Excerpt
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The ability to achieve security at physical layer has remained a formidable task for the research
community. The difficulty increases in case of multiple cooperating (i.e. exchanging and combining
information) eavesdroppers. Therefore, in this article, we characterize the secrecy rate that can be
achieved in the presence of cooperating eavesdroppers between a sink and multiple sensor nodes i.e.
SISOME scenario. We quantify how the cooperating eavesdroppers using MRC (MaximalRatio
Combining) and SD (Selection Diversity) techniques make it challenging to secure information. We then
propose a scheduling scheme where a sensor with highest secrecy capacity is scheduled to transmit data.
My analysis of intercept probability and secrecy outage probability clearly shows that using the
scheduling scheme helps to provide greater security without any additional hardware complexity or power
cost.
I. INTRODUCTION
Wireless sensor nodes (WSNs) have attracted significant attention in recent years [1]. These sensor nodes
were firstly used for military applications like navigation, monitoring and surveillance. Now they are
further developed to enhance the productivity by performing various tasks like automation and
monitoring tasks [2], [3]. Security and reliability is a critical aspect of these nodes, failure to which may
cause to leakage of sensitive information. Due to the broadcast nature of WSNs the wireless transmission
of nodes can be easily accessible to unauthorized users. In other words, it is highly vulnerable to any
eavesdropper attack. The traditional cryptographic techniques are not suitable for WSNs because they
require complex hardware and large amount of energy. Moreover, an eavesdropper with unlimited
computing power can still crack these techniques using bruteforce attack.
In this context, Physical Layer Security is emerging as an impressive way to secure the confidentiality of
the message by exploiting the characteristics of wireless channel. It was initiated by Shannon in [4] .
Later, it was further elaborated by Wyner in [5], a framework was developed for achievable secrecy rates
for a model comprising of one source, one destination and an eavesdropper. The renowned term of
secrecy capacity was defined as the difference between the capacity of the main channel and the wiretap
channel. Substantial research efforts have been dedicated to improve the secrecy capacity of the wireless
transmission. One such effort is through the introduction of artificial noise generation [6], [7]. The
artificial noise aided security approaches work by allowing the transmitters to generate a interfering signal
(called artificial noise) such that only the eavesdropper is affected by it, while the intended receiver is not
affected. Hence, it results into an increased secrecy capacity. Goeckel explored the deployment of
cooperative relays for the noise generation and achieved an improved secrecy capacity. However, these
energy hungry schemes are not suitable for WSNs. The Rayleigh channel model has been used to model
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characteristics of channel which is used commonly in literature. It has proven to be an excellent approach
to model both outdoor and indoor environments [8]. By contrast, this article investigates the use of
scheduling to increase the physicallayer security without consumption of additional power resources or
increased hardware complexity/cost. Major contributions of this article can be summarized as follows:
1. Probabilistic characterization of secrecy capacity in the presence of cooperating eavesdroppers
(for both MRC and SD) is provided in terms of intercept probability and Intercept secrecy
capacity.
2. An optimal multinode scheduling scheme is proposed without channel state (CSI) of the
eavesdroppers, in which a sensor node with highest secrecy capacity is selected for the
transmission of information over wireless channel.
3. Considering round robin algorithm as a benchmark, a closedform expression of the intercept
probability for both round robin scheduling and proposed scheme is derived.
4. Numerical results show that the proposed scheduling scheme outperforms the conventional round
robin scheduling in terms of intercept probability.
The remainder of the paper is organized as follows. Section II presents the system model of a wireless
sensor network in the presence of eavesdropping attack. Next, in Section III the closed form expressions
of intercept probability for both MRC and SD are derived for Rayleigh fading environment. Section IV
provides intercept secrecy capacity analysis for MRC and SD. Next, in Section V we describe the
conventional roundrobin scheduling as well as the optimal scheduling scheme in the perspective of
intercept probability. In Section VI numerical results provide a detailed insight into the achievable
secrecy rates in case of MRC and SD. Furthermore, a comprehensive comparison of roundrobin
scheduling and optimal scheduling scheme is presented. Finally, Section VII provides concluding remarks
along with some future work.
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II. SYSTEM MODEL
A. System Model
As shown in Fig.1.we consider a wireless sensor network consisting of a sink node and N sensor nodes
and all nodes are considered with single antenna. There are total of M eavesdroppers (each with single
antenna) in the nearest vicinity of sensor nodes. The main link (from sensor nodes to sink) is represented
by dashedblue lines and the dottedred lines represent the wiretap link (from senor nodes to
eavesdroppers). Sink node has the connectivity to the entire network. It is also considered that channel is
quasistatic between sink node and anchor node (i.e. it does not vary for a given transmission burst). It is
also considered that CSI of N sensor nodes is available only. No information regarding the channel of
eavesdropper is present at sink node. This scenario is considered due to the fact that in practice, it is
difficult of obtain CSI of all the eavesdroppers.
For notational convenience, the set of S sensor nodes is denoted by
=
 = 1,2, ...
and
eavesdroppers are represented as
=
= 1,2, ...
. Rayleigh fading model is used for characterizing
both main link and wiretap link is used throughout the paper.
Considering that S
i
transmits its signal x
i
to sink with power Pi; the signal received at sink can then be
written as,
=
+
,
(1)
where
represents the channel between S
i
and the sink with
 Rayleighdistributed. Furthermore,
represents the zero mean additive white Gaussian noise (AWGN) at sink due to receiver electronics. The
instantaneous signaltonoise ratio (SNR) at sink for ith signal is given as
=


0
,
where N
0
is the
thermal noise variance that is assumed the same for all receiving nodes. Consequently,
  is Rayleigh
5
distributed random variables its square i.e.
  will be exponentially distributed whose probability
distribution function (PDF) is given by [9, p. 188]
( ) =

> 0
Since the transmission from S
i
is also picked up by the eavesdropper, the signal received at eavesdropper
is given as,
=
+
,
(2)
where
represents the channel between S
i
and eavesdropper with
 Rayleighdistributed.
Furthermore, is the AWGN at eavesdropper. Then instantaneous SNR for ith signal at eavesdropper is
=
 
2
0
. The eavesdropper tries to decode the overheard signal assuming that it has knowledge of the
modulation scheme and encryption algorithm. The pdf of instantaneous SNR at eavesdropper will be
discussed in coming section.
Now using the Shannon capacity theorem, channel capacity of the main link from S
i
to sink is given as
[8],
( ) =
1 +


,
(3)
whereas the channel capacity from S
i
to eavesdropper can written as,
( ) =
1 +


.
(4)
The secrecy capacity is defined as the difference between the capacities of the main channel and wiretap
channel [16]. For S
i
the secrecy capacity is written as,
( ) =
( ) 
( ).
(5)
An intercept event occurs when
( )is negative capacity of main link falls below that of wiretap
link. In this case the eavesdropper will be successful in decoding the source message. The expression for
intercept probability can be written as:
,
= Pr(
( ) <
)
Where R
S
>0 is the targeted secrecy rate. If R
S
>C
secrecy
(i) then information theoretic security is
compromised and eavesdropper will be able to decode the signal. By contrast, as long as R
S
<C
secrecy
(i)
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eavesdroppers channel will be worse than the estimated secrecy rate and the wiretap code used by sensor
node will ensure perfect secrecy.
III. INTERCEPT PROBABILITY (
) ANALYSIS
A. MRC Eavesdropper
The probability density function of the instantaneous SNR at the MRC follows a chisquare distribution
[10]. The pdf of instantaneous received SNR for M eavesdroppers can be written as:
(
) =
(
)
(
)!(
)

> 0
Now the intercept probability will be:
,
= Pr(
<
)
Where R
S
>0 is the targeted secrecy rate. If R
S
>C
secrecy
then information theoretic security is
compromised and eavesdropper will be able to decode the signal. By contrast, as long as R
S
<C
secrecy
eavesdroppers channel will be worse and the wiretap code used by sensor node will insure perfect
secrecy.
,
= 1  Pr(
( ) >
)
Pr(
( ) >
) = Pr
1 +
 
1 +
 
>
Pr(
( ) >
) = Pr
1 +
 
1 +
 
> 2
Pr(
( ) >
) = Pr(
> 2 (1 +
)  1)
Pr(
( ) >
) =
(
,
)
(
)
Since
,
are independent, therefore:
(
,
) = (
) (
)
Pr(
>
) =
(
) (
)
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,
= 1 
(
) (
)
2
(
1+
)
1
0
As we know that
( ) = Pr( < ) =
( )

Hence, we obtain
,
= 1 
1  (
2
(
1 +
)
 1
) (
)
0
> 0
> 0
(12)
Where F
s
is the cumulative distribution of
which is mathematically represented as:
(
) = 1 

(13)
,
= 1 

2
(
1 +
)
 1
(
)
0
,
= 1 

2  1

2
×
(
)
(  1)! ( )

,
= 1 
+ 2

2  1
B. SD Eavesdropper
The pdf of instantaneous received SNR for M eavesdroppers using SD combining technique can be
written as [10]:
(
) =
1 


> 0
,
= Pr(
( ) <
)
,
= 1 
(
) (
)
2
(
1+
)
1
0
Similarly, using the same process for SD we get,
,
= 1 

2  1

2
×
1 


8
,
= 1  1 
1
2

2  1
IV. INTERCEPT SECRECY CAPACITY ( )
An important parameter for the analysis is the intercept secrecy capacity which is largest secrecy rate
,
such that probability of intercept is less or equal to
(
) =
A. MRC Eavesdropper
Using 1
st
order Taylor series, we obtain:

1 
also
1 
Hence, the above equation becomes
,
= 1  1 
2
1 
2  1
Solving above equation for we get:
,
= log
1 +
1 +
B. SD Eavesdropper
Similarly
1 
1
2
= 1 
2
Hence, the above equation becomes
,
= 1  1 
2
1 
2  1
Solving for R
s
it becomes
9
,
= log
1 +
1 +
V. PROPOSED SENSOR SCHEDULING SCHEME
This section proposes an optimal scheduling scheme along with deriving intercept probability expression
for traditionally used round robin scheme.
A. Round Robin Scheduling:
Let us now consider round robin scheduling and derive a closedform expression of its intercept
probability. To be precise, round robin scheduling allows N sensor nodes to take turns in transmitting
their data to the sink node. Therefore, the intercept probability in case of round robin scheduling is given
by mean of intercept probability of N sensor nodes. This expression can be written as:
=
1
,
Where
,
is the intercept probability of i
th
sensor node.
For the case of MRC it can be written as:
=
1
1 
+ 2

2  1
and for SD it becomes:
=
1
1  1 
1
2

2  1
B. Optimal Sensor Scheduling Scheme
The assumption that no CSI of eavesdropper is available at sink motivates us to think of a scheme where a
sensor node with highest secrecy capacity is chosen. It will provide the maximum protection against the
unknown capabilities of eavesdropper. To be precise, each sensor node will initially estimate its own CSI
through channel estimation and send it to sink node. This channel estimation can be carried out using
classical channel estimation techniques. When sink node will collect the CSI of all the sensor nodes, it
will then calculate the secrecy capacity of each node and among them it will choose the node with highest
secrecy capacity. It is to be pointed out here that since the channel remains only constant during single
transmission burst, therefore, it is highly unlikely that same sensor node is prioritized to send its data
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every time. However, this prioritization based transfer of data may affect Quality of Service of the entire
network. Moreover, sensors may generate different types of data streams, each having their own priority.
Although it is of high interest to consider such QoS requirements of the network, but this paper focuses
on improving the physicallayer security and to successfully defend against an eavesdropping attack.
Hence, optimal sensor scheduling condition can be mathematically written as:
Optimal Sensor
=
( )
Where S denotes the set of N sensor nodes, the optimal secrecy capacity will be given by:
( ) =
1 +
 
1 +
 
Hence the intercept probability of proposed scheme becomes:
= Pr
( ) <
= Pr
1 +
 
1 +
 
<
From the above equation it can easily be noted that for different sensor nodes
the channel gains
 
and
  are independent of each other.
Hence the above equation can be simplified as:
=
Pr
1 +
 
1 +
 
<
=
Pr(
( )
<
)
=
,
(8)
Where
,
is the intercept probability of i
th
sensor node. For the case of MRC above equation can be
written as:
=
1 
+ 2

2  1
11
Similarly for SD it becomes:
=
1  1 
1
2

2  1
VI. RESULTS ANALYSIS
This section deals with the numerical intercept probability results of optimal sensor scheduling scheme
and traditional round robin scheduling scheme.it is to be noted that for notational convenience
is
used to represent the ratio of
  and   which is also called sinktoeavesdropper ratio.
Furthermore, let denote the ratio of P
i
to N
0
i.e.
=
. For the simulations, the wireless link between
two network nodes is modeled using Rayleigh fading channel. Moreover, wireless links are considered to
be independent and identically distributed random variables.
Fig.2. Intercept probability versus No of Eavesdropper M for
MRC and SD for different values of SER
with R
s
=0.1 and N=1.
Fig.2 shows the intercept probability versus No of Eavesdropper for different SER
. It is evident
from the figure that the intercept probability monotonically increases with the increase in SER
and
M. The figure also depicts that if the adversary uses the SD combining technique then the probability of
intercept in lower as compared to MRC technique. In addition to this, the MRC diversity increases the
intercept probability very rapidly as compared to SD combining which becomes flat as the number of
eavesdroppers increase.
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Fig.3. Intercept secrecy capacity versus SER
for fading
channel for different values of k
and N=1
Fig.3 demonstrates the intercept secrecy capacity of versus number of eavesdroppers (M). It is clearly
highlighted from the above graph that the intercept secrecy capacity decreases as the number of
eavesdroppers increases. The MRC curve is steeper as compared to SD which introduces a floor with
increase in M.
Fig.4. Intercept probability versus SER
for the proposed optimal scheduling schemes and the conventional roundrobin
scheduling for different number of sensors N using MRC and SD with =10dB and R
s
= 0.1.
Fig.4. shows the intercept probability for optimal scheduling and round robin scheduling scheme for
different number of sensor nodes for increasing values of
SER
.
As the number of sensor nodes
increase from N=2 to N=4 we can clearly see that no security benefit is attained and the intercept
probability remains same. However, by increasing the number of sensor nodes from N=2 to N=4 by using
optimal sensor scheduling scheme, we can achieve a greater level of security and the intercept probability
decreases for the same value of
SER
.
Therefore, the proposed optimal sensor scheduling scheme
clearly outperforms the conventional round robin scheme.
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Fig.5. Intercept probability versus SER
of the proposed
optimal scheduling schemes and the conventional roundrobin scheduling for different values of norm. R
s
with =10dB, N= 2,4
and M=5
Fig.5. illustrates the intercept probability for N=2 and 4 for the proposed scheduling scheme and sensor
scheduling scheme against various values of R
s
for the increasing values of SER
. It is vividly
apparent from the graph that intercept probability for proposed scheme decreases very rapidly as
compared to round robin scheduling. Moreover, as the number
reaches 30dB this difference
becomes very large, which indicates the usefulness of using the proposed scheduling scheme. This shows
the obvious advantage of the proposed approach over conventional round robin scheduling. In addition to
this it can also be observed that by increasing value of
SER
the intercept probability decreases.
Fig.6. Intercept probability versus No. of sensor nodes N of the
proposed optimal scheduling schemes and the conventional roundrobin scheduling for different No of eavesdroppers with
=10dB and norm. R
s
=0.1
Fig.6. demonstrates the intercept probability of proposed scheduling and round robin scheduling for
various values of M with increasing numbers of sensor nodes. It can easily be observed that for both M =
5 and 15 the intercept probability of the round robin scheduling scheme remains unchanged even with the
increase in number of sensor nodes. However, in case of proposed scheduling scheme the intercept
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performance decreases with the increase in number of sensor nodes. This shows the obvious advantage of
the proposed approach over conventional round robin scheduling.
VII. CONCLUSION AND FUTURE RESEARCH
In this article we discussed the intercept probability behavior in case of cooperating eavesdroppers in
Rayleigh fading environment. Perhaps the most exciting result to be gained from my research is
characterization of intercept secrecy capacity when adversaries are using MRC or SD combining. We also
proposed a scheduling scheme that focuses on improving the security of wireless sensor networks. We
considered the roundrobin scheduling as a benchmark for the comparison to the proposed optimal sensor
scheduling scheme. Numerical results show that the proposed scheme outperforms the traditional round
robin scheme. Furthermore, the intercept probability of the proposed optimal sensor scheduling scheme
decreases quickly by increasing the number of sensor nodes which clearly facilitates the physical layer
security.
In this paper, We only examined secrecy capacity and intercept probability for single antenna, where each
sensor node is equipped with only one antenna for transmission and reception. However, due to the
emergent technologies like 5G and MIMO the use of multiple antennas to achieve higher data rates will
become common. Therefore, it is of great importance to extend the results of intercept probability for a
MIMO system utilizing multiple antennas. We did not consider any Quality of Service (QoS)
requirements of the network. However, in practice, some sensor nodes may have highly time critical data
which needs to be prioritized. Therefore, it is of high interest to maintain a specific level of QoS while
guaranteeing high wireless security. We leave these thoughtprovoking and interesting problems for
future work.
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VIII. REFERENCES
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network for home automation," IEEE Trans. Industrial Informatics, vol. 10, no. 1, pp. 803812, Feb. 2014.
[4] C. E. Shannon, "Communication theory of secrecy systems," Bell System Technical Journal, vol. 28, pp. 656715, 1949.
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[6] X. Zhou and M. McKay, "Secure transmission with artificial noise over fading channels: Achievable rate and optimal power
allocation," IEEE Trans. Vehicular Technology, vol. 59, no. 8, pp. 38313842, Aug. 2010.
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[8] H. Hashemi, "The indoor radio propagation channel," Proc. IEEE, vol. 81, pp. 943968, July 1993.
[9] David Tse and Pramod Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005.
[10] M. K. Simon and M.S. Alouini, Digital Communication over Fading Channels: A Unified Approach to Performance
Analysis , John Wiley and Sons, 2000.
[11] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,
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