blocklength in URLLC aided multi-
hop UAV relay links. IEEE Wirel. Commun. Lett.,
9(3):306–310.
Wang, H., Wang, J., Ding, G., Chen, J., and Yang, J.
(2020). Completion time minimization for turn-
ing angle-constrained UAV-to-UAV communications.
IEEE Trans. Veh. Technol., 69(4):4569–4574.
Ye, H.-T., Kang, X., Joung, J., and Liang, Y.-C. (2021). Op-
timization for wireless-powered IoT networks enabled
by an energy-limited UAV under practical energy con-
sumption model. IEEE Internet Things J., 10(3):567–
571.
Zeng, Y., Xu, J., and Zhang, R. (2019). Energy minimiza-
tion for wireless communication with rotary-wing
UAV. IEEE Trans. Wirel. Commun., 18(4):2329–
2345.
Zhang, S., Zhang, H., Di, B., and Song, L. (2019). Cellular
UAV-to-X communications: design and optimization
for multi-UAV networks. IEEE Trans. Wirel. Com-
mun., 18(2):1346–1359.
Zhu, X., Liang, Y., and Yan, M. (2019). A flexible colli-
sion avoidance strategy for the formation of multiple
unmanned aerial vehicles. IEEE Access, 7:140743–
140754.
WINSYS 2022 - 19th International Conference on Wireless Networks and Mobile Systems
32