Asymptotic Analysis of Secrecy Capacity in Industrial Wireless Sensor Networks


Research Paper (postgraduate), 2016

14 Pages


Free online reading

2
Industrial wireless sensor nodes (I-WSNs) have grabbed the attention of researchers all over the world
in recent years. One of the major challenges faced by the researchers is the rapid fluctuation of signal
due to machinery hindrance, thermal noise and vibration of metal. In an information-theoretic sense,
this fluctuation degrades the secrecy capacity of the system in the presence of an eavesdropper. In this
context this paper analyses the outage behavior of an industrial WSN which consists of a multiple
sensor nodes and a sink, where data is transmitted over a wireless link. It also proposes the use of
sensor scheduling to improve the physical layer security against a malicious eavesdropper, where a
sensor with higher secrecy capacity is scheduled to transmit its data to sink. For both the conventional
round-robin scheduling and the proposed optimal scheduling schemes, closed-form expressions for the
intercept probability are derived.
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 and efficiency of factories by performing
various tasks like automation and monitoring of assembly line [2], [3]. These specific types of WSNs
are referred as Industrial wireless sensor nodes (I-WSNs) [4]. Security and reliability is a critical
aspect of these nodes, failure to which may cause damage to machinery or even loss of the workers'
life as well.
Due to the broadcast nature of (I-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 (I-WSNs) because they require complex hardware and
large amount of energy. Moreover, an eavesdropper with unlimited computing power can still crack
these techniques using brute-force 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. Related to this, security schemes like cooperative relaying and artificial aided noise
[5], [6] were proposed as a solution. However, these energy hungry schemes are not suitable for (I-
WSNs). By contrast, this article investigates the use of scheduling to increase the physical-layer
security without consumption of additional power resources. Major contributions of this article can be
summarized as follows:
1. An optimal multi-node scheduling scheme is proposed without channel state (CSI) of the
eavesdropper, in which a sensor node with highest secrecy capacity is selected for the
transmission of information over wireless channel.
2. Considering round robin algorithm as a benchmark, a closed-form expression of the intercept
probability for both round robin scheduling and proposed scheme is derived.
3. Numerical results show that the proposed scheduling scheme outperforms the conventional
round robin scheduling in terms of intercept probability.

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II. Sensor Scheduling in Industrial WSNs
A.
Problem Setup
.
Fig.1. Industrial WSN consisting of one sink and N sensor nodes in the presence of an eavesdropper
As shown in Fig. 1, I consider an industrial wireless sensor network consisting of a sink node and N
sensor nodes and all nodes are considered with single antenna. The main link (from sensor nodes to
sink) is represented by dashed-blue lines and the dotted-red lines represent the wiretap link (from
senor nodes to eavesdropper). Sink node has the connectivity to the entire network. It is also
considered that channel is quasi-static between sink node and anchor node (i.e. it does not vary for a
given transmission time). 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 the eavesdropper. Furthermore, the
channel is considered to be power-limited i.e.:
1
[| ( )| ]
Where P is the average transmit signal power. For notational convenience, the set of S sensor nodes is
denoted by
=
| = 1,2, ...
. As shown in the above figure, the presence of metallic vibration,
thermal noise and obstacles will cause fluctuation in wireless fading. Keeping this fact in view,
Rayleigh fading model for characterizing both main link and wiretap link is used throughout the paper.
I consider that sensor node S
i
transmit its signal x
i
to sink, with power Pi thus the signal received at
sink can be written as:
=
+
(1)
Where
represents the time varying complex fading coefficient and represents Additive White
Gaussian Noise (AWGN) with zero mean.
is referred as channel state information which is
assumed to be independent and identically distributed. Since the channel is quasi-static hence,
= , .
The channel capacity of the main link for S
i
to sink can be given by using Shannon capacity theorem
[7].
( ) =
1 +
|
|
(2)
Where
is the signal to noise ratio of i
th
sensor node.
Sink node
S
2
Eavesdropper
·
·
·
S
1
S
N
Obsatcles
Obsatcles

4
On the other hand, eavesdropper is assumed to have knowledge of modulation scheme and encryption
algorithm. Only the source signal S
i
is assumed to be confidential. The eavesdropper having
accessibility to the wireless signal tries to decode the overheard signal. Thus the signal received by
eavesdropper is given by:
=
+
(3)
Where
is the AWGN added at eavesdropper side. We can similarly derive the expression of
channel capacity from S
i
to eavesdropper as:
( ) =
1 +
|
|
(4)
According to [8] the secrecy capacity is given by the difference between the capacity of the main
channel and the wiretap channel. Hence, the secrecy capacity from sensor node S
i
to sink node in the
presence of an eavesdropper is given by:
( ) =
( ) -
( )
(5)
In logarithmic form it can be written as:
( ) =
|
|
|
|
(6)
In general practice, industrial wireless sensor nodes communicate with sink node using orthogonal
multiple access technique. This technique can be orthogonal frequency division multiple access
(OFDMA) or simply time division multiple access (TDMA). Conventionally, given an orthonormal
channel (a sub-carrier in OFDMA or a time slot in TDMA) the node with highest throughput is
allowed to utilize channel, without considering any secrecy of data. From security point of view this
scheme is not much feasible, since a node with the highest throughput may not be the most secured
node. Moreover, sensors may generate different types of data streams, each having their on priority.
This prioritization based transfer of data may affect Quality of Service of the entire network. Although
it is of high interest to consider QoS requirements of the network, but this paper focuses on improving
the physical-layer security and to successfully defend against an eavesdropping attack.
B. Round Robin Scheduling:
Let us now consider round robin scheduling and derive a closed-form 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 derived in upcoming section.
C. 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 un-known 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

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choose the node with highest secrecy capacity. 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 +
| |
An intercept event will occur when secrecy capacity will become non-positive. Hence the intercept
probability of proposed scheme becomes:
= Pr
< 0
= Pr
1 +
| |
1 +
| |
< 0
= Pr
+ | |
+ | |
< 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
=
Pr(
+ | |
<
+ | |
)
=
Pr(| |
< | |
)
=
Pr(| | < | | )
=
,
Where
,
is the intercept probability of i
th
sensor node derived in upcoming section.
III. EXACT INTERCEPT PROBABILITY FOR RAYLEIGH FADING
The following section will derive an expression for intercept probability used in above equations for a
single sensor node. Since
,
is given by:
,
=
Pr
0
+ | |
2
<
0
+ | |
2
The instantaneous SNR at sink will be given as

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=
| |
0
=
| |
0
Average SNR is given by
=
[| | ]
0
=
[| | ]
0
Similarly, Instantaneous SNR at eavesdropper is given by:
=
[| |
2
]
0
=
[| |
2
]
0
Likewise, average SNR is:
=
[| | ]
=
[| |
2
]
0
Moreover,
| | and | | are Rayleigh distributed random variables. Their square i.e. | | and | |
will be exponentially distributed [9, p. 188], hence,
will be given by:
( ) =
-
> 0 (7)
( ) =
-
> 0 (8)
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. We can find the intercept probability using total probability theorem.
= Pr
<
>
Pr(
>
)
+ Pr
<
Pr(
)
Proceeding as in Appendix A and B, we obtain:
Pr
<
>
= 1 -
exp -
(9)
And as
will be zero when
>
and R
S
>0 therefore we get:

7
Pr
<
>
= 1
Pr(
>
) =
(10)
Pr(
<
) = 1 - Pr(
>
) =
+
By combining previous 4 equations we obtain:
=
1 -
+2
exp -
2 -1
(11)
Another important parameter in the analysis is outage secrecy probability
. It is the maximum
transfer rate that is attainable by a given intercept probability. This parameter is mathematically
represented as:
= log(1 + (1-) )bits/s/Hz
Where F is the cumulative distribution function of
| | which is given by:
( ) = 1 -
and
=
Pr
<
=
Subsequently, the intercept probability for round robin scheduling can be written as:
=
1
1 -
+ 2
exp -
2 - 1
Similarly, for optimal sensor scheduling scheme intercept probability becomes:
=
1 -
+ 2
exp -
2 - 1
IV. 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 sink-to-eavesdropper ratio.
Furthermore, let denote the ratio of P
i
to N
0
i.e.
=
.
It is worth mentioning that although the above equations for intercept probability of round robin and
optimal sensor scheduling can be used to conduct performance estimation, however, they fail to
provide a solid comprehension of the effect of number of sensor nodes on the intercept probability.
Therefore, to meticulously investigate the impact of number of sensor nodes, following sub-section
will provide the asymptotic analysis of intercept probability for round robin and optimal sensor
scheduling scheme.
A.
Asymptotic Analysis
Since the intercept probability is given by:
=
1 -
+ 2
exp -
2 - 1

8
It can also be written as:
=
1 -
1
1 + 2
exp -
2 - 1
=
1 -
1
1 + 2
| |
2
| |
2
exp -
2 - 1
| |
2
=
1 -
1
1 + 2
1 exp -
2 - 1
| |
2
It is vividly clear from the above equation that intercept probability decreases as
increases.
However, as
the intercept probability becomes:
1 - exp -
2 - 1
| |
2
Solving above equation using 1
st
order Taylor series, we obtain:
2 -1
| |
2
(12)
In case of round robin algorithm, the above equation shows that the intercept probability decays as
|
|
for a specific value of and N senor nodes. Whereas, for the case of optimal sensor scheduling
scheme, the intercept probability decays faster with the rate of
|
|
for a specific value of and N
senor nodes. This provides the motivation to use the optimal sensor scheduling scheme over
conventional round robin scheduling. In other words, increasing the number of sensor nodes in case of
optimal sensor scheduling scheme can significantly reduce the intercept probability of the industrial
wireless sensor network.
B.
Discussion
In this sub-section I will discuss the numerical results of intercept probability obtained for both round
robin scheduling and optimal sensor scheduling. 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. In addition to this, is considered to be 10dB throughout
the simulated results.
Fig.2. Outage secrecy probability versus SNR (
) for Rayleigh
fading channel for different values of
and N=1

9
Fig.3. Outage capacity versus
for Rayleigh fading channel for different values of SNR (
)
and N=1
Fig.2,3 show the outage capacity of Rayleigh fading channel versus SNR and
respectively. It is
evident from the graphs that SNR of the individual user increases, so does the outage capacity of the
individual node increases. By contrast, as the
is increased the outage capacity of the node decreases.
Fig.4. Intercept probability versus SER
of the proposed optimal scheduling schemes and the conventional round-robin
scheduling for different number of sensors with =10dB and norm. 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. Therefore, the proposed optimal sensor scheduling scheme clearly outperforms
the conventional round robin scheme.

10
Fig.5. Intercept probability versus SER
of the proposed optimal scheduling schemes and the conventional round-robin
scheduling for different values of norm. R
s
with =10dB and N= 4
Fig.5. illustrates the intercept probability for N=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 20dB this difference
becomes very large, which indicates the usefulness of using the proposed scheduling scheme.
Fig.6. Intercept probability versus No. of sensor nodes N of the proposed optimal scheduling schemes and the conventional
round-robin scheduling for different values of SER
of sensors 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 SER
with increasing numbers of sensor nodes. It can easily be observed that for
both
= 1 and
= 3 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 performance decreases with the increase in number of sensor nodes.
This shows the obvious advantage of the proposed approach over conventional round robin
scheduling.
Fig.7. Comparison between the asymptotic and the exact intercept probabilities of the proposed optimal scheduling and the
round-robin scheduling and schemes for different number of sensors with =10dB and norm. R
s
=0.1
The above figure shows the comparison of asymptotic and exact intercept probabilities for proposed
scheduling scheme and round robin scheme with increasing SER
. The asymptotic and the exact
intercept probability results match very close to each other in the region where SER is very high. This
implies that the accuracy of analysis of asymptotic behavior when
in the previous sub-
section. Fig.5. indicates that the use of proposed scheduling scheme will provide more security in case
of eavesdropping attack. Additionally, it also shows that the slope becomes much steeper by
increasing the number of sensor nodes; hence, signifying the use of proposed approach.

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V. CONCLUSION AND FUTURE RESEARCH
In this article I have proposed a scheduling scheme that focuses on improving the security of industrial
wireless sensor networks. I considered the round-robin scheduling as a benchmark for the comparison
to the proposed optimal sensor scheduling scheme. In addition to this, I also derived closed-form
expressions of the intercept probability for both the proposed optimal scheduling and the round-robin
scheduling schemes in Rayleigh fading environment. An asymptotic analysis was also given to have
an insight into the intercept probability. 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, I 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. Moreover, I 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. Keeping in view that multiple antenna can
be used to achieve greater secrecy which can lead to fascinating possibilities. I leave these thought-
provoking and interesting problems for future work.

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VI. APPENDIX A
(Derivation of (9))
Pr(
>
) =
( ,
)
Since
,
are independent, therefore:
( ,
) = ( ) ( )
Pr(
>
) =
( ) ( )
Pr(
>
) =
1
-
1
-
Pr(
>
) =
1 1
-
-
= -
1
-
-
- 1
= -
1
-
-
-
-
= -
1
+
-
Hence, we obtain:
Pr(
>
) =
+
VII. APPENDIX B
(Derivation of (10))
Pr
<
>
= (
< 2 (1 +
) - 1| >
)
=
( ,
|
>
)
(
)
=
( ,
|
>
)
(
)
Since
, are independent, therefore:
( ,
) = ( ) ( )
Hence, the above equation becomes:

13
=
( ) ( )
(
>
)
(
)
Putting the value from above derivation and solving the integral, we obtain:
= 1 -
+
+ 2
exp -
2 - 1

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VIII. REFERENCES
[1] Y. Zou, J. Zhu, X. Wang, and V. Leung, "Improving physical-layer security in wireless communications through diversity
techniques," IEEE Net. Mag., accepted to appear, May 2014.
[2] R. C. Luo and O. Chen, "Mobile sensor node deployment and asyn-chronous power management for wireless sensor
networks," IEEE Trans. Industrial Electronics, vol. 59, no. 5, pp. 2377-2385, May 2012.
[3] J.-C. Wang, C.-H. Lin, E. Siahaan, B.-W. Chen, and H.-L. Chuang, "Mixed sound event verification on wireless sensor
network for home automation," IEEE Trans. Industrial Informatics, vol. 10, no. 1, pp. 803-812, Feb. 2014.
[4] O. Kreibich, J. Neuzil, and R. Smid, "Quality-based multiple-sensor fusion in an industrial wireless sensor network for
MCM," IEEE Trans. Industrial Electronics, vol. 61, no. 9, pp. 4903-4911, Sept. 2014.
[5] H. Qin, et al., "Optimal power allocation for joint beamforming and artificial noise design in secure wireless
communications," Proc. 2011 IEEE Intern. Conf. Commun. Workshops, Kyoto, Japan, Jun. 2011.
[6] S. Goel and R. Negi, "Guaranteeing secrecy using artificial noise," IEEE Trans. Wirel. Commun., vol. 7, no. 6, pp. 2180-
2189, Jul. 2008.
[7] C. E. Shannon, "Communication theory of secrecy systems," Bell System Technical Journal, vol. 28, pp. 656-715, 1949.
[8] A. D. Wyner, "The wire-tap channel," Bell System Technical Journal, vol. 54, no. 8, pp. 1355-1387, Aug. 1975.
[9] David Tse and Pramod Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005.
14 of 14 pages

Details

Title
Asymptotic Analysis of Secrecy Capacity in Industrial Wireless Sensor Networks
Author
Year
2016
Pages
14
Catalog Number
V337117
File size
928 KB
Language
English
Tags
Secrecy capacity, Outage probability, Rayleigh fading, Wireless Sensor Network, Round robin scheduling, Physical layer security
Quote paper
Furqan Jameel (Author), 2016, Asymptotic Analysis of Secrecy Capacity in Industrial Wireless Sensor Networks, Munich, GRIN Verlag, https://www.grin.com/document/337117

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