![Vehicle Platoon Under Mobile Jamming Attacker in the literature [2]. The spacing policy considered in this paper is based on the velocity-dependent spacing policy [2]. That is, the distance between the two vehicles increases if the velocity of the preceding vehicle increases, and vice versa. The string stability requirement is highly influenced by the value of headway-time h d ; as a result this parameter plays a crucial role in operating a safe and efficient CACC system. In this structure, K i (s) = k pi + k di s is a feedback (PD) controller where k di is the bandwidth of the controller and is chosen such that k di << 1/η i [3]. The PD controller parameters k pi and k di are set up in such a way that the internal stability of the vehicle dynamics is satisfied. In [2], the feed-forward controller F i (s) = (H i (s)G i (s)s 2 ) −1 has been designed such that the zero steady state spacing error (e i (t) = 0 as t → ∞) is achievable. u b,i and u f,i also represent the controllers' output, respectively. The summation of these two outputs provide the commanded acceleration u i for the ith vehicle. Considering velocity-dependent spacing policy, the desired distance is defined as h d v i (t). Therefore, spacing error, e i (t), at each time instant t can be determined by the difference between the actual relative distance, q i−1 (t) − q i (t), measured by the radar, and the desired distance, h d v i (t), as follows:](https://www.researchgate.net/profile/Amir-Alipour-Fanid/publication/316530660/figure/fig1/AS:576569238188032@1514476226227/Vehicle-Platoon-Under-Mobile-Jamming-Attacker-in-the-literature-2-The-spacing-policy_Q320.jpg)
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String Stability Analysis of Cooperative Adaptive
Cruise Control Under Jamming Attacks
Amir Alipour-Fanid∗, Monireh Dabaghchian∗, Hengrun Zhang†and Kai Zeng∗
∗Electrical and Computer Engineering Department,
†Computer Science Department
George Mason University, Fairfax, Virginia 22030
Email: {aalipour∗, mdabaghc∗, hzhang18†, kzeng2∗}@gmu.edu
Abstract—Cooperative Adaptive Cruise Control (CACC) is
considered as a key enabling technology to automatically reg-
ulate the inter-vehicle distances in a vehicle platooning while
maintaining the string stability. Although the cyber and physical
parts in the existing CACC systems are integrated in one control
framework, the research on realistic modeling and security issues
of these systems are still largely open. A good modeling of
cyber characteristics and awareness of cyber attacks impact
on the CACC operation leads to a better understanding of
system design and defense mechanisms. In this paper, we conduct
a comprehensive analysis on the vehicle string stability by
considering a realistic wireless channel under a mobile reactive
jamming attack. We examine the stability of the platoon under
attacks by conducting extensive simulations for a wide range
of realworld lead vehicle’s acceleration profiles. We utilize time-
domain definition of string stability to delineate the impact of
the jamming attacks on the CACC system’s functionality and
string stability. We also examine the attacker’s possible locations
at which it can destabilize the string.
I. INTRODUCTION
Vehicular Cyber-physical systems (CPS) expand the capa-
bilities of the vehicles through the integration of computation,
communication, and control [1]. Vehicle platooning is one of
the important vehicular CPS applications that operates based
on tight coupling of wireless communication and physical pro-
cesses. Cooperative Adaptive Cruise Control (CACC) system
as an extension of Adaptive Cruise Control (ACC) is proposed
to constitute vehicle platooning formation [2], [3].
Based on CACC, each vehicle in the platoon uses two
sources of information, absolute relative distance measured by
the radar and acceleration information of the preceding vehicle
received through the wireless channel established apriori.
Connected vehicles equipped with CACC systems are able
to adjust inter-vehicle distances such that the traffic throughput
is increased by running as close as possible to each other
with safety guarantee. In addition, this technology reduces
fuel consumption and provides more comfort to the users in
comparison to solely human control of vehicles [4].
However, despite tremendous benefits attained by integrat-
ing the cyber (wireless communication) and physical processes
in the CACC systems, there are several critical challenges
remained.
First, considering tight coupling of cyber and control parts,
the practical modeling of these parts play an important role to
evaluate the performance of CACC system before a real imple-
mentation. Second, the CACC systems are highly susceptible
to cyber attacks that can create significant disturbances in safe
and efficient operation of these systems [5].
In a CACC enabled vehicle platoon, the distance between
vehicles may change depending on the lead vehicle’s behavior
and spacing policy [6]. This variation in inter-vehicle distance
affects the wireless channel conditions which further affects
the received-signal-strength (RSS) and packet delivery ratio.
However, in most of the existing literature, this coupling
between the system state (inter-vehicle distance) and wireless
channel conditions is ignored [2], [3], [7], [8].
In this paper, we consider a two-ray ground-reflection model
(Line-of Sight and ground-reflected propagation) between the
transmitters and the receivers and study the path loss impact
on the CACC system’s functionality [9], [10]. Furthermore,
with the assumption of two-ray ground-reflection model for
the wireless channel, we study the string stability of the CACC
system under a mobile reactive jamming attack. The attacker
jams the wireless channel established among the vehicles in
order to prevent the receivers from decoding the transmitted
packet with the purpose of destabilizing the platoon. If the
attacker is successful to jam the packet, the CACC system
will not work on the normal status until the next packet is
received successfully. We evaluate the jamming attack impact
on the string stability by employing the time-domain definition
of string stability.
We compare the string stability of two basic cases: CACC
with memory and memoryless. In the case with memory,
the follower vehicle remembers the last successfully received
acceleration information from the immediate preceding vehicle
and feeds it to the feed-forward controller. In the memoryless
case, whenever the acceleration information is lost due to
jamming or channel fading, the following vehicle just assumes
it is zero (the preceding vehicle maintains the same velocity).
Finally, by employing string stability criteria, we aim to find
the best locations for the attacker to launch jamming attacks.
Along the string, we examine the possible attacking locations
at which the attacker can destabilize the platoon.
We summarize the contributions of this paper as follows:
•We study the path loss and ground-reflected signal effects
on the CACC performance by modeling the wireless
channel as a two-ray ground-reflected propagation.
•We consider a mobile reactive jamming attack on the
wireless channels and investigate the impact of jamming
attack on the CACC functionality for the two cases of
CACC with and without memory.
•We examine the attacker’s possible locations along the
string at which it can destabilize the string.
•We conduct extensive simulations to analyze the string
stability by utilizing its time-domain definition.
Our simulation results show that the CACC based platoon
system is highly sensitive to jamming attacks and its perfor-
mance can be compromised by a reactive jammer. In addition,
we identify that the location being close to the second vehicle
following the lead vehicle is the best location for the mobile
jamming attacker to destabilize the platoon.
II. RE LATE D WOR K
Existing works [2], [3], [11] consider normal operation of
CACC system without any possibility of the packet loss due to
wireless channel condition or outsider attacker. Therefore, the
frequency response of the system is derivable in these cases
and the string stability can be analyzed in a fairly nice format
in the frequency-domain. Necessary and sufficient conditions
for string stability of a heterogeneous platoon are studied
by Naus et al. [2]. Network delay and sampling effects are
introduced in the string stability analysis in [3]. The delay is
assumed identical in all the communication links and string
stability is investigated based on different sampling interval
and headway-time. In [7], the robustness of a CACC system
to communication delays is studied and an upper bound on
the delay is derived such that the string maintains its stability.
However, the impact of distance variation between vehicles on
the channel conditions is not considered in the aforementioned
works.
There are few works focusing on the security of vehicle
platooning in terms of attacking on wireless communication
or control components. In [12], an insider attacker attacks on
controller gains of a vehicle in the platoon. The attacker has the
capability of modifying the gains such that it can destabilize
the platoon. In [13], mass-spring-damper follower dynamics
model is considered for studying the platoon performance
under attack. The new class of the attack proposed in this
paper is based on vehicle misbehavior. This work shows that
the attacker is effective when the attacker is near the rear of
the platoon. However, this work is different from our work in
terms of platoon modeling, attacker’s nature, the purpose of
the attacker and the evaluation method employed to measure
the impact of the attack. In another work [5], various security
vulnerabilities on the CACC system have been identified.
Message falsification and radio jamming attack’s effects are
studied through Vehicular Network Open Simulator. However,
the CACC control structure and jamming attacking strategies
are considered as a black box in the simulation environments.
The coupling between the system state and wireless commu-
nication channel condition is not well modeled.
III. SYS TE M MOD EL
We consider a platoon of multiple vehicles. Each vehicle
has a direct communication with its immediately following
and preceding vehicle using Dedicated Short Range Commu-
nication (DSRC) technology. There is a mobile jammer (e.g.,
a drone), attacking on the wireless communication channel
among the vehicles.
A. Vehicle String
We consider a platoon of vehicles consisting of nho-
mogenous vehicles (identical longitudinal dynamic properties)
shown in Fig 1. Each vehicle is equipped with a CACC system.
In other words, each vehicle is equipped with a radar in front
of the vehicle to measure the absolute relative distance from
the vehicle ahead of it and a DSRC technique to transmit its
acceleration information to its following vehicle.
B. Wireless Channel
Each vehicle in the platoon is equipped with DSRC system
based on which acceleration information of each vehicle is
sent every 100ms to the following vehicle. DSRC operates in
the spectrum frequency of 75MHz in the 5.9 GHz band. For
the wireless channel, we assume it is subject to Additive White
Gaussian Noise (AWGN). We consider a two-ray propagation
channel model, Line-Of-Sight (LOS) and ground-reflected
wave propagation model [10]. By this modeling, we will be
able to consider ground-reflected ray effect in addition to free
space path loss impact on the received-signal-strength (RSS).
C. Attacker
We consider a mobile jamming attacker. The jammer is
mounted on a drone flying over the platoon. Since the power
source of the drone is limited, we assume a reactive jammer
[14]. Reactive jammer has the capability of sensing chan-
nels and launching its jamming signal whenever the vehicles
transmit their acceleration information through the wireless
medium to their immediately following vehicles. All legitimate
established wireless links among each pair of transmitters and
receivers in the platoon are under jamming attack.
IV. PROBLEM FORMULATIO N
A. Longitudinal Vehicle Dynamics
The common linearized third-order state space representa-
tion used for modeling longitudinal vehicle dynamics is as
follows [3]:
˙qi(t) = vi(t),˙vi(t) = ai(t),˙ai(t) = −η−1
i+η−1
iui(t)
(1)
Where qi(t),vi(t)and ai(t)are absolute position, velocity
and acceleration of the ith vehicle, respectively. ηiand ui(t)
represent the internal actuator dynamics and the commanded
acceleration, respectively. The transfer function of the longi-
tudinal vehicle dynamics Gi(s)is derived as follows:
Gi(s) = Qi(s)
Ui(s)=1
s2(ηis+ 1) (2)
Where Qi(s) = L(qi(t)) and Ui(s) = L(ui(t)) represent
the Laplace transformation of the absolute position and the
commanded acceleration for the ith vehicle, respectively.
B. CACC Control Structure and State Space Representation
The structure of a CACC system is shown in Fig. 2. In
this model, Hi(s) = 1 + hdsrepresents the spacing policy
dynamics. Headway-time constant, hd, indicates the time that
it takes vehicle ito arrive at the same position as its preceding
vehicle (i−1). Several spacing policies have been studied
Figure 1: Vehicle Platoon Under Mobile Jamming Attacker
in the literature [2]. The spacing policy considered in this
paper is based on the velocity-dependent spacing policy [2].
That is, the distance between the two vehicles increases if the
velocity of the preceding vehicle increases, and vice versa.
The string stability requirement is highly influenced by the
value of headway-time hd; as a result this parameter plays a
crucial role in operating a safe and efficient CACC system.
In this structure, Ki(s) = kpi +kdisis a feedback (PD)
controller where kdi is the bandwidth of the controller and
is chosen such that kdi << 1/ηi[3]. The PD controller
parameters kpi and kdi are set up in such a way that the
internal stability of the vehicle dynamics is satisfied. In [2],
the feed-forward controller Fi(s) = (Hi(s)Gi(s)s2)−1has
been designed such that the zero steady state spacing error
(ei(t)=0as t→ ∞) is achievable. ub,i and uf,i also represent
the controllers’ output, respectively. The summation of these
two outputs provide the commanded acceleration uifor the
ith vehicle.
Considering velocity-dependent spacing policy, the desired
distance is defined as hdvi(t). Therefore, spacing error, ei(t),
at each time instant tcan be determined by the difference
between the actual relative distance, qi−1(t)−qi(t), measured
by the radar, and the desired distance, hdvi(t), as follows:
ei(t) = qi−1(t)−qi(t)−hdvi(t)(3)
State space representation of the CACC control structure in
Fig. 2 of the ith vehicle is given as follows [3]:
˙ei(t) = vi−1(t)−vi(t)−hdai(t)
˙vi(t) = ai(t)
˙ai(t) = −η−1
iai(t) + η−1
iui(t)
˙uf,i (t) = −h−1
duf,i (t) + h−1
d˜ui−1(t)
(4)
The acceleration of the (i−1)th vehicle, ui−1(t), is trans-
mitted through the established wireless channel to the ith
vehicle. The received acceleration information is denoted by
˜ui−1(t)at the receiver of the following vehicle, i. From (4)
we see that the output of the feed-forward controller, uf,i(t),
depends on the received acceleration, ˜ui−1(t), of the (i−1)th
vehicle. For simplicity, we omit the continuous-time domain
representation tin the remained article. By defining the state
vector xT
i= [eiviaiuf,i ], the state space variables are
augmented in one variable and from (4) the continuous-time
CACC vehicle dynamics is represented as follows:
˙xi=Aixi+Ai−1xi−1+Bsui+Bc˜ui−1(5)
Due to limited space we refer the reader to [3] for the values
of Ai,Ai−1,Bs,Bcmatrices and vectors.
C. Vehicles String State Space Representation
The state space representation of the CACC control structure
in a vehicle string is as follows [3]:
˙
¯xn=¯
An¯xn+¯
Bc˜un−1+¯
Bsul(6)
Where ˙
¯xn= [xT
1xT
2... xT
n]Trepresents the aug-
mented state space variables of the vehicles in the string.
˜un−1= [˜u0˜u1... ˜un−1]Tis a vector where its elements
denote the received acceleration information of the associated
vehicle in its immediately following vehicle and ulis an
arbitrary commanded acceleration taken by the lead vehicle.
The time-invariant matrices ¯
An,¯
Bcand ¯
Bswith constant
entities can be found in [3]. Now we drive the discrete-
time representation for the continuous-time system in (6) as
follows:
xn[k+ 1] = Anxn[k] + Bc˜un−1[k] + Bsul[k]
An=e¯
Anh,Bs=Zh
0
e¯
Anνdν. ¯
Bs,Bc=Zh
0
e¯
Anνdν. ¯
Bc
(7)
Where his the sampling interval.
D. String Stability
The lead vehicle’s acceleration and deceleration will pro-
duce spacing error eibetween each pair of vehicles in the
the platoon. String stability requires spacing error attenuation
along the vehicle string. This can be shown as follows [7]:
kenk∞<ken−1k∞< ... < ke2k∞<ke1k∞(8)
Hence, the time domain definition of the string stability will
be:
maxt|en(t)|<maxt|en−1(t)|< ...
... < maxt|e2(t)|<maxt|e1(t)|(9)
When the transfer function of CACC system is drivable, the
string stability is evaluated by the frequency domain definition
and string will be stable if the following condition is satisfied
[2]:
|Γ(jω)|=
Ei(jω)
Ei−1(jω)
≤1∀ω, i = 1, ..., n (10)
In the next section, we will incorporate jamming attack and
wireless channel condition effects to the equation (7) in order
to analyze the string stability.
V. JAMMING ATTACK O N CAC C
A. Wireless Channel and Attack Impact
Considering two-ray channel modeling, received signal’s
signal-to-noise ratio (SNR) alters as the vehicle’s distance
varies with the preceding vehicle. Moreover, the SNR drops
dramatically at some distances due to the carrier phases
cancellation of the two paths (LOS and ground-reflected)
signal. Consequentially, the SNR level attenuation due to LOS
path loss and signal cancellation due to opposite carrier phases
received from two paths, affect the successful packet delivery
ratio (PDR) in the long run and degrade the performance of
the CACC system.
A reactive jammer mounted on a drone flying over the
platoon emits its jamming signal over the wireless network
whenever it senses that the communication traffic is happening
in the network. Due to the stochastic nature of the noise and
jamming signals’ effect in the channel, the attacker’s success
is probabilistic at time kin each link between a pair of
vehicles in the platoon. We consider a signal to interference
plus noise ratio (SINR) model to derive the probability of
successful packet delivery. In this model, the jamming signal
is considered as the interference signal.
We determine vector pk= [pk
0pk
1... pk
n−1]Tsuch that
pk
i−1,i= 1, ..., n, denotes the probability of successful packet
delivery of the (i−1)th vehicle at the ith vehicle’s receiver
at time k. Thus, the PDR is defined as follows:
pk
i−1=P Pt
Lp(dk
i−1)(N0+I)≥SI N R0!i= 1, ..., n
(11)
Where Pdenotes the probability. Ptand N0are the signal
and noise powers, respectively. Idenotes the jamming signal
power and SINR0represents some constant threshold. dk
i−1
denotes the actual distance between ith vehicle and its pre-
ceding vehicle (i−1)th at discrete time k.Lp(dk
i−1)indicates
the path-loss value at a given distance and time.
Now, we define a Bernoulli random variable βk
i−1to indicate
the packet successful delivery which is defined as follows.
βk
i−1=(1, pk
i−1
0,1−pk
i−1
(12)
For k= 1,2, ... and i= 1,2, ..., n. Vector βk=
[βk
0βk
1... βk
n−1]Tshows the random variables of suc-
cessful packet delivery among each pair of vehicles at time
kand the vector pk= [pk
0pk
1...pk
n−1]Tindicates the
corresponding probabilities.
B. Memory Block
To comply with the DSRC standard protocol, the preced-
ing vehicle’s acceleration information, ui−1is sampled with
sampling time tk=kh where k= 1,2, ...and h= 100ms,
Fig 2. These information, ui−1[k], for k= 1,2, ... in the form
of packets are sent over a wireless channel to the following
vehicle, i. As the packets are transmitted through the channel,
they are subject to the channel condition and jamming attack
impact. To show this, the vector βk= [βk
0βk
1... βk
n−1]T
Figure 2: CACC Control Structure with Memory and ZOH
which has been determined in (12) as a Bernoulli random
variable is multiplied by the transmitted information. Then at
the output of the wireless channel we will have βk
i−1ui−1[k].
Now before feeding the received information to the feed-
forward controller, we use a memory block in the following
vehicle’s CACC control structure, Fig 2. The low-cost memory
has the capacity for saving only one packet information. Each
time if the memory receives the packet successfully, it updates
the memory, otherwise it keeps the last successful received
information in the memory. The following model shows how
the feed-forward controller uses the stored information in the
memory as its input:
˜ui−1[k] = βk
i−1ui−1[k] + (1 −βk
i−1)˜ui−1[k−1] (13)
For i= 1,2, ..., n where ˜ui−1[k]is the received acceleration
of the i−1th vehicle at the receiver of ith vehicle, subject to the
jamming attack and wireless channel condition impact at time
k. As it can be realized, in case of successful packet reception
(βk
i−1= 1), the output of the memory block will be ui−1[k].
However, if the packet is jammed successfully or dropped due
to path loss or ground-reflected signal effect (βk
i−1= 0), the
output of the memory block will be the last successful received
packet ˜ui−1[k−1]. Then we use ZOH (Zero Order Holder)
to convert the discrete-time signal ˜ui−1[k]to the continuous-
time signal ˜ui−1which will be fed into the feed-forward
controller Fi(s)shown in Fig 2. Now we substitute (13) in (7)
to obtain the string state space representation of the platoon
under reactive jamming attack and wireless channel condition
impact. Then we have
xn[k+ 1] = Anxn[k] + Bcβk
n−1un−1[k]
+Bc(1 −βk
n−1)˜un−1[k−1] + Bsul[k](14)
In order to analyze the string stability in the frequency-
domain using Γ(jω)in (10), the string state space equation
needs to be deterministic. However, due to the presence of
stochastic variable βk
i−1in (14), the derived string state space
is probabilistic at each given time k. Therefore, we adapt the
time-domain definition of string stability for analyzing the
string state space equation derived in (14), discussed in the
next section.
VI. STRING STAB IL IT Y ANA LYSI S
A. Simulation Setting
We consider a platoon constructed with n= 11 vehicles.
The lead vehicle’s index is zero and the rest of the vehicles
are ordered from one to ten moving down the platoon. We
assume that the vehicles are homogenous and the internal
(a) A sample lead vehicle’s acceleration profile (b) Frequency-domain string stability for ACC
mode
(c) Time-domain string stability for ACC mode
(d) A sample lead vehicle’s velocity profile (e) Frequency-domain string stability for CACC
mode
(f) Time-domain string stability for CACC mode
Figure 3: Simulation results I
actuator dynamics are identical for all vehicles in the platoon
(ηi=η= 0.1for i= 1,2, ..., n). kdi =kd= 0.5<< 1/η and
kpi =kp=k2
d= 0.25 for i= 1, ..., n are chosen to satisfy the
internal stability of the vehicle dynamics. We generate 1,000
acceleration profiles using the random phase multi-sine signal
generation method [15]. These acceleration profiles model the
lead vehicle’s real-world actions. One sample of lead vehicle’s
acceleration and the corresponding velocity profile up to 100
seconds are shown in Fig. 3(a) and 3(d), respectively. For
each acceleration profile, we compute the maximum spacing
error produced during 500 seconds at each vehicle. Then, we
average over all the maximum errors of each vehicle to find
the average maximum errors of each vehicle. We also assume
that the signal transmission power for all vehicles is fixed and
identical all the time for all scenarios. The mobile jammer’s
vertical distance from the horizontal platoon and its jamming
signal power is also fixed all the time for all scenarios.
B. Validity of Time-Domain String Stability Analysis
Existing string stability analysis are based on frequency-
domain techniques. For our modeling in (14), this method
cannot be applied because of time-varying probabilistic packet
successful delivery at each receiver in the platoon. In order
to tackle this challenge, for the first time, we analyze the
time-domain string stability under a mobile jamming attacker.
We validate our analysis through comparing frequency-domain
and time-domain approaches for the case of perfect channel
condition, no attack and normal operation of the platoon.
Figures 3(b) and 3(c) illustrate the string stability analysis of
ACC (CACC without V2V communication) systems in the
frequency and time domains, respectively. By comparing the
figures, we observe that in both domains for the headway-
time 0.5 seconds and 1.5 seconds string is unstable. However,
string is stable when the headway-time is set to 2.2 seconds
and 3 seconds. Also, for CACC systems, Figures 3(e) and 3(f)
show that in both domains for the headway-time 0.2 seconds
string is unstable. However, for the headway-time 0.5 seconds,
1 second and 2 seconds string is stable. As a result, string
stability analysis of both frequency-domain and time-domain
are highly consistent and endorse each other.
C. Two-ray Channel Modeling Impact and No Attack
We consider a two-ray propagation model for the wireless
channels among the vehicles. We assume if the received
signal’s SNR is below the threshold SN R0= 20dB, the
packet is dropped, otherwise it is decoded successfully being
fed into the feed-forward controller. We investigate chan-
nels’ condition impact by examining string stability with and
without utilizing the memory block. In case of memoryless
(without the memory block), if the packet gets lost, the vehicle
considers its preceding vehicle maintains the same velocity
(zero acceleration). Figure 4(a) illustrates that overall the path
loss degrades the performance of CACC by incrementing the
magnitude of the spacing error. But the CACC controllers can
prevent those errors from getting amplified upstream, thus still
maintain the string stability.
D. Jamming Attack Impact
We consider a jammer above the second vehicle (i= 1)
with a constant vertical distance from it. The jammer emits
its signal over the platoon wireless ad-hoc network when it
senses communication traffic. Fig. 4(b) shows the capability of
(a) Two-ray channel modeling impact on string
stability
(b) Jamming attack impact on string stability with
memory block and different headway-time
(c) Attacker’s location impact on string stability
Figure 4: Simulation results II
the reactive attacker to destabilize the platoon. However, when
the memory block is utilized, the magnitude of the propagated
error is reduced, although the string is still unstable. From
Fig. 4(b), it can also be observed that the error in the presence
of the attacker does not propagate upstream the string, if the
headway-time is increased from 1second to 1.7seconds. Note
that as illustrated in Fig. 3(c), for the ACC mode the minimum
headway-time to have a stable string is 2.2seconds, however
the string under attack is stable for the headway-time 1.7
seconds in the CACC mode with memory block.
E. Attacker’s Location Impact on String Stability
We assume the head-way time is fixed to 1second and the
memory block is used in the control structure. As Fig. 4(c)
shows, when the attacker is above the second vehicle (i= 1),
not only the error propagates upstream the string, but also
the magnitude of errors are high in comparison to the no
attack scenarios Fig. 3(f). Also, in Fig. 4(c), we show that
as the attacker moves toward down in the platoon, its ability
to destabilize the platoon is diminished. This is because as
the attacker goes far away from the lead vehicle, the produced
spacing error magnitude for the front vehicles are decreased
since the packet delivery ratio is increased. As a result, as the
attacker goes away from the lead vehicle the more spacing
error is corrected by the CACC controllers such that when the
attacker is above the sixth vehicle in the platoon the string
becomes stable. As a result the more the attacker is close
to the lead vehicle the more effective it will be in terms of
destabilizing the platoon. Therefore, we conclude that the best
location for the attacker to launch its jamming signal is above
the second vehicle (i= 1).
VII. CONCLUSIONS
In this paper, we studied the string stability of intercon-
nected vehicles equipped with CACC systems under two-
ray propagation model for the channel and mobile jamming
attacker. We incorporated channel condition and jamming
attack impact on the string state space representation and
analyzed string stability through extensive simulations. We
show that signal’s power attenuation due to two-ray path loss
model degrades the performance of the CACC system. Also,
the analysis indicates that jamming attack can adversely desta-
bilize the string. However, by increasing the headway-time and
using the memory block, the stability can be improved. Finally,
we discovered that the best possible location for the attacker
to destabilize the string is above the second vehicle and as
the attacker moves down in the string, its impact in terms of
destabilizing the platoon is diminished.
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