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This work was supported in part by Faculty Development Scheme
under Grants UGC/FDS25(14)/E04/20 and UGC/FDS14/E02/21 and
Research Matching Grant Scheme from the Research Grants Council of
Hong Kong. (Corresponding author: Yun Hou.)
Enhancing C-V2X Network Connectivity with
Distributed Mobility Control
Jingxuan Men
Yun Hou
Zhengguo Sheng
Tse-Tin Chan
Department of Electrical
and Electronic
Engineering
Department of Computing
Department of Engineering
and Design
Department of
Mathematics and
Information Technology
University of Surrey
The Hang Seng University
of Hong Kong
University of Sussex
The Education University
of Hong Kong
Guildford, UK
Hong Kong SAR, China
Brighton, UK
Hong Kong SAR, China
j.men@surrey.ac.uk
aileenhou@hsu.edu.hk
Z.Sheng@sussex.ac.uk tsetinchan@eduhk.hk
Abstract—The high mobility feature of vehicular networks
poses tremendous challenges to maintaining network
connectivity. In this paper, we investigate the possibility of
enhancing the connectivity of Cellular Vehicle-to-Everything
(C-V2X) networks through distributed trajectory adjustment.
Based on a physical layer abstraction model, we characterize the
network connectivity enhancement problem as a network utility
maximization and study its concavity. We propose a distributed
trajectory updating algorithm that dynamically adjusts the
trajectory of vehicles on top of their planned trajectory. The
algorithm is distributed and requires only geo-location
exchanges, which are readily available in V2X networks.
Simulation results show that the mobility updating algorithm
converges and improves the aggregated network utility by up to
48% compared to the scenarios without mobility tuning.
Keywords—Controlled mobility, C-V2X, vehicular network.
I. INTRODUCTION
Cellular Vehicle-to-Everything (C-V2X) is being
commercialized; however, there are still challenges that need
to be addressed, such as vehicular network coverage,
interference, and vehicle mobility. In C-V2X, there are in-
coverage scenarios and out-of-coverage scenarios. In the in-
coverage scenario, vehicles are connected to the base station
in the control plane, allowing for collision-free scheduling and
high-quality service. For communication scenarios without
network coverage, due to the nature of autonomous
scheduling, the quality of service may be degraded under the
conditions of high-density network scenarios. This is expected
for future vehicular networks, especially Unmanned Aerial
Vehicle (UAV) networks [1] and autonomous driving
networks. In high-density network scenarios, collided
message broadcasting or resource sharing may lead to
significant interference, thus affecting the reception rates.
Furthermore, in C-V2X communication scenarios, the
vehicles move at high speeds, resulting in severe Doppler
effects and a corresponding decrease in communication
quality [2]. It is well known that network connectivity is a
critical issue for future autonomous driving scenarios, as
autonomous vehicles want to disseminate their status and
warning messages to as many nearby vehicles as possible.
Also, because of the high mobility, UAV networks are prone
to possess highly dynamic, sparse, and intermittent network
topologies [3]. As a result, the multi-UAV coordination or
swarm operation places high demands on network
connectivity.
Packet Reception Rate (PRR) is the aggregated link
success probability across all receivers for one broadcast
packet. Aggregated PRR over all the transmitted packets in
the network, referred to as the network PRR hereafter,
represents the level of connectivity in the network, such that
the higher the network PRR is, the transmitted packets can be
decoded by more vehicles in the network. However, high
vehicle densities will lead to concurrent transmissions with
severe interference due to the reuse of the limited radio
resources between vehicles, which will degrade the PRR and
hence the connectivity of the vehicular network. Therefore, in
this paper, we aim to improve the network connectivity, i.e.,
the network PRR, via vehicle trajectory adjustments.
Coordinated maneuvers via trajectory data exchange help
to achieve safer and more efficient driving. The study in [4]
evaluated the potential benefits of mobility coordination
services to improve traffic speed. This research shows that
mobility coordination can bring significant benefits to traffic
mobility, but these improvements are closely related to the
surrounding traffic environment and the norms of coordinated
mobility. However, until now, most mobility studies have
focused on improving transportation traffic efficiency, and
few studies consider its potential to enhance vehicular
communication network connectivity.
Regarding vehicular network connectivity, most of the
literature focuses on scenarios with coverage of macro base
stations (MBSs). [5] modeled the spatial layout of MBSs and
vehicles as a two-dimensional Poisson point process and a
Poisson line Cox point process, respectively. The coverage
probabilities of downlink and lateral link based on Signal-to-
Interference Ratio (SIR) are derived based on a vehicle-first
association scheme using a stochastic geometry tool. In [6],
the authors analyzed the downlink coverage and rate of C-
V2X communication networks to derive the coverage
probability of the receiver and the downlink rate coverage of
the receiver. Reference [7] studied the power allocation and
trajectory planning of UAV-assisted V2X networks. To
reduce the complexity of decoding, the author proposed a
dynamic NOMA/OMA scheme and formulated an
optimization problem for the sum-rate and min-rate of
vehicles, which can achieve less decoding complexity.
However, the above work does not consider the autonomous
scheduling model of the C-V2X network, nor does it propose
any distributed mechanism to optimize the coverage or
connectivity of the C-V2X network.
In terms of distributed algorithms for connectivity
maximization, the authors in [8] proposed a distributed
updating framework of airtime scheduling, transmission
power, and flow rate to solve the congestion control problem
optimally. However, mobility, which becomes a feasible
controllable degree of freedom in future V2X networks, was
not considered in [8] as a tuning parameter. Recently, [9]
adopted node movement as an optimization parameter to
improve the single-transmitter PRR. A per-node optimization
is performed based on a “Two-Distance” (TD) model, where
the per-link reception probability is approximated using the
signal distance and the primary interference distance via a
Linear Regression approach. However, this algorithm
proposed optimizes the utility of one transmitting node only.
In this paper, we focus on adjusting the mobility of
vehicles, in addition to their original trajectories, aiming to
improve the connectivity of vehicular networks, exploiting the
abstraction of the physical layer with the TD model proposed
in [9]. We formulate an optimization problem of network
connectivity as a function of packet PRRs and investigate the
concavity of the problem with its concavity conditions. To
improve the formulated C-V2X network connectivity, we
propose a Multi-node-Mobility-Updating (MMU)
algorithm. It allows each transmitting vehicle to gradually
adjust its mobility in a distributed manner, deviating from its
original trajectory based on the understanding of each other’s
geo-location information.
The remainder of this paper is organized as follows. In
Section II, we present the system model and highlight the
challenges of distributed mobility control for autonomous C-
V2X networks. In Section III, we formulate the multi-node
Network Utility Maximization (NUM) problem and
investigate its optimality. We devise a distributed updating
framework towards the optimum in Section IV. Numerical
results are shown in Section V, and Section VI concludes the
paper. Our contributions are summarized in Table 1.
TABLE I. COMPARISONS OF RELATED OPTIMIZATION WORK
Research
work
Mobility
adjustment
Network
connectivity
V2X
sidelink
Multi
-
node
distributed
optimization
[4]
[5][6]
[7]
[8]
[9]
This paper
II. SYSTEM SETTING AND CHALLENGES
In one subframe, some vehicles in the vehicular network
are transmitting while others are receiving due to the half-
duplexing operation. The vehicles are connected using the C-
V2X mode 4, i.e., the out-of-coverage use case.
The transmitting opportunity of each vehicle is self-
scheduled through the Semi-Persistent Scheduling (SPS)
framework [10]. All vehicles are conducting the SPS lead to a
semi-static transmitter and receiver composition in the
network. That is, who will be transmitting and receiving in the
future can be predicted to some extent. Our paper adopts the
physical layer abstraction derived in [9], where the per-link
reception probability is modeled by a function of two
distances, namely the signal distance (the distance between
the transmitter and the receiver) and the primary interference
distance at the intended receiver (the distance between the
receiver and its closest interference).
Our goal is to find a mechanism that allows all the
transmitting vehicles to adjust their trajectory in a coordinated
and distributed manner so that the network PRR for all
broadcast packets, i.e., transmitted by multiple concurrent
transmitters towards all receivers in the network, is
maximized. Assume that the reception success probability of
a link is proportional to the SINR of this link, while the
average signal power and interference power are inversely
proportional to the square or higher order of the distance
associated with this link. Therefore, adjusting the distances
between the transmitter and receivers is beneficial to optimize
the link PRR. For broadcast transmissions, it is not optimal to
simply reduce the distance to a particular receiver, as this may
expand the distances to some other receivers for the
transmitter. Meanwhile, for the receiver, it increases the
interference for all the other concurrent receptions towards the
same receiver. Therefore, an adjustment of distance needs to
be derived from a network-wide perspective. The challenges
and our solutions and assumptions in this study are
summarized as follows.
• No feedback channel. To know how to adjust the
transmitter’s parameters, a transmitter needs to estimate
the SINR for its receivers, which is usually obtained
through feedback (e.g., the HARQ in traditional
LTE/5G systems) from receivers. However, the
autonomous mode of C-V2X does not have a feedback
channel. To tackle this issue, we use the Two-Distance
(TD) model from [9] to predict the link success
probability as a function of distances only. The model
enables a vehicle to estimate the PRR without SINR
feedback, but only from the readily available geo-
location of vehicles.
• There is no global information about the interferers, i.e.,
vehicles transmitting packets using the same resources.
However, with the SPS mechanism used in C-V2X,
vehicles make periodic transmissions over the same set
of resources in most cases. The typical number of
periodic transmissions made by a vehicle is 5-15 when
the resource allocation period is set to 100ms in LTE-
V2X [11]. That means over 80%-93% chances, the
estimation of the concurrent transmitters is accurate.
• Direct adjustments over distances cannot guarantee
feasible solutions in vehicles’ trajectory. The distance to
any receiver is the smaller the better. However, a
transmitter cannot move close to all the receivers
simultaneously. To solve this problem, we impose a
feasibility constraint on the NUM problem to penalize
the infeasible distances. The concavity of the
constrained problem is discussed in Section III.
III. PROBLEM FORMULATION AND ITS CONCAVITY
We measure the connectivity of a C-V2X network using
the network-level aggregated PRR. As the utility associated
with a transmitter-receiver link from node i to node j is
proportional to the success probability of the reception Pi,j, the
network-level multi-node utility is represented as follows
,
,
i j
i j
U P
∈ ∈
=
x x
RT
(1)
where Tx and Rx represent the set of all transmitting and
receiving nodes in the network, respectively.
The link success probability Pi,j is a function of two
distances according to the Two-Distance (TD) model in [9] as
shown in (2). The signal distance, i.e., di,j, is the distance
between the transmitting node i and the receiving node j. The
primary interference distance, i.e., lj, is the distance between
the closest interfering node and the receiving node j. Hence,
, , ,
( , ) log log ,
i j i j j j i j j j j
P d l d l
α β γ
= + + (2)
where αj, βj, and γj are machine-learned coefficients, and the
values of αj, βj, and γj are receiver-specific as their values
depend on how many transmitters are surrounding j as well as
the strengths of the interferences.
To keep the distance solutions feasible, we restrict the
distance variables in the optimization problem by the Law of
Cosines. That is, the transmitter i and any two of its receivers,
j and k, form a triangle. Let di,j, di,k be the distances from
transmitter i to receivers j and k, respectively, and Cj,k be the
distance between receivers j and k. According to the Law of
Cosines, while is the angle between side (, ) and (, ), we
have
2 2 2
, , , , ,
2 cos .
i j i k i j i k j k
d d d d C
θ
+ − = (3)
As node i moves freely in the RoI, we have
1 cos 1
θ
− ≤ ≤
.
Thus, for any position of i, di,j and di,k should obey to
2 2
, , ,
( ) .
i j i k j k
d d C
− ≤ (4)
, , ,
.
i j i k j k
d d C
+ ≥ (5)
The inequality (4) is added to the maximization problem to
reflect the realistic constraint such that the three distances
must belong to the same triangle. Equation (5) is omitted as it
will not affect the second-order partial derivatives and hence
not change the concavity. Thus, the optimization over d is
formulated as
,
,
, ,
log(1 )
i j
i j
d i j i j
U P
∈ ∈ ∈ ∈
= +
max
x x x x
T R T R
(6)
s.t.
2 2
, , ,
( )
i j i k j k
d d C
− ≤
, .
i k j
∀ ∈ ≠ ∈
x x
T R
To take account of the fairness among various links and to
avoid negative utilities, log (1+. ) is applied to the reception
probabilities of each link to reduce the gain in the distance
when Pi,j is already high. Blending in the constraint in (6) by
the Lagrangian multiplier [12], with λi,j,k being the shadow
price, we obtain the non-constrained optimization problem
,
,
, ,
log(1 log log )
i j
j i j j j j
d i j i j
d l
α β γ
∈ ∈ = + + +
max
x x
T R L
2 2
, , , , ,
(( ) ).
i j k i j i k j k
i j k j
d d C
λ
≠
− − −
(7)
The Lagrangian multiplier in (7) shows that when
2
, ,
( )
i j i k
d d−
is greater than
2
,
j k
C
, there will be a penalty, i.e., the utility U
will be reduced. Conversely, when
2
, ,
( )
i j i k
d d− is less than
2
,
j k
C
,
U will become larger due to a reward from the pricing
mechanism, i.e., having a negative price.
In the following, we will prove that the formulated
problem (7) is concave under certain conditions to show the
feasibility of developing a distributed updating method
toward the unique global optimum.
The gradient of (7) w.r.t. di,j can be derived as
, , , , ,
( log )
1 1 1
1 1
j j
i j
j
i j i j i j i j i j
l
d d P d P
β
α
∈
∂
∂= ⋅ ⋅ + ⋅
∂ + ∂ +
Lx
R
, , , ,
(2 2 ).
i j k i j i k
k j
d d
λ
≠
− −
(8)
The second term in the above derivation represents the impact
of link (i, j) as the primary interference to all other concurrent
links aiming at receiver j. For a link from another transmitter
to j, if transmitter i happens to be the closest interferer to
receiver node j, its primary interference distance lj is di,j.
Suppose there are N concurrent transmitters, and i is the
closest transmitting node to j among the N nodes. In this case,
di,j will appear N–1 times in the second term, i.e., link di,j is the
primary interference for all other N–1 transmissions. If i is the
second closest transmitting node to j among all transmitting
nodes, then di,j will appear in the second term only once, i.e.,
link lj is the primary interference for link q* to j, where q* is
the closest transmitter to j. In all other cases, di,j does not
appear in the second term, and the first-order partial derivation
is 0 for that term.
Using ri,j to represent the number of times that i is the
primary interferer of j, i.e., lj = di,j, we have
,
, , , ,
, , ,
1
(2 2 ),
1
j i j j
i j k i j i k
k j
i j i j i j
rd d
d d P
α β λ
≠
+
∂= ⋅ − −
∂ +
L (9)
where
,
1, when is the closest transmitter t
o
1, when is the 2nd closest transmitt
er to
0,
otherwise.
i j
N
r
−
=
i j,
i j,
.
In the following, we will analyze the concavity of the
maximization problem (7). Since the log is a monotonic
concave function, it will not violate the concavity of a
concave function. Therefore, the derivative component
associated with the log function is omitted in the following
stage of the concavity investigation. First, we investigate the
diagonal elements in the Hessian Matrix. They are
2
, , ,
2 2
, ,
1
( ) 2 .
j i j j i j k
k j
i j i j
r
d d
α β λ
≠
∂= − + ⋅ −
∂
L (10)
For the non-diagonal elements in the Hessian Matrix, we
have the following observations:
• The second-order mixed partial derivatives w.r.t. the
same transmitter i is
2
, ,
, ,
2 .
i j k
i j i k
d d
λ
∂=
∂ ∂
L (11)
• The second-order mixed partial derivatives across
different transmitter nodes i and q is
2
, ,
0.
q i
i j q k
d d ≠
∂
=
∂ ∂
L (12)
In the following, let us re-index the distance variables in the
network using a one-dimensional index m, m =1, 2, …, T∙R,
where T·R is the total number of links existing for T
transmitters and R receivers. Then, based on (11) and (12), the
following relation holds for diagonal elements and non-
diagonal elements in the Hessian
( , ) ( , ) ,
m
m n
H m m H m n
≠
= − + ∆
and
,2
,
1
( ) .
m j i j j
i j
rd
α β
∆ = − + ⋅
(13)
In the following, we will prove that under certain
circumstances, the Hessian Matrix is a definite negative
2
( , ) ( , )
T
m m n
m m n m
V HV H m m V H m n V V
≠
= +
2
( , ) ( , )
m m m n
m m n m n m
H m n V H m n V V
≠ ≠
= − +∆ +
2 2
( , )( ) .
m m m n
m m n m
V H m n V V
≠
= ∆ − −
(14)
In (14), the sign of the latter term is always negative, while
m
∆
may be positive or negative. It is noticeable that when
m
∆
is negative or sufficiently small positive, we have for any non-
zero V,
0
T
V HV <, and hence the problem is concave.
The abovementioned concavity condition (i.e.,
m
∆
is
either a negative value or a sufficiently small positive value)
is easy to satisfy whenever d
i,j
is small or large. On one hand,
when the distance d
i,j
is small, link (i, j) is likely to be the
primary interference, resulting in a big r
i,j
= N–1, as shown in
(9). Given that the signs of α
j
and β
j
are negative and positive,
respectively, the multiples of β
j
make
m
∆
likely to be a
negative value. On the other hand, when d
i,j
is large, it results
in a small positive
m
∆
. In conclusion, the problem is likely to
be concave in realistic cases.
It is worth noting that being a negative log function over
the distances, the original unconstrained utility maximization
in (1) is a convex problem, i.e., the smaller the distances are,
the larger the U is. While the constrained utility maximization
in (6) is a concave problem, the choice of distance variables
becomes limited. This guides us to develop a distributed
updating method to achieve optimal network utility for
vehicle trajectories.
IV.
U
PDATING
M
ETHOD
Provided the autonomous nature of C-V2X networks,
distributed updating methods implemented on each
transmitting node to adjust their mobility are more desired
than a centralized mechanism. For the concave maximization
problem defined in (7), a distributed gradient-based updating
method is developed for each vehicle to adjust its position
gradually according to its current gradient associated with the
objective function
L
to improve connectivity, as shown in
(15)
.
,
, , , , ,
, ,
1
( ) ( )(2 ( ) 2 ( )),
( ) ( )
j i j j
i j i j k i j i k
k j
i j i j
r
G t t d t d t
d t P t
α β λ
≠
+
= ⋅ − −
(15)
The increment in d
i,j
should be proportional to the current
gradient so that the adjustment of d
i,j
always aims for better
connectivity. That is
, ,
( 1) ( ) ( ).
i j i d i j
d t d t G t
δ
+ = + ⋅
(16)
In terms of the shadow price update, when the condition is not
violated, i.e., the penalty λ
i,j,k
is reduced and vice versa. Thus,
we have:
(17)
Equations (15-17) reveal the iterative interaction between
the shadow price and the distance. When the distance
constraint is violated, λ
i,j,k
will become larger in the upcoming
iteration, as shown in (17). The larger λ
i,j,k
will further lead to
a smaller or larger gradient of
,
i j
d
in (15) if
, ,
i j i k
d d
>
or
, ,
i j i k
d d
<
, respectively. That is, if
, ,
0
i j i k
d d
− >
, the
,
i j
d
will
become smaller to bring down the difference between
,
i j
d
and
,
i k
d
, so that the constraint may be less violated and vice
versa. On the contrary, when the distance constraint is not
violated, λ
i,j,k
will go smaller and
,
i j
d
will be adjusted towards
a more stringent constraint. Therefore, it is observed that the
shadow price, when iterating, helps to regulate the distance
variables under the Law of Cosines. This improves the
feasibility of the updated distance variables.
An iterative updating method for vehicles’ trajectory,
called
Multi-node-Mobility-Updating
(MMU) Algorithm, is
proposed as follows for each iteration t, each transmitter i:
Step 1: works out the gradient
,
( )
i j
G t
and
, ,
( )
i j k
G t
λ
of
the current iteration t for all j.
•
Step 2: calculates the direction vector to indicate the
moving direction for all receiver j by
, ,
( ) ( ) ( ) ( ),
i j i j i j
t Pos t Pos t d t
τ
= −
uuuuur
where Pos
i
(t) is the position of transmitters, and Pos
j
(t)
is the current position of receivers at iteration t. Both
positions are 2-D vectors containing the x- and y-
coordinates.
•
Step 3: obtains the wanted position of transmitters with
respect to j by moving a distance along the calculated
direction, for all j. The distance is proportional to the
gradient
,
( )
i j
G t
obtained in step 1, where
, , ,
( 1) ( ) ( ) ( ).
i j i d i j i j
Pos t Pos t t G t
δ τ
+ = + ⋅ ⋅
uuuuur
•
Step 4: computes the updated position of i as the centroid
of
,
( 1)
i j
Pos t +
across all j’s obtained in step 3, where
,
( 1) ( 1) .
i i j
j
Pos t mean Pos t
+ = +
If there is no vehicle within 3 meters from the updated
position, move to the updated position.
•
Step 5: If
( 1) ( )
i i pos
Pos t Pos t Th+ − <
, terminate the
algorithm and stop updating. Otherwise, go to step 6.
•
Step 6: updates all of its associated shadow prices and go
back to step 1.
In the above steps, constants
d
δ
and
λ
δ
are step sizes, and
po s
Th
is a small threshold for the algorithm to stop. They are
all empirical values gained in Section V. Equation (16) is a
standard approach to update distances strictly based on the
current gradient. However, for a certain update in the distance,
there are unlimited possible positions (e.g., on a circle) for the
transmitter i to move to fulfill the new distance w.r.t. to the
receiver j. Also, for multiple receivers, one transmitter will
update and gain multiple wanted distances. Therefore, in step
3, we use a greedy approach to make the transmitter move
strictly towards/away from the receiver by a wanted distance
along the straight line between itself and the receiver. This
will give a virtual “per-receiver wanted” position for
transmitter i w.r.t. receiver j for the next t, i.e., the
,( 1)
i j
Pos t +
in step 3. Then, in step 4, a unified update of transmitter i’s
position is set to be the centroid of the all virtual per-receiver
wanted positions.
As seen in steps 1-6, our distributed algorithm is based on
geo-location exchanges, which are readily available in V2X
networks, and only local variables, i.e., the shadow prices
needed in (15) are all local shadow prices maintained by node
i. In section V, we will verify that such a distributed algorithm
will guide the vehicles to move toward positions with better
connectivity.
V.
N
UMERICAL
R
ESULTS
In this section, we perform simulations to visualize the
mobility evolvement, test the convergence of our MMU
algorithm, and verify the effectiveness of our algorithm in
randomly generated topologies. Key parameters used for the
physical layer abstraction adopted can be found in Table 2.
TABLE II. P
ARAMETERS
F
OR
P
HY
A
BSTRACTION
Parameters Value
RoI
400*400 m
Transmission power 26 dBm
carrier frequency 2GHz
Noise power -112.45 dBm
Number of subframes 10240
Number of sub-channels 2
Channel model Winner model
Resource pool size 16 = 2 subchannels * 8 subframes
Two driving schemes are tested, namely the UAV mode
and the vehicle swarm platooning (VSP) mode. Vehicles in
UAV mode have no predefined trajectory. They start with
random initial positions and fly freely in all directions. Our
MMU algorithm controls the UAVs to update their positions
in iterations to maintain connectivity. This connectivity-
oriented scenario is seen in many rescue and mission-critical
use cases, where the UAVs form a connected network to
provide temporary coverage for the rescue. Autonomous
vehicles in the VSP mode have their own planned trajectory,
i.e., driving along roads with lane settings at a constant speed.
Our MMU algorithm will derive a position update in each
iteration based on the vehicles’ current positions. The updated
position derived by our MMU is a modification of the initial
desired trajectory of the vehicle to achieve better connectivity.
a.
UAV scenario case study
The results in the UAV scenario obtained are shown in
Fig. 1-2. As can be seen in Fig. 1, the location of the
transmitting UAVs (starting from “Tx
i
(start)” and ending at
“Tx
i
(end)”) are updated iteratively according to the algorithm.
Simulation results show that all transmitters gradually update
their location with shrinking step sizes. The location update
stops when the transmitter is too close to any of the receivers,
i.e., the distance between a transmitter and a receiver is 3
meters. This demonstrates that even though all the transmitters
perform the MMU algorithm independently, their movements
are coordinated and converged at the end. To verify the
effectiveness of the algorithm, the new position is used to
calculate the network utility
( )
U t
after each movement.
Compared to the case where the transmitters do not adjust
their trajectory, the normalized utility gain at iteration t could
be computed by
( ) (0)
( ) .
(0)
U
U t U
gain t U
−
=
(18)
Fig. 1. Moving updates for UAV mode.
In Fig. 2, it can be observed that no matter
d
δ
is equal to
10, 5, or 1, after 4000, 8000, and 45000 position updates, the
algorithm converges and gradually achieves a gain of 73% in
terms of network utility, compared to the constant mobility
case. The final positions of transmitters are better than the
original positions because they minimize the wanted signal
distance and maximize the unwanted interference distance.
Also, in contrast to the greedy approach, where the
transmitters will always move infinitely close to the receiver,
the final positions controlled by the MMU algorithm are not
infinitely close to the receiver, which is attributed to fairness
considerations.
Fig. 2. The normalized gain in network utility.
b.
VSP scenario case study
For the VSP scenarios, we assume a road composed of 6
lanes in a downward direction in Fig. 3. Initially, TX and RX
vehicles’ are platooning along the lanes using the same
constant speed, and all the TX vehicles are behind the RX
vehicles (demonstrated by the red markers). This is a poorly
connected topology, as TX and RX vehicles are apart from
each other. The TX vehicles then perform the MMU algorithm
to look for better trajectories to enhance the connectivity to
RX vehicles. They can accelerate or decelerate to achieve the
position changes given by MMU in each iteration. The MMU
algorithm guide all the TX vehicles to first speed up to catch
0123456
Iteration t
10
4
0
10
20
30
40
50
60
70
80
gain
U
(t) (%)
d
=10
d
=5
d
=1
up with the RX vehicles for a while, i.e., corresponding to the
loose circles in Fig 3. As the desired topology is achieved, the
TX vehicles decelerate to use the same speed as the RX, and
their relative distance remains unchanged after that. In this
scenario, the vehicles are not allowed to change lanes, so the
horizontal movements of the vehicles are limited.
Nevertheless, Fig. 4 shows that our MMU algorithm is still
effective and leads the vehicles to autonomously adjust their
trajectories to achieve a better-connected topology at the end
(demonstrated by the blue markers). The utility gain climbs
continuously and stabilizes at 70% compared to the initial
topology.
Fig. 3. Moving updates with road restrictions.
Fig. 4. The normalized gain in network utility with road restrictions.
c.
Gain verification with random topologies
To verify the effectiveness of our program with random
initial topologies, simulations are done with uniformly
dropped vehicles in the field for the UAV mode. Table 3
shows the parameters used in our simulations.
TABLE III. P
ARAMETERS
F
OR
R
ANDOM
V
EHICLE
D
EPLOYMENT
Parameters Value
Tx dropping distribution Uniformly distributed in RoI
Rx dropping distribution
Evenly distributed in RoI, chosen from
([100,100], [100,300], [120,220],
[250,150], [300,100], [300,300])
Maximum iterations 5000
Step size
d
δ
,
λ
δ
10, 1
Fig. 5 shows the average gain in network utility for one
hundred randomly generated topologies. The average gain is
found to decrease while the vehicles’ density increases.
This
is because the high density of vehicles will limit the trajectory
adjustment and thus reduce the overall gain. Moreover, Fig. 5
validates that our algorithm updates vehicles’ locations to
achieve higher network utility by 20-48% in terms of the
aggregated packet reception.
Fig. 5. The average gain of 100 tests.
VI.
C
ONCLUSION
In this paper, we formulated the distributed maximization
problem for C-V2X network connectivity over mobility
adjustment and proved the concavity of the problem. We
developed a Multi-node-Mobility-Update (MMU) algorithm
to dynamically adjust the vehicle movements in vehicular
networks to maximize the aggregated network utility. The
proposed MMU algorithm is demonstrated to converge with
the distributed mobility updates. Compared to the fixed
trajectory scenario, our MMU algorithm improves the
network utility by up to 48%.
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0 1000 2000 3 000 4000 5000 6000 7000 8000 9000 10000
Iteration t
0
10
20
30
40
50
60
70
80
gain
U
(t) (%)
