2014 IEEE 2014 International Conference on Computer, Communication, and Control Technology (14CT 2014), September 2 -4,2014 - Langkawi, Kedah, Malaysia

Physical Layer Secrecy Performance with

Transmitter Antenna Selection over

Dissimilar Fading Channels

Dac-Binh Ha, Member, IEEE, Nguyen-Son Vo Duy Tan University, Da Nang, Vietnam

Email: hadacbinh@duytan.edu.vn.vonguyenson@gmail.com

Abstract-In this paper, we investigate the physical layer secrecy performance of a multi-input single-output system. The system consists of multiple antennas at transmitter and single antenna at receiver in the presence of a passive eavesdropper with single antenna over dissimilar fading channels. On the assumption that legal channel is subject to Rayleigh fading while illegal channel undergoes Hoyt fading, expressions for the existence probabilities of secrecy capacity and secrecy outage are derived by using statistical characteristics of signal-to-noise ratio. Analytical results are verified by Monte-Carlo simulations.

I. IN T RODUCTION

Unlike wired networks, the broadcast nature of media in wireless networks allows potential eavesdroppers easily to

overhear the transmitted data leading to the fact that security issues become more prominent in wireless networks. Recently, many researchers have paid attention to these issues to en­hance the security capacity of wireless networks, especially at physical layer (PHY) such as key-based security [1]-[4] and keyless security [5]-[7]. Besides, how to find out the capacity of system to ensure the security is one of the most interesting issues in this field. For example, in [8]-[10], PHY secrecy for a quasi-static Rayleigh fading wire-tap channel with single antenna and multiple antennas has been investigated. In [8], on the assumption that two legitimate partners communicate over the same independent fading channel with an eavesdropper channel, the authors have defined the secrecy capacity in terms of outage probability and provided a complete characterization of the maximum transmission rate. At this maximum rate, the eavesdropper is unable to decode any information. In [9], the PHY secrecy of a communication scheme consisting of a transmitter with multiple antennas using transmitter antenna

selection (TAS) and a receiver with single antenna has been investigated in the presence of a eavesdropper with multi­ple antennas. The authors in [10] have analyzed the impact of antenna correlation on secrecy performance of multiple­input multiple-output wiretap channels where the transmitter employs transmit antenna selection while the receiver and eavesdropper perform maximal-ratio combining with arbitrary correlation.

However, all above studies assume that the main channel and the wiretap channel are subject to the same fading. This assumption is weakened due to the movement of wireless

devices, especially the flexibility of eavesdropping devices. In this paper, we focus on the P HY secrecy performance of sys­tem consisting of a transmitter with multiple antennas and a re­ceiver with single antenna, in the presence of a passive eaves­dropper with single antenna over dissimilar RayleighlHoyt fad­ing channels. Rayleigh fading is a reasonable model for both tropospheric and ionospheric signal propagation as well as the effect of heavily built-up urban environments on radio signals.

Meanwhile, Hoyt fading is typically observed on satellite links subject to strong ionosphere scintillation. The transmitter uses TAS scheme on the main channel to exploit the advantages of

TAS scheme such as low cost and low complexity [9]. In this system, the receiver informs the transmitter the best antenna

index through the open channel (i.e., non-secure) at low rate. Afterwards, the transmitter uses this antenna to transmit the signal to the receiver. Although the receiver is able to access the open channel, it only gets the antenna index and has no information about the main channel. Thus, the eavesdropper is not able to exploit any additional diversity from multiple transmission antennas. The objective of this paper is to derive expressions for both the probabilities of secrecy capacity and secrecy outage using statistical characteristics of signal-to­noise ratio (SNR). These expressions allow us to assess the security capability of the considered multiple-input single­output (MISO) systems.

The rest of this paper is organized as follows. Section II presents the system and channel model. Secrecy capacity of the considered system is analyzed in Section m. In Section IV, we show the numerical results and we conclude our work in Section V.

II. SYSTEM AND CHANN EL MODEL

We consider the system illustrated in Fig. 1. Alice and Bob are two legitimate users of the MISO system, Alice wants to send messages to Bob, while Eve is a passive eavesdropper

trying to extract the information from Alice without actively attack. Alice has MT antennas while Bob and Eve have one antenna each. The legal channel is assumed to be an undergo Rayleigh fading, while the eavesdropper experiences Hoyt fading. Alice sends the signal x(t) to Bob. The received signal

978-1-4799-4555-9/14/$31.00 ©2014 IEEE 140

MT antennas

� Main Channel ----) Wiretap Channel

:L �

Figure 1. MISO system with TAS.

y(t) at Bob has the following form

y(t) = hMx (t) + nM, (1)

where hM is the Rayleigh fading coefficient between the transmitter antenna at Alice and the receiver antenna at Bob, and nM is complex Gaussian noise with zero mean and power

NM· The instantaneous SNR at Bob is "fM = PMlhMI2 /NM and

the average SNR is 1'M = PME [lhM12J /NM, PM here is the

average received power at Bob. In single-input single-output (SISO) system, the probability density function (PDF) of "fM is 1 _ :1.M.

f'YM("(M) =::-e 'YM "fM (2)

In MISO system, when Alice uses TAS scheme [9], the PDF of "fM is

MT _ :1.M. ( _ :1.M. ) Mr-l f'YM("(M) = 1'M e 'YM 1-e 'YM (3)

If Eve is capable of eavesdropping the signal sent by Alice, the received signal z(t) at Eve is written by

z(t) = hwx(t) + nw (4) where hw is the Hoyt fading coefficient between the trans­mitter antenna at Alice and the receiver antenna at Eve, and nw is the complex Gaussian noise with zero mean and power

Nw. The instantaneous SNR at Eve is "fw = Pwlhwl2/Nw and

the average SNR is 1'W = Pw E [Ihw 12J / Nw, Pw here is the average received power at Eve. The PDF of "fw is [11]

2 (1+q2)2"l'W 4 f bw) = 1 + q e - 4q2'Yw 10 (l-q J"l'w ) "l'w 2q'Yw 4q2"l'w (5)

where 0 :s; q :s; 1 is the desired signal of Hoyt fading parameter, Hoyt distribution is in the range of one-sided Gaussian fading (q = 0) to Rayleigh fading (q = 1), and 10(.) is the zero-th order modified Bessel function of the first kind.

We can rewrite (5) as follows

a2 f"iW ("(w) = �e -1'W 'YW 10 (�"fw) "fw "fw

1+q2 1-q4 where a = �, b= �.

III. SECRECY CAPACITY ANALYSIS

A. Preliminaries

(6)

Basically, the capacities of SISO communication channel and SISO eavesdropper channel are respectively given by

CM = log2 [1 + "fMl· Cw = log2 [1 + "fw 1 .

(7)

(8)

And in [8], we have the instantaneous secrecy capacity written as follows

Cs {[CM -Cwl+ { IOg2 [1 + "fMl-Iog2 [1 + "fwl, 0,

"fM>"fw "fM:S;"fw

(9)

B. Existence of Secrecy Capacity

Assuming that the main channel and the eavesdropper

channel are independent of each other, we can derive the probability of the existence of a non-zero secrecy capacity as the following form

Pes

x

P(Cs > 0) = P("(M > "fw)

1000 Io'YM f'YM'YW("(M,"fw)d"fMd"fW

1000 Io'YM f'YM ("(M)f'Yw ("(W)d"fMd"fw DO b21(21)! Mr-l MT! m L221(l!)2a41+1 L m!(MT -1- m)!(-l)

1=0 m=O [ 1 � a2TL1'M1'W 1 (10) 1 + m - � [(1 + m)1'w + a21'Mt+1

We also present (14) in the Appendix for more detailed derivation. It is should be noticed that we have used the

infinite-series representation of Io(x) given in [11] as below

00 21 Io(X) = L22�(I!)2 (11)

1=0

C. Secrecy Outage Probability

The secrecy outage probability can be defined as

Pout P(Cs < Rs) P(Cs < Rsl"fM > "fW)P("(M > "fw)

+ P(Cs < Rsl"fM :s; "fW)P("(M :s; "fw) Ifll + 1fl2 (12)

14 1

1.0

7 V /

/ / U.8

/ / 0.6

0.4 II / /

0.2 / / /

� V -------10 -5

V V V / / / /

/ / / /

II II - Analysis

• Simulation: Y" = -10 dB

• Simulation: Yw = 0 dB

P'" 0 Simulation: Y" = 10 dB

.. Simulation: Y" = 20 dB

10 15

r,,(dB) 20 25 30

Figure 2. Existence probability of non-zero secrecy capacity with different

,w VS·'M· 1.0

�/ U.8 /J ij4,/ (fA

/II / � �/ I!

0.6

0.4 II; '/ 0.2 W' Y

-10 -5

- Analysis • Simulation: M" = 1 -• Simulation: MT = 2 -0 Simulation: M" = 3 _

.. Simulation: M" = 4

10 15 20 25 30

r,,(dB)

Figure 3. Existence probability of non-zero secrecy capacity with different MT VS·'M·

where Rs > 0 is the secrecy rate, from [8], [9], <PI and <P2 are respectively determined as follows

<PI roo r IrM(rM)f,w(rw)d'YMd'YW Jo J,w <P2 P(rM :S 'Yw) = 1-P(rM > 'Yw) = 1 - Pes.

(13)

By using [12, eqs. 6.451, 8.350, and 8.352], we calculate <PI as shown in (15) (see Appendix). Substituting (13) and (15) for <PI and <P2 in (12), we finally obtain the secrecy outage probability Pout.

IV. NUMERICAL RESULTS

In this paper, we use Monte Carlo simulations and analyze to demonstrate the performance of physical layer secrecy of our considered system. In particular, the number of trial iterations for each simulation result is 106 with q = 0.5 and we use the first 20 terms of the infinite series (I = 20) for our analysis (refer to [11]). Here, we provide numerical

1.0 1 �-, �

- Analysis r---�\ \ • Simulation: Yw = -10 dB

U.8

0.6

0.4

0.2

-10 -5

\ ' \ \

I \ \

\ \ \

\ • Simulation: Yw = 0 dB

0 Simulation: Yw = 10 dB

\- .. Simulation: 'Yw = 20 dB

\ \ 1 \ 1\

I \ \ \ \ \ \ "" "" � � '-, t'----- '-,

20 25 30

Figure 4. Secrecy outage probability with different,w vs. 'M.

1.0 ..--_,",�o-----,----;,------------,

"'"" "" - Analysis _

" \ " • Simulation: M" = 1 0.81--+--'\\\' \ 'tf-\\:---t-- • Simulation: MT = 2 -

\' 0 Simulation: MT = 3 _

f\ \ \ .. Simulation: MT = 4 U.61---+----HI\\-'� \-t--r----r------t----!

L..............--+-\\-\\ \ \ 0.4,--- \\ ) \ -\'S""'--\+-\ --+---+---+---1

-10 -5 20 25 30

Figure 5. Secrecy outage probability with different MT VS. 'M.

and analytical results for the existence probability of secrecy capacity and the probability of secrecy outage.

A. Existence probability of secrecy capacity

Fig. 2 shows the existence probability of secrecy capacity for RayleighlHoyt fading. From this figure, it can be seen that when we keep SNR 'Yw of Eve consistent and increase SNR 'YM of Bob, the existence probability of secrecy capacity Pes increases. In addition, if 'YM is fixed and 'Yw increases, Pes decreases. From (9), these results are correct because when

'YM increases, the received signal at Bob is better than the received signal at Eve. In other words, when 'YM increases, the capacity of the legal channel is greater than that of the illegal channel.

Under the effect of MT, as we can see in Fig. 3, Pes increases in accordance with the increase of MT. In other words, in order to enhance the secrecy of this system, we should increase the number of antennas at the transmitter.

B. Secrecy outage probability

Similarly, Fig. 4 shows the secrecy outage probability for RayleighlHoyt fading (Rs = 1bitf sf Hz). In this figure, we

142

1.0

7 V /

/ / 0.8

r.

/ I 0.6

0.4 / / /

/ / 0.2 -

...-------: V ----' -10 -5

V V V / /

/ / D

/ / I 7

/ / - Analysis

• Simulation: 'Yw = -10 dB

• Simulation: 1w = 0 dB

0 Simulation: 'Yw = 10 dB P .. Simulation: 'Yw = 20 dB

10 15

r,,(dB) 20 25 30

Figure 6. Existence probability of non-zero secrecy capacity (Rayleigh! Rayleigh fading) with different I'W vs. I'M.

"5 0':

1.0

0.8

0.6

�---, "" r--I---1\\ '\ - Analysis

• Simulation: 'Yw = -10 dB

\ 1\ \ • Simulation: 'Yw = 0 dB

0 Simulation: 'Yw = 10 dB \ \ \ .. Simulation: 'Yw = 20 dB

\ \ � 1 0.4 \ \ \

\ \ \ \ 1\ \ '\

0.2 \l\ \ 1\ -10 -5

"'--� 10 15

;V,,(dB) ",'---- "-.,

20 25 30

Figure 7. Secrecy outage probability (Rayleigh/Rayleigh fading) with differ­

ent I'w vs. I'M.

can see that if the SNR IW of Eve is consistent and the SNR

1M of Bob increases, the secrecy outage probability Pout decreases. However, if we do not change 1M and increase

IW' Pout increases. Considering the effect of MT, from Fig.

5, we can see that Pout decreases according to the increase of MT. In other words, this result shows that higher level of

secrecy can be achieved by increasing the number of antennas

at the transmitter.

To ensure the correctness of our analysis, we also simulate

and analyze RayleighlRayleigh fading channels with q = 1. In

this case, it should be noticed that MATHEMATICA cannot support the expressions if q = 1 because of indeterminate

expression 0°, so we use q = 1 .001 instead of q = 1. The results are shown in Fig. 6, Fig. 7, Fig. 8 and Fig. 9.

As can be seen obviously from all the above results, the existence probability of secrecy capacity decreases, but the

secrecy outage performance increases according to the increase

of SNR and the number of antennas at the transmitter. We

also reach a further conclusion that the secrecy performance

of the wiretap channel with Hoyt fading outperforms that of

1.0

0.8 II /II

III 0.6

tLi d.1

') �

0.4

0.2

-10 -5

�v 174/ riA 1

V

- Analysis

• Simulation: M" = 1 -

• Simulation: MT = 2 -0 Simulation: M" = 3 _

.. Simulation: M" = 4

20 25 30

Figure 8. Existence probability of non-zero secrecy capacity with different MT vs. I'M·

"5 0 Il-

1.0 � 0.8

0.6

0.4

0.2

-10 -5

\\'t \\' \ �\ \ 1\\\ I

� \

\\ \ s\\ \; �

- Analysis _ • Simulation: M" = 1 • Simulation: M" = 2 -0 Simulation: MT = 3 _

.. Simulation: MT = 4

� � � I--

20 25 30

Figure 9. Secrecy outage probability with different MT VS. I'M.

the wiretap channel with Rayleigh fading.

V. CONCLUSION

We have presented four infinite-series representations for the

existence probability of secrecy capacity and the probability of

secrecy outage. Based on these expressions, we have evaluated

the secrecy capacity performance of the considered MISO

systems with TAS scheme at the transmitter where the main

channel undergoes Rayleigh fading and the eavesdropper's channel is subject to Hoyt fading. In this system, we can

increase the level of secrecy by increasing the number of an­tennas at the transmitter as well as obviously by increasing the

SNR of system. The correctness of our analysis is investigated

by analysis and simulation results.

ApPENDIX

Here we calculate Pes and !PI as (14) and (15), respectively. Note that y = 2Rs(1 +,w)-1.

143

P(Cs > 0)

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