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Age of Information Based URLLC Transmission for UAVs on Pylon Turn

Article in IEEE Transactions on Vehicular Technology · January 2024

DOI: 10.1109/TVT.2024.3358844

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 1

Age of Information Based URLLC Transmission for

UAVs on Pylon Turn
Jiaxing Wang, Member, IEEE, Lin Bai, Senior Member, IEEE, Zhengru Fang, Student Member, IEEE,
Rui Han, Member, IEEE, Jingjing Wang, Senior Member, IEEE, and Jinho Choi, Fellow, IEEE

Abstract—Unlike center users, edge users are unable to achieve URLLC, including data timeliness and energy efficiency [1].
reliable data transmission due to severe path loss, and the Moreover, edge users may not be supported with URLLC
resulting frequent retransmissions not only bring additional due to the poor link quality and quality of service (QoS).
energy consumption but also lead to unacceptable latency. To
achieve the performance requirements of ultra-reliable low la- To narrow the performance gap between 5G URLLC and
tency communication (URLLC), we propose an unmanned aerial the various KPI requirements of the next generation URLLC
vehicle (UAV)-aided URLLC scheme for the edge users, in which (xURLLC), it is essential to thoroughly investigate additional
the age of information (AoI) is utilized as the indicator of system design methodologies and innovative technologies.
latency. Inspired by the pylon turn of gunboat aircraft, the same Because of the limited transmission power and severe non-
flight pattern is used at the fixed-wing UAV in the proposed
scenario. To reduce the AoI of edge users, we optimize the line-of-sight (NLoS) channel fading, the reliability and latency
hovering radius of the UAV while considering its aerodynamic performance of edge users cannot be guaranteed to meet the
model. In addition, to reduce the complexity of solving, we requirements of time-sensitive tasks [2]. In order to realize the
simplify the original AoI minimization problem and derive its timely update at the edge of the cell under the constraint of re-
closed-form result as a suboptimal solution. Simulation results liability, several technologies have been proposed to optimize
show that our proposed UAV-aided URLLC scheme is beneficial
as its average AoI is lower than those of the fixed radius the age of information (AoI), which serves as an innovative
schemes, and the near-optimal AoI performance is achieved by metric to evaluate the timeliness of received data [3]. Mean-
the proposed low complexity method. while, a high-altitude platform, particularly the unmanned
Index Terms—UAV communications, ultra-reliable low latency aerial vehicle (UAV) enhanced communication networks has
communication (URLLC), pylon turn, edge users, age of infor- been widely recognized for their dynamic deployment advan-
mation (AoI). tages. Exploiting a UAV as a transmission relay potentially
improves reliability and data timeliness, especially for edge
I. I NTRODUCTION users in the wireless communication network [4]. Besides,
there are several types of analytical methodologies to derive
A. Motivations
the closed-form of system AoI, including the classic graphical

I N the context of beyond 5G (B5G) and the 6th genera-

tion (6G) mobile communication, ultra-reliable low latency
communication (URLLC) is considered to be one of the key
method and the stochastic hybrid systems (SHSs) method. To
mitigate the computational complexity, the graphical method
would be the better choice for a UAV-aided data collection
enablers. Researchers and engineers focused on B5G and 6G system.
have made great efforts to meet the demands of URLLC, while The Third Generation Partnership Project (3GPP) proposed
5G-based URLLC did not fully achieve the desired targets, fundamental guidance for keeping a reliable connection be-
especially for data timeliness and excessive dissipation. In tween UAVs and existing ground-based users. In the proposed
order to deliver satisfactory services to these applications, 6G protocols of 3GPP, several basic parameters of the UAV
communication systems must meet additional requirements communication networks are given, including the traditional
for certain key performance indicators (KPIs) along with height and speed. Moreover, the communication links of UAV-
This work was partly supported by the National Natural Science Foundation aided networks are categorized as control link (CL) and data
of China under Grant No. U22B2008 and No. 62222101, partly supported link (DL). Although CL only has a relatively small network
by Aeronautical Science Foundation of China (ASFC) under Grant No. capacity (the data rate is about 60-100 kbps), it is designed
2022Z071051013, partly supported by the Beijing Natural Science Foundation
under Grant No. L232043 and No. L222039, and partly supported by the for command transmission and data updates under the rigorous
Fundamental Research Funds for the Central Universities. (Corresponding constraints of reliability and timeliness. DL is utilized for the
author: Jingjing Wang) transmission of media data between UAVs and a base station
Jiaxing Wang, Lin Bai and Jingjing Wang are with the School of
Cyber Science and Technology, Beihang University, Beijing 100191, (BS) with a data rate of up to 50 Mbps. Therefore, UAV-aided
China. Lin Bai is also with Beijing Laboratory for General Avia- networks need to satisfy the demands of highly reliable and
tion Technology, Beihang University, Beijing 100191, China (e-mail: low latency, i.e., providing a URLLC service is essential [5].
{wang jx, l.bai, drwangjj}@buaa.edu.cn).
Zhengru Fang is with the Department of Computer Science, City University Additionally, the mobility of UAV has not been adequately
of Hong Kong, China (e-mail: zhefang4@my.cityu.edu.hk). considered. Especially for fixed-wing UAVs, because they
Rui Han is with the Tsinghua Space Center, Tsinghua University, Beijing cannot hover at a fixed point, the service to ground users is
100084, China (email: ruihan@mail.tsinghua.edu.cn).
Jinho Choi is with the School of Information Technology, Deakin Univer- intermittent when the cell range is large. In some scenarios,
sity, Geelong, VIC 3220, Australia (e-mail: jinho.choi@deakin.edu.au). such as the Internet of Things (IoT), the Internet of Vehicle
 2

and machine type communication (MTC), ground-based users latency performance for the uplink transmission [15]. Finally,
are designed to update status intermittently, and they need to Ren et al. considered the 3-D air-to-ground channel model of
be collected and processed when the UAV flies over. Those UAV when transmitting the control information with URLLC
scenarios are suitable for the fixed-wing UAV, which can in [16].
provide low energy consumption and long sailing service [6]. 2) AoI-oriented performance analysis: Since traditional
Besides, although flight energy consumption and flight end-to-end latency cannot accurately reflect the freshness of
aerodynamics are ignored in most of the existing works for information at the monitoring [17], the concept of AoI was
simplicity, they are critical for fixed-wing UAVs. In the classic proposed and received a wide range of attention [18], [19].
cruise scheme of fixed-wing UAVs, pylon turn is a common AoI responds to the freshness of the user’s information, which
way. Pylon turn is a maneuver that the UAV flies in a circle is critical, especially for situational information. Its value can
at a certain height, with its inner wing pointing to the target be interpreted as the age of the user’s posture information.
on the ground, which was first applied in the AC-47D1 for The average AoI with different queue models was analyzed
combat use. Compared with a dive bomber, which has only in [20]–[23], including M/M/1, D/G/1, G/G/1 and so on. In
one chance to attack after entering the attack path, pylon turn addition, the peak AoI of different systems was studied in
provides continuous firepower output towards the target. In [24]–[26]. In [24], the peak AoI was analyzed with service
addition, the strike accuracy of pylon turn is high enough and preemptions and request delay. In [25], the formulation of
causes no loss of target during the attack. Motivated by this, peak AoI for edge computing in IoT networks with different
we use a similar method to build a stable data link between queue models was derived by Chiariotti et al. In addition,
the fixed-wing UAV and ground BS without frequent beam the optimal update rate for IoT devices was obtained by Hu
switching, which guarantees high-capacity backhaul links. et al. under the constraints of AoI and Peak AoI [26]. On
this basis, the AoI of a system with multiple sources was
B. Related works derived by Yates et al. in [27] and the AoI in an energy
harvesting system with different multiple access methods was
In this subsection, we review the previous studies about
studied by Fang et al. in [28]. Recently, the AoI performance
UAV-aided communication networks, with an emphasis on
of the UAV-aided communication networks has attracted a lot
URLLC services, the AoI-oriented system analysis, and the
of attention. In [29], [30], Han and Feng et al. analyzed the AoI
UAV flight strategy analysis.
performance of the IoT networks in terms of the computing
1) URLLC of users: As a key technology for B5G and
resources and deployment of UAVs. In [31], a URLLC-enabled
6G, URLLC has been widely studied in the literature. In
system was introduced by Basnayaka et al., in which the UAV
[7], Yue et al. summarized some related cases, challenges
was deployed as a relay and the system AoI and decoding error
and approaches of URLLC in cellular networks. In [8], the
were analyzed by the SHSs method. In addition, the multiple
tail, risk, and scale of URLLC for 5G wireless networks and
UAVs deployment and scheduling problem was studied in [32],
beyond were studied. Specifically, Xu et al. and Bahbahani
in which the UAVs were introduced as relays to realize massive
et al. analyzed the key techniques of physical and medium
URLLC. Besides, Liu et al. presented a data collection scheme
access control (MAC) layers for URLLC in [9] and [10],
with UAV for the wireless sensor networks, in which the AoI
respectively. To further enhance the data transmission relia-
of sensors was optimized [33].
bility and obtain lower latency, a UAV is utilized in some
3) UAV flight strategy analysis: Although UAVs can en-
wireless communication systems to support URLLC services
hance the performance of traditional wireless communication
[11]–[16]. In [11], Ranjha et al. proposed an IoT scheme in
networks, their flight characteristics also bring new challenges.
which the UAV and reconfigurable intelligent surface (RIS)
Due to the limited energy, the trajectory of UAV needs to
were used for short URLLC command packet transmission.
be optimized, which has been considered in [34]–[36]. In
The passive beamforming of RIS antenna was performed and
addition, to achieve more accurate theoretical results, Al-
the optimal position of the UAV was analyzed to improve the
Hourani et al. analyzed the air-to-ground channel and proposed
system decoding error rate. In [12], a UAV-assisted URLLC
the hybrid channel model in [37]. In [38], the capacity of
service system was introduced by Ranjha et al., in which the
aeronautical channels of different flight phases was analyzed.
joint power control and resource allocation problems were
In [39], Zhang analyzed the coverage capability of fixed-wing
analyzed to reduce the energy consumption of IoT devices.
UAVs in different scenarios in 5G and beyond. In addition,
In addition, Ranjha et al. envisioned the application of UAV-
a cooperative transmission model with multiple UAVs was
assisted URLLC systems for future agriculture in [13]. In
proposed in [40], in which the millimeter wave backhaul
[14], a multi-UAV relay scheme was analyzed by Xi et al.,
was used to increase the spatial throughput effectively. At
in which the resource allocation problem for enhanced mobile
the same, the coverage optimization problem with multiple
broadband downlink and URLLC uplink information delivery
rotary-wing UAVs was solved by Li et al. in [41]. In [42], an
were analyzed and solved. Besides, a UAV relaying URLLC
energy efficiency optimization scheme for the solar-powered
system considering both downlink and uplink performance was
UAV-aided communication network was proposed by Song
proposed by Cai et al., in which the achievable rate of the
et al., in which the flight radius and speed of UAV were
uplink was optimized with the constraint of reliability and
taken into account as the constraints of optimization problems.
1 AC-47D is one of a series of fixed-wing gunships developed by the United Furthermore, Zeng et al. also considered the relationship
States Air Force. between the energy consumption of a fixed-wing UAV for
 3

TABLE I
C ONTRASTING O UR C ONTRIBUTION TO THE R EFERENCE

[11] [16] [18] [27] [29] [30] [31] [32] [33] [40] [42] [43] Proposed work
AoI optimization ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
URLLC service ✓ ✓ ✓ ✓ ✓
UAV-aided communication ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Dynamic service ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
Queueing system ✓ ✓ ✓ ✓ ✓ ✓ ✓
UAV aerodynamic model ✓ ✓ ✓
Pylon turn ✓ ✓ ✓

flight and its speed and trajectory radius when the trajectory
Decoding successfully
optimization problem was formulated and solved in [43]. 𝜇 …
UAV with server
However, most of the existing research focused only on the Decoding error
Edge user
relationship between power consumption, flight radius and Air-to-ground link
flight speed, but no further consideration is given to the more 𝒓𝒃
Backhaul link
accurate aerodynamic model of the UAV. 𝒉
Unlike the previous works, since the pylon turn pattern
is adopted, we take more precise consideration of the aero- BS
dynamic model of fixed-wing UAVs. In the meanwhile, we Packet 𝑹𝟏
𝑹𝟐
have comprehensively considered the relationship among UAV
flight aerodynamics, data transmission reliability and the av-
erage AoI of the ground users.
Fig. 1. System model of the proposed UAV-aided communication network.

C. Contributions
A summary of the contributions of this paper is given below: proposed URLLC scheme and AoI optimization method are
1) A UAV-aided URLLC scheme with pylon turn pattern is investigated in Section V. Finally, the article is concluded in
proposed for the edge users, in which the reliability of Section VI.
the transmission, the average AoI, and the aerodynamic
model of UAV are jointly analyzed. To the best of the II. S YSTEM M ODEL
authors’ knowledge, this is the first paper that employs In this paper, a UAV-aided communication system is con-
pylon turn for UAV-aided communication networks with sidered as as shown in Fig. 1, in which the users located
consideration of the aerodynamic model for the URLLC within a cell are served by the BS at the center of the cell.
performance analysis. However, due to the path loss and limited transmit power, the
2) In order to achieve the optimal average AoI, the origi- QoS requirements of the users at the cell edge may not be
nal complex optimization problem is simplified and its guaranteed. It is assumed that the cell edge is modeled as a
closed-form solution is obtained as a suboptimal solution ring with inside radius R2 and outer radius R1 . There are K
of the original problem. users located within the ring uniformly and the kth user is
3) The simulation results indicate that the proposed scheme denoted by uk with k ∈ {1, 2, . . . , K}. The coordinates of uk
and optimization method are effective in improving is given by pu,k = (rk , θk , 0) according to polar coordinate
the performance of URLLC. It is shown that our system.
proposed UAV-aided URLLC scheme is beneficial in In order to meet the demands of edge users, a fixed-
terms of achieving lower average AoI than the fixed wing UAV is deployed as an edge computing center above
radius schemes, and the near-optimal AoI performance the edge of the cell with altitude h. The UAV collects and
is achieved by the proposed method with lower compu- processes packets from edge users, and then sends back the
tational complexity. processed information to the BS. Because the fixed-wing
Table I provides a clear and conspicuous comparison between UAV is unable to hover at a fixed point, the service of edge
our novel contributions and the existing literature. computing is dynamic, i.e., the UAV serves different users
around the trajectory with a time division scheme. To achieve
the tasks of omnidirectional data collection and large-capacity
D. Organization backhaul, an omnidirectional antenna and a directional antenna
The rest of this article is structured as follows. In Section are equipped on the UAV as the receive antenna and transmit
II, we introduce the system model of the proposed UAV- antenna, respectively. Motivated by the pylon turn pattern for
aided URLLC scheme for edges. Then, the reliability of combat use, the UAV can fly in a circle with a bank angle and
the transmission, the average AoI of the system, and the keep the directional antenna pointing to the BS while hovering
aerodynamic model of the UAV are jointly analyzed in Section to collect data without frequent beam switch. In this pattern,
III. The optimal problem of average AoI is introduced and the UAV can send back the information of edge users with a
solved in Section IV. Moreover, the simulation results of the continuous and stable backhaul. In addition, we assume that
 4

the center users are sufficiently close to the BS that they can Hence, the received signal-to-noise ratio (SNR) of uk at
complete the data transmission on their own. time t can be expressed as
It is assumed that the hovering radius of the UAV is rb ,
Pk gk2 (t)
and the hovering cycle is T . Denote by pb = (rb , θb , h) the ζk (t) = , (8)
coordinate of UAV in polar coordinate system. Edge user uk σ2
generates an update packet and transmits it to the UAV when where Pk is the transmission power of uk and σ 2 denotes the
the UAV reaches directly above it, i.e., the azimuth angles of power of additive Gaussian white noise at the UAV. Besides,
uk and UAV are the same (θk = θb ). Then, the UAV processes it is assumed that all users have the same transmit power, i.e.,
each update packet collected from the users one by one and Pk = P for all k ∈ {1, 2, . . . , K}.
sends it back to the BS when the signal processing is finished It is evident that the flight parameters of the UAV play a
on time. crucial role in deploying URLLC service, especially hovering
When the UAV appears directly above edge user uk , the radius rb . With a larger rb , the UAV is closer to the edge
distance between them can be expressed as users and obtains a greater probability of LoS channels, which
q also reduces path loss during data transmission. Thus, a large
2
dk = h2 + (rk − rb ) . (1) hovering radius can enhance the reliability of edge users.
In this paper, we consider the probabilistic line-of-sight (LoS) However, limited by the flight characteristics of UAV, the flight
channels between edge users and UAV as in [37]. The proba- cycle T of UAV becomes larger as rb increases. As a result, the
bility of LoS channel is given by status of edge users is updated less frequently. Therefore, the
hovering radius of the UAV needs to be reasonably optimized
1 to achieve the reliability and low latency of transmission.
pLoS
k = , (2)
1 + α exp(−β(γk − α))
where α and β are the coefficients related to the transmission III. P ROBLEM F ORMULATION
environment and γk is the elevation angle between uk and
UAV, which can be obtained as In this section, we analyze several key properties including
  the reliability of transmission, the aerodynamic model con-
h straints of UAV and the time latency of edge users. Since these
γk = arctan . (3)
|rk − rb | properties affect each other, we need to clarify the relationships
Here, |x| denotes the absolute value of x. The probability of and achieve a holistic optimization of the system. In particular,
NLoS channels can be given by because the traditional end-to-end latency does not accurately
reflect the status freshness of edge users, we incorporate AoI
pNLoS
k = 1 − pLoS
k . (4) as a metric of the latency performance in the URLLC scheme.
Then, the path loss model of air-to-ground link between UAV
and uk at time t can be formulated as A. Probability of decoding error
gk (t) = ak hk (t), (5) In this system, the wireless channel gk (t) is time-varying
and it is strongly influenced by the probability of LoS channel.
where ak is the large scale path loss and hk (t) represents the
Therefore, we take the average in the time domain to simplify
small scale fading of the air-to-ground channel. Specifically,
the theoretical analysis. According to Eq. (5), we can obtain
the large scale path loss can be expressed as
(√ P
Et a2k h2k (t)
 
λ0 dξkL , LoS, Et [ζk (t)] =
ak = √ ξN (6) σ2
ηλ0 dk , NLoS, P a2 
= 2k E h2k (t) ,

(9)
where λ0 is the path-loss for wireless channels at the reference σ
distance, which is usually set to 1 meter and η is the additional where E[X] denotes the expectation of random variable X.
path-loss coefficient of NLoS situation. In addition, ξL and ξN Substituting Eq. (7) into Eq. (9), we can have
correspond to the channel coefficients for the two different  r
r !2 
cases of LoS and NLoS.  2  K 0 1
Besides, the small scale fading can be modeled as the Rician E hk,LoS = E  ĥk (t) + h̃k (t) 
1 + K0 1 + K0
and Rayleigh channel models for LoS and NLoS, respectively.
Thus, at time t, the small scale fading of uk can be expressed K0 h i 1 h i
= E ĥ2k (t) + E h̃2k (t)
as 1 + K0 1 + K0
(q
K0
q
1 = 1, (10)
1+K0 ĥk (t) + 1+K0 h̃k (t), LoS,
hk (t) = (7)
h̃k (t), NLoS, and h i
E h2k,NLoS = E h̃2k (t) = 1.
 
(11)
where K0 is the Rician factor, |ĥk (t)| = 1 is a complex
number which indicates the LoS propagation environments According to Eqs. (9)-(11), we can obtain the average SNR
and h̃k (t) ∼ CN (0, 1) indicates the NLoS propagation en- P a2k
vironments. ζ̄k = Et [ζk (t)] = . (12)
σ2
 5

Since the update packets of the users are predetermined in

the form of short messages, the short packet channel coding x-z plane
scheme can be employed for the purpose of reliable commu- 𝐿 𝐿 cos 𝜙
nication in this paper. Hence, finite block length information
theory is suitable for analyzing the decoding error probability Centripetal 𝜙 Fuselage line
at the UAV. Suppose that each update packet contains l bits and acceleration
is encoded to a block of n bits. Then, the average probability
of decoding error for uk can be formulated as 𝐿 sin 𝜙
   𝑉
 

nlog2 1 + ζ̄k − l

𝑊
  
εk = E Q  s 
 
   ,
 (13)
2
n (log22 e) 1 − 1
  
2
( k)
1+ ζ̄ x-y plane
𝑉
R∞ 2
− t2
where Q(x) = √12π x e dt is the Q-function. In Eq. (13), 𝐷 𝐹
the expectation is carried out over random variable ζ̄k , which Centripetal acceleration
has two cases: LoS and NLoS. Therefore, εk can be expressed
as
    Fig. 2. Force analysis of UAV with pylon turn pattern.

X nlog2 1 + ζ̄kc − l
  
   c
εk = Q  s 
 
   pk ,
  set to 0 in the pylon turn mode. Therefore, the force analysis
c 2 of the UAV system is as follows:
n (log22 e) 1 − 1
   
c 2
( k)
1+ ζ̄
(14) L cos ϕ = W, (18)
where c ∈ {LoS, NLoS} and L sin ϕ = ma, (19)
 F = D, (20)
 P λ0 dk2ξL , c = LoS,
c σ2
ζ̄k = 2ξN (15) where a and m are the centripetal acceleration and weight of
ηP λ d
0 k

σ2 , c = NLoS. UAV, respectively. According to the law of uniform circular
motion, the centripetal acceleration of UAV is

B. UAV energy consumption model V2

a= . (21)
rb
Due to limited energy, the hovering radius and speed of
UAV have to be set reasonably, which are closely related to its Lemma 1. The flight energy consumption required for pylon
aerodynamic conditions. Unlike rotary-wing UAVs, fixed-wing turn can be expressed as
UAVs need to meet more complex aerodynamic conditions in  34
4m2 g 2 rb2

flight, especially at the pylon turn mode [44]. As shown in 1
Pf = F V = CD ρA . (22)
Fig. 2, the UAV undertakes two sets of balancing forces when 2 CL2 ρ2 A2 rb2 − 4m2
it performs pylon turn: weight (W) and lift (L) in the vertical Proof. Combining Eq. (18) and Eq. (19), we can have
plane, as well as drag (D) and thrust (F) in the horizontal
plane. In this paper, it is assumed that the attack angle of the m2 V 2
L2 = m 2 g 2 + , (23)
UAV is constant. Therefore, the magnitude of drag and lift, rb4
respectively, can be expressed as
where g is the Gravitational acceleration. Substituting Eq. (23)
1 into Eq. (17), we obtain
D = CD ρAV 2 , (16)
2 1 2 2 2 4 m2 V 4
1 CL ρ A V = m2 g 2 + . (24)
L = CL ρAV 2 , (17) 4 rb2
2
The solution of Eq. (24) is
where CD and CL are the force coefficients of drag and thrust,
respectively, A is the wing area, ρ is the density of air, and V
s
4m2 g 2 rb2
is the linear velocity of UAV. V2 = , (25)
CL2 ρ2 A2 rb2 − 4m2
When the UAV uses pylon turn for attack runs, the vertical
component of the lift balances the weight and the horizontal and the speed of V can be expressed as
component provides the centripetal forces. In the direction s
of the UAV’s motion, the thrust overcomes drags to provide 4m2 g 2 r2
V = 4 2 2 2 2 b . (26)
acceleration in the instantaneous velocity direction, which is CL ρ A rb − 4m2
 6

Packet Send to Processed by Packet Send to Processed by ∆ 𝒕

generation the UAV the UAV generation the UAV the UAV

𝒕
Traditional
end-to-end latency Current
moment
Age of information

𝑄 𝑄 ,
𝑄 , 𝑄 , 𝑄 ,
,
∆ 0
Fig. 3. Relationship between traditional end-to-end latency and AoI.
𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝑢 , 𝒕
𝑈 , 𝑈 , 𝑈 , 𝑈 ,

Substituting Eq. (25) into Eq. (16), we can have 𝑉 , 𝑉 , 𝑉 , 𝑉 ,

s
1 4m2 g 2 rb2 Fig. 4. The AoI of uk without decoding error.
F = D = CD ρA . (27)
2 CL ρ2 A2 rb2 − 4m2
2

Then, according to Eq. (26) and Eq. (27), we can obtain Eq. the queue time contains waiting time and service time. It can
(22), which completes the proof. be seen from Fig. 4 that the AoI ∆k (t) grows linearly with
In practice, the flight energy of UAV cannot exceed its t when the newest packet is not processed and becomes the
maximum value, i.e., age of the last packet t − uk,I (t) when the newest packet is
processed.
Pf ≤ Pfmax . (28) Then, during the observation time window τ , the average
In addition, the period T (the time required for flying one lap) AoI of uk becomes
of UAV for pylon turn can be expressed as 1 τ
Z
< ∆k >τ = ∆k (t) dt. (31)
2πrb τ 0
T = r . (29)
4 4m2 g 2 rb2 It is assumed that the random process ∆k (t) is ergodic. In
2 ρ2 A2 r 2 −4m2
CL b practice, we usually make τ = u′k,I and set the observation
window length to infinity to obtain the average system AoI as
C. Age of information follows:
Z τ
Traditional URLLC can reflect the end-to-end latency while
∆¯ k = lim < ∆k >τ = lim 1 ∆k (t) dt. (32)
not providing a reasonable measure of the state update interval τ →∞ τ →∞ τ 0
at the terminals. It is an important indicator in some scenarios,
such as the IoT, IoV and wireless sensor networks. AoI not According to Fig. 4, the integral in Eq. (31) can be ob-
only accurately reflects the waiting and service time at the tained by accumulating the area of irregular shape Q̃k,1 and
server, but also takes the frequency of data generation into ac- trapezoids {Qk,2 , Qk,3 , . . . , Qk,I }, i.e.,
count. The relationship between traditional end-to-end latency 1 XI
and AoI is shown in Fig. 3. It can be seen that traditional end- < ∆ >τ = (Q̃k,1 + Qk,i )
τ i=2
to-end latency only measures the time between data generated PI
Q̃k,1 I − 1 i=2 Qk,i
by the source and processed by the receiver. The AoI will = + . (33)
τ τ I −1
continue to grow until the next packet is successfully processed
by the receiver. Thus, it accurately reflects the freshness of The area of trapezoid Qk,i can be obtained by subtracting the
the information and is suitable for measuring the URLLC area of isosceles triangle with waist length Vk,i from the area
performance in the scenarios considered in this paper. of another isosceles triangle with waist length Uk,i + Vk,i , i.e.,
To facilitate understanding of the definition of AoI, first 1 1 2
consider a scenario in which all packets can be decoded Qk,i = (Uk,i + Vk,i )2 − Vk,i , i ∈ {2, 3, . . . , I} , (34)
2 2
correctly at the UAV. As shown in Fig. 4, at time t, the AoI In this paper, the decoding error at the UAV is considered,
∆k (t) of uk can be expressed as the following random process: i.e., some packets cannot be decoded successfully and the
∆k (t) = t − uk,I (t), (30) AoI cannot renew after signal processing. For example, as
shown in Fig. 5 the update packet generated at time uk,3 is
where uk,I (t) is the generation time of the latest processed not successfully decoded at time u′k,3 . Then, the AoI ∆k (t)
packet at the receiver, which is denoted by the blue point increases linearly with time until the packet generated at uk,4
in Fig. 4. I is the index of this packet. In addition, the is decoding successfully at time u′k,4 . Denote by Ûk,i the time
timestamp when this packet has been processed is u′k,I (t), interval between the generation time of the (i−1)th and the ith
which is denoted by the green point. In Fig. 4, the generation packets that are decoded successfully. The corresponding time
time interval between the (i − 1)th and the ith packets is interval contains the sum of time intervals of several original
denoted by Uk,i . The queue time of the ith packet is denoted packet generation, i.e.,
by Vk,i , which can be seen as the time gap between the packet
(1) (2) (S )
generation time uk,i and the precessed time u′k,i . In general, Ûk,i = Ûk,i + Ûk,i + · · · + Ûk,ii , (35)
 7

∆𝒌 (𝒕) Lemma 2. With the average decoding error probability εk ,

we can obtain E[S] and E[S 2 ] as follows:
𝑄෠𝑘,3
𝑄෠ 𝑘,𝐼መ 1
𝑄෠𝑘,2 E[S] = , (42)
1 − εk
1 + εk
E[S 2 ] = . (43)
(1 − εk )2
𝑄෨ 𝑘,1 𝑄𝑘,2 𝑄𝑘,2 𝑄𝑘,4 𝑄𝑘,𝐼
∆𝑘 (0) Proof. After successful decoding, the probability that (i − 1)
′
𝑢𝑘,1 𝑢𝑘,1 𝑢𝑘,2 ′
𝑢𝑘,2 𝑢𝑘,3 ′
𝑢𝑘,3 ′
𝑢𝑘,4 𝑢𝑘,4 𝑢𝑘,𝐼 ′
𝑢𝑘,𝐼 𝒕 consecutive decoding errors occur and the ith packet is decod-
𝑈𝑘,2 𝑈𝑘,3 𝑈𝑘,4 𝑈𝑘,𝐼 ing successfully can be expressed as
𝑉𝑘,1 𝑉𝑘,2 𝑉𝑘,3 𝑉𝑘,4
p(S = i) = εki−1 (1 − εk ), i = 1, 2, 3, . . . . (44)
෡𝑘,2
𝑈 ෡𝑘,3
𝑈 ෡𝑘,𝐼መ
𝑈
Then, the expectation E[S] can be calculated by
𝑉෠𝑘,1 𝑉෠𝑘,2 𝑉෠𝑘,𝐼መ
∞
X
Fig. 5. The AoI of uk with considering the decoding error. E[S] = (i · p(S = i))
i=1
X∞

where Si is the number of original packets generated during = iεki−1 (1 − εk )

i=1
the (i − 1)th and the ith successful packets. However, the first ∞
(Si − 1) packets are decoded with errors. Then, the area of
X
= (1 − εk ) iεi−1
k . (45)
isosceles triangle Q̂k,i with considering the decoding error can i=1
be calculated by
For the infinite series in Eq. (45), we can translate it into the
1
Si
1 2 following form:
(s)
X
Q̂k,i = ( Ûk,i + V̂k,i )2 − V̂k,i ∞ ∞
2 s=1 2 X X
′
iεki−1 = εik
PSi (s) 2
( s=1 Ûk,i ) XSi (s) i=1 i=1
= + V̂k,i Û . (36) ∞
!′
2 s=1 k,i X
= εik . (46)
Substituting Eq. (33) and Eq. (36) into Eq. (32), we can obtain i=1
PIˆk According to the properties of geometric progression, we can
Q̃k,1 Iˆk − 1 i=2 Q̂k,i
∆k = lim ( + ) have
τ →∞ τ τ Iˆk − 1 ∞
!′  ′
E[Q̂k ]
X
i εk (1 − εnk )
= , (37) εk = lim
i→∞ 1 − εk
E[Ûk ] i=1
1
where Iˆk is the index of the latest received packet from uk , = . (47)
(1 − εk )2
which is decoded successfully. In addition, according to Eq.
Then, substituting Eq. (47) into Eq. (45), we can get Eq. (42),
(35) and Eq. (36), we can calculate the expectation E[Ûk ] and
which completes the proof. The proof on Eq. (43) is similar
E[Q̂k ] as follows:
to that of Eq. (42), and we ignore it here.
E[Ûk ] = T E[S], (38) The average system time including waiting time and service
time can be approximated by the following lemma.
and
X    Lemma 3. The average system time of uk can be approxi-
1 Si (s) 2
XSi (s)
E[Q̂k ] = E ( Û ) +E V̂k,i Û . (39) mated by
2 s=1 k,i s=1 k,i h i 1
E V̂k ≈ , (48)
In Eq. (39), the expectations can be further simplified into the µ−λ
following form: where µ is the service rate of UAV and λ is the rate of arrival,
X  which can be calculated by
Si (s) 2
E ( Ûk,i ) = T 2 E[S 2 ], (40) K
s=1 λ= . (49)
T
and
 XSi  X 
(s) Si (s) Proof. As shown in Fig. 6, the queue at the UAV during a
E V̂k,i Ûk,i = E (Ûk,i · V̂k,i )
s=1 s=1 hovering cycle can be regarded as a single server queue, in
which the packet arrival interval is equal to the time interval for
h i
= T E [S] E V̂k . (41)
the UAV to fly from above one user to the next adjacent user.
 8

𝐾… 2 1 Served packets IV. O PTIMIZATION OF THE HOVERING RADIUS

Unserved packets
𝜇 In this paper, we aim to minimize the average AoI for all
Packet generation
K edge users with limited UAV flight energy consumption,
time of edge user
i.e.,
𝑉
K
𝜔1 𝜔2⋯ 𝜔𝑘−1 𝜔𝑘 ⋯ 𝜔𝐾 𝜔1 𝜔2⋯ 1 X
P1 : min ∆k (55)
𝑇
rb K
0 k=1
Uniformly distributed in 0 − 𝑇 s.t. 0 < rb ≤ R1 , (55a)
µ
Fig. 6. Data collection and queuing model of all the K edge users at the > 1, (55b)
UAV. λ
Pf ≤ Pfmax , (55c)

We take u1 as the starting reference point, i.e., θ1 = 0. Because where the objective is the average system AoI of all the cell
the edge users are uniformly distributed in a circle representing edge users, while the inequality constraint in (55a) gives the
the edge of the cell, the azimuth angles {θ2 , θ3 , . . . , θK } of maximum hovering radius of UAV. In addition, (55b) is the
remaining K − 1 users are uniformly distributed from 0 to constraint to ensure the stability of the queue and (55c) is the
2π. Then, the update packet generation time of the remaining constraint of maximum flight energy of UAV.
K −1 users is uniformly distributed from 0 to T in one period, Due to the error probability of the data transmission, the
i.e., the times of packets arrival at the queue {ω2 , ω3 , . . . , ωK } flight energy consumption of UAV, and the average AoI
follow that shall be considered simultaneously in optimization problem
ωk ∼ U (0, T ). (50) P1 , which makes it complex and hard to solve. Therefore
some simplifications and approximations below are necessary.
With the aim of determining the time interval between any Firstly, to facilitate the calculation of decoding error probabil-
two adjacent packets Ωk = ωk − ωk−1 , using the properties ity εk , we replace the original Q-function in Eq. (13) with a
of order statistics of uniform distribution [45], the probability linear approximation as [31]
density function (PDF) of Ωk can be found as 
1,
 ξ¯k ≤ ϕ,
√ ¯
K −1 x K−2 εk ≈ 2 − β n(ξk − φ), ϕ < ξ¯k < δ,
1
(56)
fΩk (x) = 1− . (51)
¯

T T 
0, ξk ≥ δ,
When K is large, the above distribution can be approximated l
where β = q1 , φ = 2 n − 1, ϕ = φ − 1√
, and
by an exponential distribution with parameter K
T , i.e., 2l 2β n
2π 2 n −1
1√
 
K δ = φ+ 2β n
. In order to guarantee the reliability of the
Ωk ∼ E . (52) transmission, we hope that the decoding error probability is
T
as close to 0 as possible. Therefore, the average SNR of uk
Then, the original queue can be approximated as an M/M/1 should satisfy ξ¯k > δ, which can be set as the constraint of
queue with arrival rate λ = K
T and service rate µ. Then, the
the optimization problem P1 . With this constraint, the average
system time can be approximated as Eq. (48). AoI of uk can be formulated by

Substituting Eqs. (38)-(43) and Eq. (48) into Eq. (37), we ˜k ≈ T +

∆
T
. (57)
can obtain the average AoI of uk as 2 Tµ − K

T (1 + εk ) T Then, we can solve the following optimization problem to

∆k ≈ + . (53) obtain the hovering radius of UAV:
2(1 − εk ) Tµ − K
Finally, the average AoI of all the cell edge users are T T
P2 : min + (58)
rb 2 Tµ − K
K
¯ = 1
X s.t. 0 < rb ≤ R1 , (58a)
∆ ∆k . (54) µ
K > 1, (58b)
k=1
λ
Based on the above analysis, we can see that AoI is related Pf ≤ Pfmax , (58c)
to several factors such as packet generation interval, UAV ξ¯k > δ, ∀k. (58d)
cruise period, and queue time. Since we ignore the time used
for signal transmission in space, the traditional latency is the The solution of the above optimization problem P2 can be
same as the queue time in this paper. A low AoI tends to obtained by solving the following equation:
indicate that the system also has a low latency, but if the packet  
generation interval is large, a low latency may not result in a d T2 + T µ−K
T

low AoI. = 0, (59)

drb
 9

and the solution is It means that the minimum radius should satisfy the constraints
s p of flight power consumption, queue stability, and decoding
m2 + m4 + 4C12 C3 error probability. In addition, the maximum radius should
r̂b = , (60)
2C12 satisfy the constraints of decoding error probability and cell
√
m2 g 2 ( 2K+K )
4 range. Otherwise, the optimal radius can be calculated by Eq.
where C1 = 21 CL ρA and C3 = (2πµ)4
. From (59).
constraint (58b), the hovering radius needs to satisfy It can be seen from Eq. (14) and Eq. (53) that due to the
presence of εk , it is difficult to find a closed-form solution in
s p
m2 + m4 + 4C12 C4
rb > υ1 = , (61) the form of optimization problem P1 . While the optimization
2C12 problem P2 makes a reasonable linear approximation to the
4 2 2
where C4 = K16πm4 µg4 . In addition, due to the limited flight Q-function in εk , eliminating the computational overhead of
energy, the constraint (58c) needs to be guaranteed, i.e., the Q-function. By turning the signal-to-noise ratio into a
s constraint, an approximate solution to the original problem is
m2 C5 derived. Therefore, compared with the original problem, the
rb ≥ υ2 = 2 (62) optimization solution process is significantly simplified.
C1 C5 − m2 g 2
 max  43
P
with C5 = Cf2 and C2 = 12 CD ρA. Finally, the constraint V. S IMULATION R ESULTS
(58d) can be considered in the following two cases:
The simulation results of the proposed UAV-aided URLLC
1) Case 1: Suppose that the probability of LoS channel is
scheme with pylon turn are presented in this section. The
very high. Then, the transmitted signal just needs to satisfy
parameters used for simulations are listed in Table II. In this
the SNR threshold δ after passing through the LoS channel,
section, the correctness of the theoretical analysis and the
i.e,
1 effectiveness of the hover radius optimization algorithm are
   ≥ 1 − p1 , (63) verified through various simulation scenarios. As shown in
1 + αexp −β arctan dhk − α Fig. 5, when a packet decoding error occurs, the AoI of users
P λ0 2ξL will not be updated promptly. In addition, it can be found from
d ≥ δ, (64) Eq. (43) that the AoI and the decoding error probability are
σ2 k
coupled to each other. Thus the simulation analysis of the AoI
where p1 is a constant greater than 0 but close to 0.
performance already reflects the decoding error probability
2) Case 2: Suppose that the probability of LoS channel is
of the system and we do not perform a separate simulation
not high enough. Then the transmitted signal needs to satisfy
analysis for decoding error probability in this section.
the SNR threshold δ after passing through the NLoS channel,
First, the average AoI of all the K edge users are shown in
i.e,
1 Fig. 7, where the results of theoretical analysis are obtained
1−    > p1 , (65) by Eq. (54). In the simulation, we set P = 0.1 W, K = 100,
1 + αexp −β arctan dhk − α
K0 = 5, l = 32 bits, n = 108 bits and µ = 0.2. It can be
P λ0 2ξN seen that the theoretical results are basically consistent with
ηdk ≥ δ. (66) the simulation results, especially when the flight altitude of
σ2
Let the solutions of Eq. (63), Eq. (64) and Eq. (66) be a1 , UAV is low and the hovering radius is close to the region of
a2 and a3 , respectively, when the equal sign holds. Then the edge users. The smallest gap between theoretical results and
feasibility interval of constraint (58d) can be given by simulation results are 6% and 19% for h = 200 m and h =
400 m, respectively. When the SNR is low, the results of the
max {rk − x̂k } < rb < min {rk + x̂k } , (67) theoretical analysis of the decoding error probability will have
where x̂k can be obtained by a large deviation from the actual results, because we take the
 small-scale fading as the expectation for the analysis. Hence,
a1 , a2 ≤ a1 ≤ a3 ,
 the gap between the results of theory analysis and simulation
x̂k = a2 , a1 < a2 ≤ a3 , (68) increases when h becomes larger. In addition, the reason for


a3 , a2 < a3 < a1 . the gap becoming large when rb is small is the same. This gap
will become smaller if we can have a more accurate analysis
Combining the constraints above, the hovering radius should of the decoding error probability of the channel, which will
satisfy be considered in the future.
rbmin < rb < rbmax , (69) In
 addition,
 due to the average small-scale fading coefficient
where rbmin = max {max {rk − x̂k } , υ1 , υ2 } and rbmax = Et h2k (t) is considered in the theoretical analysis, we show
min {min {rk + x̂k } , R1 }. Finally, we can obtain the optimal the simulation results where the small-scale fading coefficient
hovering radius of UAV as is equal to 1 for comparison in Fig. 7. We can find that the
 simulation results are more in agreement with the theoretical
min min
rb , r̂b ≤ rb ,
 analysis when the small-scale fading is ignored. Therefore, in
rb⋆ = r̂b , rbmin < r̂b < rbmax , (70) some scenarios where only large-scale fading is considered,

 max
rb , r̂b ≥ rbmax . our analysis will achieve better performance.
 10

TABLE II
3500
S UMMARY OF PARAMETERS USED IN SIMULATION Proposed method, h=200m
Comparison method, h=200m
Optimal, h=200m
3000
Parameter Value Proposed method, h=400m
Comparison method, h=400m
Optimal, h=400m
Radius of cell (R1 ) 2 km 2500

Average AoI (s)

1400
Radius of BS edge (R2 ) 1.5 km
2000 1200
Flight altitude of UAV (h) [50 m, 400 m] 1000

Weight of UAV (m) 200 kg 1500 800

0.12 0.13 0.14

Gravitational acceleration (g) 9.8 m/s2
1000

Wing area of UAV (A) 7 m2

500
Maximum flight energy of UAV (Pfmax ) 120 W 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
P (W)
Density of air (ρ) 1.225 kg/m3
Fig. 8. Average AoI versus transmission power of edge users.
Lift force coefficients (CL ) 1.2
Drag force coefficients (CD ) 0.07
Transmission power of users (P ) [0.02 W, 0.2 W] by the comparison method in Fig. 8. In addition, the optimal
Parameter of channel (α) 4.88 hovering radius of the UAV is obtained by an exhaustive
method, which is denoted as the optimal method in Fig. 8,
Parameter of channel (β) 0.429
and the AoI obtained at this radius is a lower bound for
Rician factor (K0 ) 5, 8 this optimal problem. In the simulation, we set K = 100,
Path-loss reference at 1 m (λ0 ) -40 dB K0 = 5, l = 32 bits, n = 108 bits and µ = 0.2. It can be
Excessive path-loss coefficient of NLoS (η) -10 dB seen from Fig. 8 that the proposed method can achieve the
lowest AoI than the other methods for comparison, and the
Path-loss exponents of LoS (ξL ) -1
proposed method has a maximum deviation from the optimal
Path-loss exponents of NLoS (ξN ) -1.5 scenario of approximately 2%. In addition, the performance of
Noise power (σ 2 ) -100 dB the proposed method decreases when the transmission power
is relatively small due to the theoretical analysis deviation of
Number of information (l) 16 bits, 32 bits
the decoding error probability at low SNR. Usually, to realize
Encoding length (n) [50 bits, 300 bits] URLLC, we have to ensure that the received SNR cannot
Number of cell edge users (K) [50, 500] be too low, thus also guaranteeing the effectiveness of our
Service rate of UAV (µ) [0.2, 2.2]
proposed method. When h = 400 m, we can find that as the
transmission power increases, the average AoI of the system
decreases because the probability of decoding errors decreases
accordingly. However, when the decoding error probability is
5000
Simulation result, h=200 m
low enough, the average AoI no longer varies significantly
Theoretical analysis result, h=200 m
4500
Simulation result, h=400 m
with the increase in transmission power.
Theoretical analysis result, h=400 m
4000 Simulation result, h=200 m (hk(t)=1) Fig. 9 shows the average AoI of the system at different
3500
Simulation result, h=400 m (hk(t)=1) flight altitudes of UAV. The effectiveness of our proposed
Average AoI (s)

1200
3000
algorithm at different altitudes of the UAV is demonstrated.
1100
In the simulation, we set K = 100, P = 0.1 W, l = 32 bits,
2500 1000
n = 108 bits, and µ = 0.2. We find that the system AoI
2000 900
decreases significantly as the UAV altitude increases from 50
1500 1660 1680 1700 to 100 meters. However, as the altitude of UAV continues
1000 to increase, the system AoI increases slowly. This is because
500
when the flight altitude of UAV is 50 m, the LoS channel
1300 1400 1500 1600 1700 1800 1900 2000
rb (m)
probability between the UAV and edge users becomes low.
Then, the path loss is severe and the decoding error probability
Fig. 7. Average AoI of the system with different hovering radius. is higher. The ground users do not deliver their status up to
date successfully while the UAV is flying over. Therefore, the
average AoI is large. However, when h continues to increase,
In Fig. 8, we show the average AoI of the edge users with the distance between the UAV and edge users increases rapidly,
different transmission power and flight altitude of UAV. In and the path loss becomes large even though the LoS channel
the simulation, we added two cases that UAV performs pylon probability is high. Hence, there is an optimal flight altitude
turn at fixed radius and optimal radius to compare with the of UAV for this system. In this simulation, the optimal h is
proposed scheme. Specifically, the UAV hovers with radius about 200 m. Besides, it can be seen that the channel with a
R2 + R1 −R2
2
as the fixed radius scheme, which is denoted larger Rician Factor can achieve a lower average AoI due to
 11

4000 5000
Proposed method, K0=5 Proposed method, K=100
Comparison method, K0=5 Comparison method, K=100
4500 Optimal, K=100
3500 Optimal, K0=5
Comparison method, K=500
Proposed method, K0=8 4000 Compared method, K=500
3000 Comparison method, K0=8 Optimal, K=500
Optimal, K0=8 3500
Average AoI (s)

Average AoI (s)

1100
2500
3000
1000 940
2000 2500
900 920

2000 900
1500 800

200 210 220 230 240 250 1500 880

1000 0.496 0.498 0.5 0.502 0.504
1000

500
50 100 150 200 250 300 350 400 500
0.2 0.3 0.4 0.5 0.6 0.7
h (m)

Fig. 9. Average AoI versus flight altitude of UAV. Fig. 11. Average AoI versus service rate of UAV.

970 1150
Proposed method, =0.2 Proposed method, l=16 bits
Comparison method, =0.2 Comparison method, l=16 bits
960 Optimal, =0.2 1100 Optimal, l=16 bits
Proposed method, =0.5 Comparison method, l=32 bits
950 Comparison method, =0.5 1050 Proposed method, l=32 bits
Optimal, =0.5 Optimal, l=32 bits

Average AoI (s)

940 1000
Average AoI (s)

930 950

920 900

910 850

800
900

750
890 50 100 150 200 250 300
n (bits)
880
50 100 150 200 250 300
K Fig. 12. Average AoI versus block length of updating packets.

Fig. 10. Average AoI versus number of the edge users.

increases to 0.7. Likewise, when K = 100, the average AoI
almost does not change with the increase of µ. The reason
the more reliable transmission performance. is the same as that in Fig. 10. When the service rate of the
The simulation results of average AoI with different num- UAV is large enough compared to the packet arrival rate, any
bers of edge users are shown in Fig. 10. In the simulation, further increase in the service rate does not affect the average
we set h = 200 m, P = 0.1 W, K0 = 5, l = 32 bits, and AoI of the system. In this system, the packet arrival rate is
n = 108 bits. It can be found that when µ = 0.2, the AoI proportional to the number of edge users.
increases as the number of users increases, especially when Fig. 12 shows the average AoI with different block lengths
K > 200. This is because a larger K means that packets will of updating packets. In the simulation, we set h = 200 m,
arrive at the queue more frequently. Then the average waiting P = 0.1 W, K0 = 5, K = 100, and µ = 0.2. It can be
time for every packet increases. In addition, when µ = 0.5, found from the simulation results that the average AoI can
the average AoI remains almost unchanged as the number of be improved by decreasing the original message length l or
users increases. This is because, for µ = 0.5, there is almost increasing the encoded block length. Similar to the relationship
no waiting time for each updating packet in the queue, even between K and µ, the roles of l and n are relative for AoI. This
if K increases to 500. An excessive number of users may is because both larger n and smaller l can reduce the decoding
lead to a continuous increase in the length of the queue and error probability and improve the success rate of AoI updates.
the system cannot reach a stable state. Therefore, we need to In addition, when the block length of updating packets n is
reasonably select the number of users according to the service large enough, the AoI will not change significantly. In this
rate of the UAV in practice. case, the AoI is mainly determined by the queue waiting time
In Fig. 11, we show the average AoI with different service at the UAV and the hovering cycle. Therefore, it is crucial
rates of UAV. In the simulation, we set h = 200 m, P = to select an appropriate code length for the given information
0.1 W, K0 = 5, l = 32 bits, and n = 108 bits. Similar to length.
the results in Fig. 10, it can be found that the average AoI Based on the analysis of the above simulation results, the
decreases dramatically as µ increases from 0.2 to 0.4 when proposed scheme can be used in IoT scenarios in which the
K = 500. Then, it remains almost constant even though µ remote sensors are deployed far away from the BS. In this
 12

scenario, the remote sensors can not send the information to [12] A. Ranjha and G. Kaddoum, “Quasi-optimization of uplink power
BS due to the severe path loss. Hence, the UAV is employed to for enabling green URLLC in mobile UAV-assisted IoT networks: A
perturbation-based approach,” IEEE Internet Things J., vol. 8, no. 3,
collect the information from the sensors and send it back to the pp. 1674-1686, Feb. 2021
BS. Due to the sensors monitoring environmental information [13] A. Ranjha, G. Kaddoum, and K. Dev, “Facilitating URLLC in UAV-
continuously, they do not need to be updated results in real- assisted relay systems with multiple-mobile robots for 6G networks: A
prospective of agriculture 4.0,” IEEE Trans. Ind. Inf. , vol. 18, no. 7, pp.
time, and their AoI is acceptable on an hourly scale as in the 4954-4965, Jul. 2022.
simulation. [14] X. Xi, X. Cao, P. Yang, J. Chen, T. Q. S. Quek, and D. Wu, “Network
resource allocation for eMBB payload and URLLC control information
communication multiplexing in a multi-UAV relay network,” IEEE Trans.
VI. C ONCLUSION Commun., vol. 69, no. 3, pp. 1802-1817, Mar. 2021.
[15] Y. Cai, X. Jiang, M. Liu, N. Zhao, Y. Chen, and X. Wang, “Resource
In this paper, a UAV-aided URLLC scheme has been allocation for URLLC-oriented two-way UAV relaying,” IEEE Trans.
Veh. Technol., vol. 71, no. 3, pp. 3344-3349, Mar. 2022.
proposed for edge users and its AoI was analyzed and op- [16] H. Ren, C. Pan, K. Wang, Y. Deng, M. Elkashlan, and A. Nallanathan,
timized in terms of the decoding error probability and the “Achievable data rate for URLLC-enabled UAV systems with 3-D channel
UAV aerodynamic performance. Inspired by the pylon turn model,” IEEE Wireless Commun. Lett., vol. 8, no. 6, pp. 1587-1590, Dec.
2019.
of gunboat aircraft, the same hovering pattern was used in [17] J. Wang, L. Bai, J. Chen and J. Wang, “Starling flocks-inspired resource
the fixed-wing communication UAV. In order to obtain the allocation for ISAC-aided green ad hoc networks,” IEEE Trans. Green
optimal hovering radius, the original complex optimization Commun. Networking, vol. 7, no. 1, pp. 444-454, Mar. 2023.
[18] M. Costa, M. Codreanu, and A. Ephremides, “On the age of information
problem has been reasonably simplified and its closed-form in status update systems with packet management,” IEEE Trans. Inf.
solution was obtained as a suboptimal solution to the original Theory, vol. 62, no. 4, pp. 1897-1910, Apr. 2016.
problem. Simulation results showed that the proposed AoI [19] R. Han, J. Liu, L. Bai, and J. Liu, “Epidemic theory-inspired integrated
sensing and communication networks: Design and analysis,” IEEE Com-
optimization method can obtain higher transmission reliability mun. Mag., vol. 61, no. 5, pp. 33-39, May 2023.
and lower AoI than the scheme with a fixed hovering radius. In [20] N. Akar, O. Doğan, and E. U. Atay, “Finding the exact distribution of
addition, the proposed optimization method was demonstrated (peak) age of information for queues of PH/PH/1/1 and M/PH/1/2 type,”
IEEE Trans. Commun., vol. 68, no. 9, pp. 5661-5672, Sep. 2020.
to achieve the near-optimal AoI performance with a low
[21] A. Soysal and S. Ulukus, “Age of information in G/G/1/1 systems: Age
computational complexity. expressions, bounds, special cases, and optimization,” IEEE Trans. Inf.
Theory, vol. 67, no. 11, pp. 7477-7489, Nov. 2021.
[22] J. -B. Seo and J. Choi, “On the outage probability of peak age-of-
R EFERENCES information for D/G/1 queuing systems,” IEEE Commun. Lett. , vol. 23,
no. 6, pp. 1021-1024, Jun. 2019.
[1] J. Khan and L. Jacob, “Availability maximization framework for CoMP [23] S. S. Hosseini, P. Azmi and N. Mokari, “Minimizing average age of
enabled URLLC with short packets,” IEEE Networking Lett., vol. 2, no. information in reliable covert communication on time-varying channels,”
1, pp. 1-4, Mar. 2020. IEEE Trans. Veh. Technol., doi: 10.1109/TVT.2023.3303674 (early ac-
[2] Y. Wang, Z. Hu, X. Wen, Z. Lu and J. Miao, “Minimizing data collection cess).
time with collaborative UAVs in wireless sensor networks,” IEEE Access [24] J. P. Champati, R. R. Avula, T. J. Oechtering, and J. Gross, “Minimum
, vol. 8, pp. 98659-98669, May 2020. achievable peak age of information under service preemptions and request
[3] H. Sun, Y. Zhou, J. Tang, Z. Kang, X. Wang and T. Q. S. Quek, “Average delay,” IEEE J. Sel. Areas Commun., vol. 39, no. 5, pp. 1365-1379, May
AoI-minimal trajectory design for UAV-assisted IoT data collection 2021.
system: A safe-TD3 approach,” IEEE Wireless Commun. Lett., doi: [25] F. Chiariotti, O. Vikhrova, B. Soret, and P. Popovski, “Peak age of
10.1109/LWC.2023.3335037 (early access). information distribution for edge computing with wireless links,” IEEE
[4] J. Wang, R. Han, L. Bai, T. Zhang, J. Liu and J. Choi, “Coordinated beam- Trans. Commun., vol. 69, no. 5, pp. 3176-3191, May 2021.
forming for UAV-aided millimeter-wave communications using GPML- [26] L. Hu, Z. Chen, Y. Jia, M. Wang, and T. Q. S. Quek, “Asymptotically
based channel estimation,” IEEE Trans. Cognit. Commun. Networking, optimal arrival rate for IoT networks with AoI and peak AoI constraints,”
vol. 7, no. 1, pp. 100-109, Mar. 2021. IEEE Commun. Lett., vol. 25, no. 12, pp. 3853-3857, Dec. 2021.
[5] H. Ren, C. Pan, K. Wang, Y. Deng, M. Elkashlan and A. Nallanathan, [27] R. D. Yates and S. K. Kaul, “The age of information: Real-time status
“Achievable data rate for URLLC-enabled UAV systems with 3-D channel updating by multiple sources,” IEEE Trans. Inf. Theory, vol. 65, no. 3,
model,” IEEE Wireless Commun. Lett., vol. 8, no. 6, pp. 1587-1590, Dec. pp. 1807-1827, Mar. 2019.
2019. [28] Z. Fang, J. Wang, Y. Ren, Z. Han, H. V. Poor, and L. Hanzo, “Age of in-
[6] X. Yan, X. Fang, C. Deng and X. Wang, “Joint optimization of resource formation in energy harvesting aided massive multiple access networks,”
allocation and trajectory control for mobile group users in fixed-wing IEEE J. Sel. Areas Commun., vol. 40, no. 5, pp. 1441-1456, May 2022.
UAV-enabled wireless network,” IEEE Trans. Wireless Commun., doi: [29] R. Han, J. Wang, L. Bai, J. Liu, and J. Choi, “Age of information and
10.1109/TWC.2023.3290748 (early access). performance analysis for UAV-aided IoT systems,” IEEE Internet Things
[7] C. Yue, V. Miloslavskaya, M. Shirvanimoghaddam, B. Vucetic, and Y. Li, J., vol. 8, no. 19, pp. 14447-14457, Oct. 2021.
“Efficient decoders for short block length codes in 6G URLLC,” IEEE [30] H. Feng, J. Wang, Z. Fang, J. Chen and D. -T. Do, “Evaluating AoI-
Commun. Mag., vol. 61, no. 4, pp. 84-90, Apr. 2023. centric HARQ protocols for UAV networks,” IEEE Trans. Commun., doi:
[8] M. E. Haque, F. Tariq, M. R. A. Khandaker, K. -K. Wong, and Y. Zhang, 10.1109/TCOMM.2023.3320696 (early access).
“A survey of scheduling in 5G URLLC and outlook for emerging 6G [31] C. M. W. Basnayaka, D. N. K. Jayakody, and Z. Chang, “Age-of-
systems,” IEEE Access, vol. 11, pp. 34372-34396, 2023. information-based URLLC-enabled UAV wireless communications sys-
[9] D. Xu, K. Yu, L. Zhen, K. -K. R. Choo, and M. Guizani, “Quan- tem,” IEEE Internet Things J. , vol. 9, no. 12, pp. 10212-10223, Jun.
tum learning on structured code with computing traps for secure 2022.
URLLC in industrial IoT scenarios,” IEEE Internet Things J., doi: [32] X. Zhang, J. Wang, and H. V. Poor, “AoI-driven statistical delay and
10.1109/JIOT.2023.3268608 (early access). error-rate bounded QoS provisioning for mURLLC over UAV-multimedia
[10] M. S. Bahbahani, E. Alsusa, and A. Hammadi, “A directional TDMA 6G mobile networks using FBC,” IEEE J. Sel. Areas Commun., vol. 39,
protocol for high throughput URLLC in mmWave vehicular networks,” no. 11, pp. 3425-3443, Nov. 2021.
IEEE Trans. Veh. Technol., vol. 72, no. 3, pp. 3584-3599, Mar. 2023. [33] J. Liu, P. Tong, X. Wang, B. Bai, and H. Dai, “UAV-aided data collection
[11] A. Ranjha and G. Kaddoum, “URLLC facilitated by mobile UAV relay for information freshness in wireless sensor networks,” IEEE Trans.
and RIS: A joint design of passive beamforming, blocklength, and UAV Wireless Commun., vol. 20, no. 4, pp. 2368-2382, Apr. 2021.
positioning,” IEEE Internet Things J., vol. 8, no. 6, pp. 4618-4627, Mar. [34] D. Wang, Y. Yang, X. Li, C. Wang, F. Liu, and Y. Hu, “Energy-efficient
2021. and secure power allocation and trajectory optimization for UAV-enabled
 13

data collection in wireless sensor networks,” J. Commun. Inf. Networks, Lin Bai (Senior Member, IEEE) received the B.Sc.
vol. 7, no. 3, pp. 333-348, Sep. 2022. degree in electronic and information engineering
[35] C. Zhang, S. Liang, C. He, and K. Wang, “Multi-UAV trajectory design from the Huazhong University of Science and Tech-
and power control based on deep reinforcement learning,” J. Commun. nology, Wuhan, China, in 2004, the M.Sc. degree
Inf. Networks, vol. 7, no. 2, pp. 192-201, Jun. 2022. (Hons.) in communication systems from the Univer-
[36] J. Wang, Z. Jiao, J. Chen, X. Hou, T. Yang and D. Lan, “Blockchain- sity of Wales, Swansea, U.K., in 2007, and the Ph.D.
aided secure access control for UAV computing networks,” IEEE Trans. degree in advanced telecommunications from the
Network Sci. Eng., doi: 10.1109/TNSE.2023.3324639 (early access). School of Engineering, Swansea University, U.K.,
[37] A. Al-Hourani, S. Kandeepan, and S. Lardner, “Optimal LAP altitude in 2010. Since 2011, he has been with Beihang
for maximum coverage,” IEEE Wireless Commun. Lett., vol. 3, no. 6, pp. University (Beijing University of Aeronautics and
569-572, Dec. 2014. Astronautics, BUAA), Beijing, China, where he is
[38] J. Zhang, T. Chen, S. Zhong, J. Wang, W. Zhang, X. Zuo, R. G. Maunder, currently a Professor at the School of Cyber Science and Technology. His
and L. Hanzo, “Aeronautical ad hoc networking for the Internet-Above- research interests include multiple-input multiple-output (MIMO), Internet-of
the-Clouds,” Proc. IEEE , vol. 107, no. 5, pp. 868-911, May 2019. Things (IoT), and unmanned aerial vehicle (UAV) communications. He has
[39] S. Zhang, “Research on emergency coverage capability of fixed-wing authored two books published by Springer in 2012 and 2014. He has served
UAV based on 5G,” in Proc. International Wireless Communications and as a Symposium Co-Chair of IEEE GLOBECOM 2019 and a Tutorial Co-
Mobile Computing (IWCMC), Limassol, Cyprus, pp. 680-684, Jul. 2020. Chair of IEEE/CIC ICCC 2019. He is the founding Chair of IEEE ComSoc
[40] J. Liu, M. Sheng, R. Lyu, Y. Shi, and J. Li, “Access points in the air: Wireless Communications Technical Committee Special Interest Group (SIG)
Modeling and optimization of fixed-wing UAV network,” IEEE J. Sel. on Space Air Ground Integrated (SAGI) Communications. He has served
Areas Commun., vol. 38, no. 12, pp. 2824-2835, Dec. 2020. as an Editor for IEEE TRANSACTIONS ON SIGNAL PROCESSING and
[41] X. Li, H. Yao, J. Wang, X. Xu, C. Jiang, and L. Hanzo, “A near-optimal IEEE WIRELESS COMMUNICATIONS LETTERS, a Lead Guest Editor for
UAV-aided radio coverage strategy for dense urban areas,” IEEE Trans. IEEE Wireless Communications, and a Guest Editor for IEEE INTERNET
Veh. Technol., vol. 68, no. 9, pp. 9098-9109, Sep. 2019. OF THINGS JOURNAL. He is currently serving as an Editor for IEEE
[42] X. Song, Z. Chang, X. Guo, P. Wu, and T. Hämäläinen, “Energy TRANSACTIONS ON WIRELESS COMMUNICATIONS and the Managing
efficient optimization for solar-powered UAV communications system,” Editor for Journal of Communications and Information Networks. He is a
in Proc. IEEE International Conference on Communications Workshops Distinguished Lecturer of the IEEE Communications Society and the IEEE
(ICC Workshops), Montreal, QC, Canada, pp. 1-6, Jul. 2021. Vehicular Technology Society.
[43] Y. Zeng and R. Zhang, “Energy-efficient UAV communication with
trajectory optimization,” IEEE Trans. Wireless Commun., vol. 16, no.
6, pp. 3747-3760, Jun. 2017.
[44] A, Filippone, Flight performance of fixed and rotary wing aircraft.
Elsevier, 2006.
[45] H. A. David and H. N. Nagaraja, Order Statistics, 3rd edition, John
Wiley and Sons, New York, 2003.

Zhengru Fang received his B.S. degree (Hons.)

in electronics and information engineering from the
Huazhong University of Science and Technology
(HUST), Wuhan, China, in 2019 and received his
M.S. degree (Hons.) from Tsinghua University, Bei-
jing, China, in 2022. Currently, he is pursuing his
PhD degree in the Department of Computer Science
at City University of Hong Kong. His research
interests include collaborative perception, V2X, age
of information, and wireless sensing. He has been
serving as a Reviewer for IEEE JSAC, IEEE IoTJ,
IEEE TVT, IEEE WCL, IEEE CL, IEEE VTM, etc.

Jiaxing Wang (Member, IEEE) received his B.S.

degree in Information Engineering from Nanjing RUI HAN (S’18, M’22) received the Ph.D. degree
University of Aeronautics and Astronautics, Jiangsu, in cyber security from Beihang University, Beijing,
China, in 2017 and the Ph.D. degree in Transporta- China, in 2022. Dr. Han is currently a Research
tion Information Engineering and Control from Bei- Fellow at National Research Center, Tsinghua Uni-
hang University, Beijing, China, in 2023. Dr. Wang versity, Beijing, China. Her current research inter-
is currently a Post-Doctoral Researcher at School of ests include the Internet of things (IoT), unmanned
Cyber Science and Technology, Beihang University, aerial vehicle (UAV) communications, and satellite
Beijing, China. His research interests include MIMO communications.
communications, UAV communications and ad hoc
networks.
 14

Jingjing Wang (S’14-M’19-SM’21) received his

B.Sc. degree in electronic information engineering
from the Dalian University of Technology, Liaoning,
China in 2014 and the Ph.D. degree in information
and communication engineering from the Tsinghua
University, Beijing, China in 2019, both with the
highest honors. From 2017 to 2018, he visited the
next generation wireless group chaired by Prof.
Lajos Hanzo in the University of Southampton, UK.
Dr. Wang is currently a Professor at the School of
Cyber Science and Technology, Beihang University,
Beijing, China. His research interests include AI enhanced next-generation
wireless networks, UAV networking and swarm intelligence. He has published
over 100 IEEE Journal/Conference papers. He is currently serving as an Editor
for the IEEE Wireless Communications Letter and the IEEE Open Journal
of the Communications Society. He has served as a Guest Editor for IEEE
Internet of Things Journal. Dr. Wang was a recipient of the Best Journal Paper
Award of IEEE ComSoc Technical Committee on Green Communications &
Computing in 2018, the Best Paper Award of the IEEE ICC and the IEEE
IWCMC in 2019.

Jinho Choi (SM’02-F’22) was born in Seoul, Korea.

He received B.E. (magna cum laude) degree in elec-
tronics engineering in 1989 from Sogang University,
Seoul, and M.S.E. and Ph.D. degrees in electrical
engineering from Korea Advanced Institute of Sci-
ence and Technology (KAIST) in 1991 and 1994,
respectively. He is with the School of Information
Technology, Burwood, Deakin University, Australia,
as a Professor. Prior to joining Deakin in 2018, he
was with Swansea University, United Kingdom, as a
Professor/Chair in Wireless, and Gwangju Institute
of Science and Technology (GIST), Korea, as a Professor. His research
interests include the Internet of Things (IoT), wireless communications, and
statistical signal processing. He authored two books published by Cambridge
University Press in 2006 and 2010. Prof. Choi received a number of best
paper awards including the 1999 Best Paper Award for Signal Processing
from EURASIP. He is on the list of World’s Top 2% Scientists by Stanford
University. Currently, he is an Editor of IEEE Trans. Communications and
IEEE Wireless Communications Letters and a Division Editor of Journal of
Communications and Networks (JCN). We also had served as an Associate
Editor or Editor of other journals including IEEE Communications Letters,
JCN, IEEE Trans. Vehicular Technology, and ETRI journal.

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