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1
Performance Analysis of Delay-Constrained
Wireless Energy Harvesting Communication
Networks under Jamming Attacks
Dusit Niyato1, Ping Wang1, Dong In Kim2, Zhu Han3, and Lu Xiao1
1School of Computer Engineering, Nanyang Technological University (NTU), Singapore
2School of Information and Communication Engineering, Sungkyunkwan University (SKKU), Korea
3Department of Electrical and Computer Engineering, University of Houston, Texas, USA
Abstract—In wireless energy harvesting communication net-
works, a user receives wireless energy released by an ambient
or dedicated energy source, and uses that energy for delay
constrained data transmission. However, such data transmission
can be susceptible to a jamming attack from a nearby attacker
also harvesting from the wireless energy source. In this paper, we
consider such a scenario and present performance analysis. In
particular, we develop an analytical model for the network based
on a Markov chain to obtain various performance measures for
the user including throughput and delay distribution. The perfor-
mance evaluation shows some interesting results. For example,
under the jamming attack, there is the maximum throughput
achievable by the user. We also validate the analytical model
using simulation.
Index Terms—Wireless harvesting communication networks,
jamming attack, delay-constrained.
I. INT ROD UC TI ON
Wireless energy harvesting or wireless powered commu-
nication networks allow a user’s device to receive wireless
energy (e.g., RF signals) transferred from energy sources [1].
The device can use the energy for data transmission, removing
reliance on limited supplied energy from a battery or external
sources. The data generated by the user can be real-time
(e.g., multimedia or biosignal) that it has to be transmitted
before a certain deadline. However, the data transmission by
the user can be susceptible to jamming by a malicious node
(i.e., an attacker) trying to disrupt the operation or degrade
the performance of the network. The attacker can also receive
the energy from the same wireless energy source, incurring
zero cost in jamming. Therefore, it is important to analyze
the the wireless energy harvesting communication network to
investigate the network performance (e.g., delay performance),
impact of the jamming attack (e.g., detrimental throughput),
and optimal parameter setting (e.g., packet generation rate).
Jamming attack has been considered in wireless networks
as it can cause severe performance degradation or interruption
of network operations. Traditionally, the attacker uses fixed
energy supply to perform jamming. The authors of [2] an-
alyzed the IEEE 802.11 networks under different jamming
attack strategies (e.g., periodic and random jamming). A
Markov chain model was developed to investigate the effect
of jamming. The optimization of the network with users and
attackers was investigated, e.g., using game theory [3], [4],
[5], [6]. Particularly, the authors of [5] presented an analytical
model of jamming attack in time-critical wireless applications.
The jamming attack detection based on estimation (JADE)
scheme was also proposed to achieve robust jamming detection
for the user. A Markov decision process was used [7] to
find an optimal transmission policy under the attack. In the
wireless energy harvesting communication network, the major
security concern is eavesdropping in which eavesdroppers exist
in the network and secretly decode information from the
users. A few works analyzed and optimized secrecy rate in
the network, e.g., [8], [9], [10]. [11] considered a jammer,
but to jam eavesdroppers to improve the secrecy rate of the
legitimate users. None of existing work considers the jamming
attack to degrade the user’s performance in the wireless energy
harvesting communication network.
In this paper, we consider the wireless energy harvesting
communication networks with a user and attacker. The user
transmits delay constrained packets to a receiver. If the packet
cannot be successfully transmitted before its deadline, it will
be dropped. There is a wireless energy source in the network,
releasing or transferring wireless energy. The user harvests the
energy and uses it for packet transmission. However, a nearby
attacker can also receive the energy and use the energy for the
jamming attack. We present an analytical model based on a
Markov chain to analyze the performance of the network under
the jamming attack. We derive the throughput of the user (i.e.,
the total amount of packets per unit time that are transmitted
successfully before the deadline). The performance evaluation
provides the model validation using simulation.
Note that [12] considers a similar jamming attack in wire-
less powered communication network. However, it does not
consider delay constrained data transmission. Additionally, the
energy harvesting process of the user and attacker are assumed
to be independent.
The rest of this paper is organized as follows. Section II
describes the system model and states the assumptions used
in this paper. Section III presents the Markov chain model
and derive performance measures. Section IV presents the
performance evaluation. Section V summarizes the paper.
2
II. SY ST EM MO DE L
A. Network Model
+
-
+
-
User
Wireless
energy
source
Energy
storage
Transmitter
Attacker
Jamming
attack
Receiver
Packet
arrival
Packet drop
Fig. 1. System model.
We consider the wireless energy transfer/harvesting com-
munication network as shown in Fig. 1. In the network,
there are the legitimate user and attacker. The user harvests
wireless energy from the wireless energy source (e.g., an RF
source). The harvested energy is stored in the energy storage
of the user and the energy is used to transmit his/her packet.
The packet generated by a user’s application will be stored
in the data queue. However, the packet has the maximum
delay limit (i.e., deadline). That is, if the packet cannot be
transmitted successfully before the deadline, the packet will
be discarded from the queue. The maximum delay limit is
fixed for all packets and it is measured from when the packet
is generated. The attacker secretly harvests energy from the
wireless energy source. Similarly, the harvested energy is
stored in the energy storage. The attacker requires certain
units of energy to perform a jamming attack. If the jamming
attack is performed, the packet transmission by the user will
be corrupted. If the deadline of the corrupted packet is not
reached, the user will re-transmit the packet.
Note that the energy level of the energy storage of the user
and the energy unit of the attacker can be different, depending
on their circuit characteristics. Additionally, we consider the
out-of-band energy transfer/harvesting network. In particular,
the user and attacker can harvest energy, transmit a packet,
and perform the jamming attack simultaneously.
B. Assumptions
To analyze the performance of the wireless energy trans-
fer/harvesting communication network with jamming attack,
we will develop an analytical model based on a Markov chain.
We make the following assumptions for the user.
•We consider a time slotted system, where packet trans-
mission and jamming attack align to a time slot structure.
•The packet arrival/generation probability of the user is
denoted by α.
•The maximum delay limit (i.e., deadline) of the packet is
denoted by Dtime slots.
•The successful packet transmission probability (i.e., with-
out the jamming attack) of the user is denoted by µ.
•The maximum energy level of the energy storage of the
user is denoted by E.
•The wireless energy source transfers energy with prob-
ability λ. Therefore, the energy level of the user can
increase by one with the probability λ.
•If the user transmits a packet, the energy level of the
storage decreases by one..
The following assumptions are made for the attacker.
•Given that the wireless energy source transfers energy,
the attacker can harvest one unit of the energy with
probability γ.
•The maximum units of the energy storage of the attacker
is denoted by B. Without loss of generality, the attacker
performs the jamming attack when there is Bunits of
energy in its storage.
•The attacker cannot harvest wireless energy from the
user’s transmission (e.g., the user transmits at much lower
power than that of the energy source).
III. QUEUEING MODEL
In this section, we present a Markov chain model (i.e., a
queueing model) to analyze the performance of the user in
the wireless energy harvesting communication network with
the attacker. We first show the state space. Then we explain
the delay state transition and the transition matrix afterward.
A. State Space
The discrete-time Markov chain of the network has the
following state space,
Ω = D0,D1, . . . , DD,E,B;Dd∈ {0,1},
E ∈ {0,1, . . . , E },B ∈ {0,1, . . . , B},(1)
where Ddrepresents the number of packets that is experi-
encing the delay of dtime slots. Since only one packet can
be generated in a time slot, the maximum number of packets
having a certain delay is one. Erepresents the energy level of
the user, and Brepresents the unit of energy that the attacker
accumulates.
B. Delay State Transition
In every time slot, the packet can arrive at the queue of
the user. Similarly, if there is enough energy in the energy
storage of the user, the packet may depart from the queue.
We model the delay state of the packet using variables Ddfor
d= 0,1, . . . , D.
There are four cases associated with the delay state transi-
tion.
1) Without packet arrival and without packet departure: In
this case, the delay of each packet will increase by one,
and there is no new packet in the queue of the user.
The state will be Dd=Dd−1, for d=D, D −1, . . . , 1
and D0= 0. In particular, The delay dof a packet will
3
become d+ 1 in each time slot, and there is no new
packet with the delay 0. Note that the packet with the
maximum delay Dwill be removed from the queue by
either successfully transmitted or discarded (i.e., DD=
DD−1). The probability for this case is (1 −α)(1 −
ˆµ(E,B)).
2) With packet arrival and without packet departure: The
delay of each packet will increase by one, and there is
new packet in the queue. The state will be Dd=Dd−1,
for d=D, D −1, . . . , 1and D0= 1. Here, the new
packet will have the delay 0. The probability for this
case is α(1 −ˆµ(E,B)).
3) Without packet arrival and with packet departure: The
head-of-queue packet with the largest delay in the queue
will be removed. The largest delay is denoted by dL=
maxd∈{D,D−1,...,0}Ddsubject to Dd= 1. In this case,
the state will become Dd=Dd−1, for d=dL, dL−
1, . . . , 1and D0= 0. Again, there is no packet with the
delay 0. The probability for this case is (1 −α)ˆµ(E,B).
4) With packet arrival and with packet departure: Similarly,
the head-of-queue packet with the largest delay will be
removed. The state will be Dd=Dd−1, for d=dL, dL−
1, . . . , 1and D0= 1. The probability for this case is
αˆµ(E,B).
ˆµ(E,B)is the actual packet departure probability. This prob-
ability can be defined based on the energy states of the user
and attacker (i.e., Eand B, respectively) as follows:
ˆµ(E,B) = µ, E>0and B =B,
0,otherwise.(2)
The packet departure probability is the successful packet
transmission if the user has enough energy, and the attacker
does not perform the jamming attack due to insufficient energy.
Otherwise, the packet will not be successfully transmitted.
Figure 2 illustrates an example of state transition. The
maximum delay limit is D= 3. The current state is
(D0,D1,D2,D3) = (1,0,1,0). For example, without packet
arrival and without packet departure, the state D2is shifted
to D3, and the state D0is shifted to D1. The new state
becomes (0,1,0,1). For another example, with packet arrival
and with packet departure, the state D2is clear to 0 (i.e.,
packet departure), the state D0is shifted to D1, and the state
D0is set to 1 (i.e., packet arrival). The new state then becomes
(1,1,0,0).
C. Transition Matrix
Let Dq(E,B)denote the transition matrix of the delay state
when there are qpackets in the queue given the energy states
Eand Bof the user and attacker, respectively. The element of
the matrix Dq(E,B)corresponds to the current delay state
(D0, . . . , DD)and the next delay state (D′
0, . . . , D′
D). The
element of this matrix is obtained as presented in Section III-B.
Then, the matrix Dq(E,B)is derived based on the different
cases as follows:
D0,D1,D2,D3
1, 0, 1, 0
With packet arrival and
without packet departure
Without packet arrival and
without packet departure
Without packet arrival and
with packet departure
With packet arrival and
with packet departure
D0,D1,D2,D3
1, 1, 0, 0
D0,D1,D2,D3
0, 1, 0, 0
D0,D1,D2,D3
1, 1, 0, 1
D0,D1,D2,D3
0, 1, 0, 1
Fig. 2. Example of state transition.
•For q= 0, there is no packet transmission, and hence
the energy of the user will increase if there is wireless
energy transfer, or will remain the same if there is no
wireless energy from the energy source. Therefore, the
elements of matrix Dq=0(E,B)in other rows except that
associated with the state (D0, . . . , DD) = (0, . . . , 0) will
be zero.
•For q > 0, there could be packet transmission, and
hence the energy of the user will decrease. Therefore,
the elements of matrix Dq>0(E,B)associated with the
state (D0, . . . , DD) = (0, . . . , 0) will be zero.
Then, the transition matrix of the delay state and energy state
of the user can be expressed as in (3) and (4). 0is a matrix
of ones with an appropriate size. D(E,B) = Dq=0(E,B) +
Dq>0(E,B).λ′= 1 −λis the probability that there is no
energy arrival (i.e., the energy source does not transfer wireless
energy). The matrices E(B)and E′(B)correspond to the cases
that there is and there is no energy arrival, respectively. Each
row of matrices E(B)and E′(B)corresponds to the energy
level of the user. In this case, the energy level decreases if
there is no energy arrival, and the user transmits a packet
(i.e., q > 0). The energy level increases if there is energy
arrival, and the user does not transmit a packet (i.e., q= 0).
Otherwise, the energy level remains the same.
Finally, we derive the transition matrix Pof the delay state,
energy states of the user and attacker, and it is expressed as in
(5), where γ′= 1−γis the probability that the attacker cannot
harvest wireless energy from the energy source. The row of
matrix Pcorresponds to the units of energy in the storage
of the attacker. In this case, the energy unit of the attacker
increases only when the energy source transfers energy (i.e.,
E(B)) and the attacker can successfully harvest the energy
(i.e., γ). When the attacker accumulates enough energy to
perform the jamming attack, the energy state is reset to zero
or one if it cannot or it can harvest the energy in that slot,
respectively.
D. Performance Measures
To obtain the performance measure of the network, we
obtain the steady state probability of the Markov chain. Let
π(D0,D1, . . . , DD,E,B)denote the steady state probability.
Its vector is denoted by
π, which is obtained from solving
4
E′(B) =
λ′D(E= 0,B)0
λ′Dq>0(E= 1,B)λ′Dq=0(E= 1,B)0
.........
λ′Dq>0(E=E−1,B)λ′Dq=0(E=E−1,B)0
λ′Dq>0(E=E, B)λ′Dq=0(E=E, B)
,(3)
E(B) =
0λD(E= 0,B)
0λDq>0(E= 1,B)λDq=0(E= 1,B)
.........
0λDq>0(E=E−1,B)λDq=0(E=E−1,B)
0λ(Dq>0(E=E, B) + Dq=0(E=E, B))
,(4)
P=
E′(B= 0) + γ′E(B= 0) γE(B= 0)
E′(B= 1) + γ′E(B= 1) γE(B= 1)
......
E′(B=B−1) + γ′E(B=B−1) γE(B=B−1)
E′(B=B) + γ′E(B=B)γE(B=B)· · · 0
,
(5)
π⊤P=
π⊤and
π⊤
1= 1, where
1is a vector of ones with
an appropriate size.
•The throughput τof the user can be obtained from (6),
where 1(X)is an indicator function, returning 1 if Xis
true and 0 otherwise.
•The delay distribution ϕd(i.e., the probability that the
successfully transmitted packet experiences the delay d
time slots) is obtained from
ϕd=ˆ
ϕd
D
d′=0 ˆ
ϕd′
,(7)
where ˆ
ϕdgiven in (9) is the overall probabil-
ity that the successfully transmitted packet experi-
ences the delay dtime slots. It is the probability
that the head-of-queue packet with the largest delay
dis successfully transmitted. The indicator function
1 (Dd= 1&Dd+1 = 0& · · · &DD= 0) returns one for
the delay variable Dd= 1 (i.e., the head-of-queue packet
has the delay d), where for other larger delay Dd′= 0
for d′=d+ 1, . . . , D. The delay distribution is obtained
by normalizing this overall probability.
•The average delay is obtained from
d=
D
d=0
dϕd.(8)
•The attack hit rate his the probability that the jamming
attack successfully corrupts the packet transmission of
the user. The attack hit rate is obtained from (10). It is
obtained similar to that of the throughput, except that
the attacker must accumulate enough energy (i.e., B=
B) and it performs the jamming attack when the user
transmits a packet.
•The average energy level of the user is obtained from
(11).
IV. PERFORMANCE EVALUATION
A. Parameter Setting
We consider the wireless energy harvesting network as
shown in Fig. 1 with a user and attacker. The energy storage
of the user has the capacity of 10 levels of energy. Unless
otherwise stated, for the user, the packet arrival probability
is 0.8 and the successful packet transmission probability is
1.0 (i.e., without a jamming attack from the attacker). The
maximum delay limit of the user is 5 time slots. The wireless
energy transfer probability is 0.4. For the attacker, if the wire-
less energy is available, it can harvest one unit of energy with
the probability of 0.5. The attacker requires 3 units of energy
to perform the jamming attack to the user’s transmission.
B. Numerical Results
We first show the throughput of the user when the packet
arrival probability (i.e., rate) is varied. Figure 3 shows that
first the throughput increases as the packet arrival probability
increases. However, at a certain point, the throughput decreases
and becomes constant. The throughput decreases as more
packets are generated, they will suffer from the jamming from
the attacker. Therefore, the throughput decreases. This increase
and decrease effect does not happen if there is no jamming
attack. That is, the throughput only increases and becomes sat-
urated. We observe that there is the packet arrival probability
5
τ=
1
D0=0
· · ·
1
DD=0
E
E=1
B−1
B=0
µπ(D0,D1, . . . , DD,E,B)1 D
d=0
Dd>0,(6)
ˆ
ϕd=
1
D0=0
···
1
DD=0
E
E=1
B−1
B=0
µπ(D0,D1, . . . , DD,E,B)1 (Dd= 1&Dd+1 = 0& · · · &DD= 0) ,(9)
h=
1
D0=0
· · ·
1
DD=0
E
E=1
B=B
π(D0,D1, . . . , DD,E,B)1 D
d=0
Dd>0,(10)
e=
1
D0=0
· · ·
1
DD=0
E
E=0
B
B=0
Eπ(D0,D1, . . . , DD,E,B),(11)
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.25
0.3
0.35
0.4
Energy required to attack=3 units
Energy required to attack=4 units
Energy required to attack=5 units
Packet arrival probability
Throughput
Analysis
Simulation
Without attack
Fig. 3. Throughput of a user under different packet arrival probability.
that yields the highest throughput, which can be obtained from
the proposed analytical model. Additionally, the analytical
results obtained from the queueing model is well validated
by the simulation. Note that when the attacker requires more
units of energy to perform the jamming, the attacker has less
opportunity to attack, and hence the throughput of the user is
higher.
Figure 4 shows the delay distribution of the user under
a jamming attack. As expected, when the packet arrival
probability increases, the probabilities of large delay increase
(e.g., delays of 4 and 5 time slots), while those of the small
delays decrease. Clearly, when the packet arrival probability is
very high (e.g., above 0.7), most of the packets experience the
delay of 5 time slots, and hence the corresponding probability
constantly increases. Figure 4 also shows that the analytical
results are accurately matched with the simulation results.
Figure 5 shows the average packet delay of the user when
the wireless energy transfer probability is varied. As there
is more energy, the user can transmit the packet earlier,
increasing the throughput and reducing the delay. However,
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.2
0.4
0.6
0.8
1
Packet arrival probability
Probability
Delay=1
Delay=2 Delay=3
Delay=4
Delay=5
Analysis
Simulation
Fig. 4. Delay distribution under different packet arrival probability.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Energy transfer probability
Average delay
Arrival prob = 0.2 (analysis)
Arrival prob = 0.2 (simulation)
Arrival prob = 0.5 (analysis)
Arrival prob = 0.5 (simulation)
Arrival prob = 0.8 (analysis)
Arrival prob = 0.8 (simulation)
Fig. 5. Average delay under different wireless energy transfer probability.
we observe an interesting result that if the energy transfer
probability is higher than the demand of the user, the average
delay can increase. This is due to the fact that when there is not
6
enough energy, many packets which reach the deadline will
be dropped. By contrast, the rest of packets which have small
delay will have higher chance to be transmitted successfully.
However, if there is enough energy, many packets can be
successfully transmitted, even through their delay is large.
Therefore, the overall delay (i.e., average delay) decreases.
Note that, as expected, when the packet arrival probability
increases, the delay increases.
1 2 3 4 5 6 7
0.34
0.36
0.38
0.4
Maximum delay
Throughput
Analysis
Simulation
No attack
1 2 3 4 5 6 7
0
2
4
6
8
Maximum delay
Average delay
Analysis
Simulation
No attack
Fig. 6. Throughput and average delay under different maximum delay limit.
Next, we show some interesting result when the maximum
delay limit (i.e., deadline) is varied. As shown in Fig. 6,
without attack, as expected, when the delay deadline increases,
the user has more time to transmit a packet, and hence the
throughput slightly increases. However, under the jamming
attack, the throughput of the user decreases. This is due to the
fact that when the maximum delay limit increases, the packet
can remain in the queue of the user longer. The transmission
can be jammed and the packet has to be retransmitted a few
more times, consuming more energy from the storage (i.e.,
average energy level of the user decreases as shown in Fig. 7).
This can be also observed from the attack hit rate, which is
increasing as the maximum delay limit of the user increases.
Therefore, under the jamming attack, there is an adverse effect
of increasing the maximum delay limit, not only increasing
average delay, but also decreasing throughput.
V. SU MM ARY
We have analyzed the wireless energy harvesting com-
munication network with a legitimate user transmitting data
to a receiver and an attacker performing jamming attack to
the user’s data transmission. The data transmission of the
user is delay constrained that a packet will be dropped if
it cannot be successfully transmitted before the deadline.
We have developed an analytical model based on a Markov
chain for the network capturing the delay state and energy
states of the user and attacker. Various performance measures
(e.g., throughput and delay distribution) have been obtained.
Performance evaluation has revealed some unexpected results.
1 2 3 4 5 6 7
0.05
0.055
0.06
0.065
0.07
Maximum delay
Attack hit rate
Analysis
Simulation
1 2 3 4 5 6 7
0.35
0.4
0.45
0.5
0.55
Maximum delay
Average energy level of user
Analysis
Simulation
No attack
Fig. 7. Attack hit probability and average energy level of a user under different
maximum delay limit.
For example, there is an optimal throughput for the user under
different packet arrival rate under the jamming attack.
ACK NOW LE DG EM EN TS
This work was supported in part by the National Research
Foundation of Korea (NRF) grant funded by the Korean
government (MSIP) (2014R1A5A1011478).
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