Communications and Network, 2013, 5, 4247 http://dx.doi.org/10.4236/cn.2013.53B2009 Published Online September 2013 (http://www.scirp.org/journal/cn) Secure Communications for TwoWay Relay Networks Via Relay Chatt i ng Jun Xiong1, Dongtang M a1, Chunguo Liu2, Xin Wang1 1School of Electronic Science and Engineering, National University of Defense Technology, Changsha, China 2National Key Laboratory of Blind Signals Processing, Chengdu, China Email: xj8765@nudt.edu.cn, dongtangma@nudt.edu.cn, schg_liu@126.com, wxwirelss@nudt.edu.cn Received May, 2013 ABSTRACT In this paper, we investigate a twoway relay network consisting of two sources, multiple coo perative relays and an ea vesdropper. To enhance secure communications, a new relay chatting based on transmission scheme is proposed. Spe cifically, the proposed scheme selects a best relay that maximize the sum mutual information among the sources to for ward the sources’ signals using an amplifyandfor ward protocol, an d the remaining r elays transmit interf erence signals to confuse the eavesdropper via distributed beam forming. It can be found that the proposed scheme with relay chatting does not require the knowledge of the eavesdropper’s channel, and outperforms the joint relay and jammer selection scheme, which introduces the interference into the sources. Numerical results show that the secrecy outage probability of the proposed scheme converg es to zero as the transmit power increases. Keywords: Twoway Relay Networks; Physical Layer Security; Relay Chatting 1. Introduction Recently, there has been considerable interest in physical layer security, which exploits randomness properties of wireless channels. It was pioneered in the 1970s by Wyner [1], who introduced the wiretap channel and demonstrated that when the wiretap channel is a de graded version of the main channel, the source and the legitimate receiver can exchange secure messages at a nonzero rate. The result was later extended to the scalar Gaussian channels [2] and broadcast channels [3]. With the additional spatial degrees of freedom (DoF) provided by multiantenna systems, the limitation that the main channel could be worse than the eavesdropper channel can be overcome. In particular, the secrecy capacity in Gaussian multipleinput multipleoutput (MIMO) wire tap channel was studied in [4,5]. However, due to cost and size limitations, multiple antennas may not be available at network nodes. In these scenarios, cooperation is an effective way to enable sin gleantenna nodes to enjoy the benefits of multiantenna systems. And some recent works have been proposed to obtain security using cooperative relays [611]. In these works, proper relay or jammer selection schemes seem to be interesting approaches, which provide a good trade off between secrecy performance and system complexity [911]. Opportunistic relay selection in oneway relay net works with secrecy constraints was addressed in [9], where the proposed scheme involved the joint selection of a relay and a jamming node to enhance the security. Following a similar idea, a joint relay and jammer selec tion were investigated for twoway cooperative networks in [10]. Different from [9], the proposed algorithms in [10] selected three relay nodes to enhance security, where the first selected node operated in the conventional relay mode and forwarded the sources’ signals, and the second and third nodes acted as jammers to confuse the eavesdropper in the first and second phase, respectively. However, the secrecy outage probability wou ld converge to a fixed value as the transmit power increases since the selected singleantenna jammer nodes introduced inter ference into the legitimate receiver [9,10]. Most recently, a relay chatting based on transmission scheme was pro posed to enhance secure communications for oneway relay networks in [11], where a b est relay was selected to forward the source’s signal using an am plifyandforward (AF) protocol, and the remaining re lays transmitted a jamming signal to confuse the eaves dropper via distributed beam forming. It was shown that the use of opportunistic relay chatting gu aranteed that th e outage probability converged to zero at high transmit power. Motivated by [11], we extend relay chatting based transmission scheme to twoway relay networks in this paper. Specially, a best relay that maximize the sum mu tual information among the two sources is selected to C opyright © 2013 SciRes. CN
J. XIONG ET AL. 43 forward the sources’ signals, and two chatting groups formed from the remaining relays transmit artificial in terference to degrade the eavesdropper in the first and second phase, respectively. It can be found that the pro posed relay chatting scheme does not require the knowl edge of the eavesdropper’s channel state information (CSI), and obtains better secrecy performance than the joint relay and jammer selection scheme proposed in [10]. The reminder of this paper is organized as follows. We present the system model and signal model in Section 2. In Section 3, the relay chatting based transmission scheme is presented. Numerical results are provided in Section 4, and the conclusion s are drawn in Section 5. Notations: Vectors and matrices are typed in boldface letters, and variables are italic letters; the transpose, complex conjugate, Hermitian, and inverse of are , , T A A A and , respectively; 1 A I denotes a identity matrix; denotes statistical ex pectation while denotes the probability of an input event; NN Ε , max 0 Pr x . 2. System Model and Signal Model 2.1. System Model We assume a network configuration consisting of two sources S1 and S2, one eavesdropper E, and a relay node set 1, 2,, in SK with K nodes. Each node is equipped with a single omnidirectional antenna and operates in a halfduplex mode. In Figure 1, it schematically shows the system model. As the relay nodes cannot transmit and receive simultaneously, the total communication process is performed by two phases. In the first phase, S1 and S2 broadcast their messages 1 and 2 , and the best relay node listens, where the criterion for the best relay selection will be discussed later. At the same time, a chat tin g group with size , denoted by * R 1 N 1 112 ,,, N RR R , is formed from the remaining relays and trans mits a random messages 1K 1 via distributed beamform * * * 1 ,SR h * 2 ,SR h 2 ,SE h *1 , S h 1 1 N 1 ,SE h *2 , S h 1 2 N Figure 1. System model with two sources S1 and S2, a relay node set, and one eave sdropper E. ing. In the second phase, the best relay node forwards the source messages to the corresponding destinations based on AF protocol while a new chatting group of size 2, denoted as N ,,, N RR R 2 212 , transmits a random message 2 using a new beam forming vector. We as sume that the eavesdropper E can overhear the signals from the two phases. The channel gain from node i to node j is denoted by ,ij , which is modeled as a zeromean, independent, cir cularlysymmetric complex Gaussian random variable with the variance h 2 ,ij , where 2 ,,ij ij d , ,ij denotes the Euclidean distance between node i and node j, and d represents the p athloss exponen t. Furthermor e, addi tive white Gaussian noise (AWGN) with zero mean and unit variance is assumed at each receiver. 2.2. Signal Model In the first phase, the two sources send information symbols 1 and 2 , respectively, which are mapped to a PSK set. The received signals at the best relay node and eavesdropper E can be, respectively, expressed as * R ** ** 12 1 12 112 21 1 1211 ,, 1,1,2 11 , , T SS R RSR SRR T ESSE SSERE E yPhsPhsPxn yPhsPhsPxn hf hf * 1 R (1) where 21,1, 2 i siΕ, * n and 1 n denote the noise at and the eavesdropper E, respectively. * R 1121 ,, , ,,, N T ERERERE hh h h with , i E h i R denoting the channel gain from the relay node of the chatting group to the eavesdropper E. And 1 *** * 12 1 ,,, N T RRRRRRR hh h h with , i R h denoting the channel gain from the relay node of the chatting group 1 to the best relay node . is the beamforming vector and i R * R1 f1 is the interference signal with 2 11xΕ. In order to make the interference signal invisible to the best relay node while only degrading the eavesdropper’s reception, 1 should be constructed to satisfy *1 f 0 T R hf and 111 H ff . 1 P denotes the transmit power of the relay chatting group 1 . In the second phase, is selected to amplify its re ceived signal, and forwards it to S1 and S2. At the same time, a new chatting group of size , denoted by 2 * R 2 N , creates a new beamforming vector 2 to transmit inter ference signal. Similarly, we should make the interfer ence signal invisible to the two sources. Hence, 2 should be located at its null space of the two sources’ Copyright © 2013 SciRes. CN
J. XIONG ET AL. 44 channels, i.e., 12 2 ,Thh 0 * R and 22 , where 1 and 2 h denote the channels from the relay node of the chatting group 2 to the sources S1 and S2, respec tively. As such, the signals transmitted from the best re lay node can be expressed as 1 Hff h * R * R , y (2) where *** 12 12 22 ,, SS RS RSR hPh 1PP and * P denotes the transmit power of the node * . Since each source knows the own transmit signal i, it can cancel the selfinterference [10]. Thus, each source can extract the message from the other source. As such, the residual signals at S1 and S2 can be respectively expressed as i 1, 2s ** ** 212 1 ** ** 121 2 12 ,, , 21 ,, , , , SRS SRRSR SRS SRRSR yPhhshn yPhhshn 1 2 n n (3) where 1 and 2 denote the noise at the sources S1 and S2, respectively. n n On the other hand, the received signal at the eaves dropper can be expressed as *** * 12 1 ** 22 21 ,, ,, 22 2 ,, ES S RESR RESR T RE ERER 2 2 PhhsPhh s Pxhnn hf y h (4) where with 212 2 ,,, N T ERERERE hh h , i E h denot ing the channel gain from the relay node of the cha t ting group 2 to the eavesdropper E. 2 i R P denotes the transmit power of the relay chatting group . 2 2 is the interference signal with 2 21xΕ, and 2 n de notes the noise at the eavesdropper E. 3. Secure Communications with Relay Chatting In this section, we discuss the relay selection for the proposed secure scheme with relay chatting. Then, we provide the secrecy outage probability as the metric of the secrecy performance. 3.1. Relay Selection We define i as the signal to interferenceplusnoise ratio (SINR) of the virtual channel i (for ). They can be calculated as j SS ,ij 1,2,j * 212 *1 22 2,, 12 2, , 1 SRS SR RS Phh h * (5a) ** 121 *2 22 2,, 22 2, . 1 SRS SR RS Ph h h (5b) Thus, the sum mutual information among the sources can be expressed as 12 21 212 11 ;; 22 1 2log 11, S sys II I where (6) 2 1 ;log1 2 ij i ys I scalar factor with ,1,2,iji j and the12 is due to the f units are required in two phases. Equation (6) can be used as the criterion for the best lection, i.e., act that two time relay se *argmax in S RS RI 12 argmax 11. (7) in RS We can find that the relay selection strategy based on Equation (7) is no t dependent on the eavesdro ppe In addition, the relay selection can be implemented in a distributed way [12], since each node only requires its lo secrecy outage es the outage prob ed destinations are r’s CSI. cal CSI to calculate Equation (7). 3.2. Secrecy Outage Probability We use the secrecy outage probability as the metric of secrecy performance. The meaning of the probability is twofold. First, it provid ability for the case where the intend unable to decode the messages from the sources reliably. It also gives the metric for the case where the message transmission is not perfectly secure, i.e., there exists some information leakage to the eavesdropper E [13]. In order to calculate the secrecy outage probability, we firstly have to get the SINR of the links i SE for 1, 2i . We assume a simple case in which the eaves dropper applies maximal ratio combining (MRC), so as to ceived examine the efficiency of the proposed scheme. Ac cording to MRC, the eavesdropper E comb re signals by multiplying 1 ines the y and 2 y with proper weighting factors. 11 22 , ii i EE E yyy (8) where i y represents the cbining signal for the source i S and om 1, 12 ES j N *,, ii SSE iPh (9) ** 2, 22, ii ES j SRE SR i N Ph h (10) ,1,2,iji j . 1, 2 S N and 2, 2 S N with represent wer the total interference and noise po terms in1 y and 2 y, denoted by respectively , Copyright © 2013 SciRes. CN
J. XIONG ET AL. 45 1 1, 1 22 2,1 1, jj ES j T SSER NE Ph P hf (11) ** 2 2, 2 * 2 2 2, 1. jj SR RE h (12) 2 22 22,, ES j T SR NE RE Ph hP hf Thus, the SINR of th e link can as i SEbe calculated 11 ** 2 . i SRE Ph ** * 22 2 , 22 ,1 2 2 2 22 2 22 2 ,, , 1 1 ii i jj i jj SSE ET SSE RE SR T SR E RE SRRE Ph Ph P h Ph hPh hf hf (13) The instantaneous secrecy rate with the relay node set for the source can be expressed as [10] in Si S 22 11 log 1log 1, 22 i Si Rj E (14) where ne sec ,1,2,iji j. The overall secrecy performance of the twoway relay twork is characterized by the sum of the two sources’ recy rate, i.e., 12 21 22 21 21 11 1log EE 21 12 12 2 11 11 log log . 211 SSS EE RRR (15) For a target secrecy rate , the secrecy outage probability can be expressed as fows [13,1 0 Rllo4] 0 21 00 12 2 Pr 11 Pr2 . 11 so SS R EE PR RR R (16) it Power In this subsection, we do some quantitative analy the asymptotic performance for the proposed schem high transmit power range. Following the similar idea from [10], we assume that rces, e samer words, as the source’s transmit power 3.3. Performance Analysis at High Transm sis on e in the transmit power for all nodes including two sou the selected best relay and the relay chatting set is th . In othe S P, i S P, * P and i P also go to infinity. In this case, we can obtain ** *** ,, 2 22 ,, , lim , ij S ii j SRS SR i P RS SRSR Ph h hhh (17) 2 2 1 ** **** 2 2 2 ,1 lim i SE PT SE h h h , 2 2 2 22 2 2 2 ,, , , , i j i jij SE E RE SR T E RESRSRSR hh hh h h f hf (18) where 2 ,1,2,iji j n see that . We cai grows rapidly as increases, while S P i rresp (16), th transm convergo a fixed value then the coonding cnnels. Therefore, baon tion e secrecy outage probability can go to zero at highit pow erical Resu In rots a 2D square toy withi es t ha er, i.e., at dep sed 0 as ds on Equa 0so S PR R S P. 4. Numlts this section, we pvide numerical resul in order to validate the effectiveness of the proposed scheme. The simulation environment consists of two sources S1 and S2, one eavesdropper E, and a relay node cluster. We assume that all nodes are located inpologn a 11 unit square. We co S2, and E are located at nsider this scenario where S1, 11 ,0,1 SS XY, 22 ,1,1 SS XY, and ,0.5,0 EE XY, respectively. The K relay nodes spread randomly within theare space. For example, Figure 2 gives the simu lation scenario with K squ 8 relays. 00.1 0.20.3 0.40.5 0.6 0.70.8 0.91 0 0.1 0.2 0.3 0.4 0.5 1 0.6 0.7 0.8 0.9 X Y S1 S2 E Rel a y S2 E S1 Figure 2. The 1 × 1 simulation scenario with K = 8 relays. Copyright © 2013 SciRes. CN
J. XIONG ET AL. 46 We assume that the sources, the best relay , and the chatting group transmit with the same 2 . The pathlos * R power, i.e., s exponent is *,1, ii SRS R PPPPi set to 3 . All the remain used as chatting relays, i.e., In Figure 3, the secrecy ou ing relay nodes are s hbeen shown as functions of the transmit power The tar get secrecy rate is set asbits/s/Hz. It can be seen that the relay chattingme canize zeroap poaching outage probe tranower in creases. Meanwhile, as tnumber of t relay nodes increases, the secrecy ourobability poundly de creases. A similar obcan be foFigure 4, which presents thtage probility with dif ferent target secrecy rate. The transmwer is set to 10 dB. The secrormamed by inviting more relays into cooperation due to the op portun 1K 12 NN probab1K. tageilitieave S P. real smit p he rof und in ab it po nce can be i 03R sche ability as th he tage p servation e secrecy ou 0 R ecy perf S P prov  istic use of the multiple relays. 02 46 810 12 14 16 1820 10 4 10 3 10 2 10 1 10 0 Ps[dB] S ec rec y Outage P roba bility Rel ay Cha ttin g K= 4 Rel ay Cha ttin g K= 6 Rel ay Cha ttin g K= 8 Figure 3. Secrecy outage probability versus the transmit power PS with different number of relays K. 01234567 10 6 10 5 10 4 10 3 10 2 10 1 10 R0[b i ts /s/Hz] Secrecy Outage Probability Relay Chat ting K = 4 Relay Chat ting K = 6 Relay Chat ting K = 8 Figure 4. Secrecy outage probability versus the target se crecy rate R with different number of relays K. 05 1015 20 2530 10 5 10 4 10 3 10 2 10 1 10 0 Ps[dB] Secrecy Out age P robabilit y Rel ay Chat tin g OSMSISR Figure 5. Secrecy outage probability versus the transmit Next, wempare the proposed relay chattng scheme with the joint relay and jammer selection scheme pro posed in [10]. It is assumed in [10] that the jammers transmit with a power subject to the relayjammer power ratio power PS.. coi , i.e., JR PPL 10L where P de. denotes the transmr of the selected jammer noWe give the simulation results of the optimal selectio n with maximum sum instantaneous secrecy rate (OSMSISR) in Section IIIA of [10]. It can be found that the OSMSISR scheme requires the precise knowledge of the eavesdropper’s channel, which is hard to obtain, e.g., a passive eaves dropper [14]. However, the proposed relay chatting in the previous section avoids the use of the eavesdropper’s CSI. Figure 5 presents the secrecy outage probability of both schemes, where the target secrecy rate is set to it powe 03.5R bits/s/Hz and the number of relay nodes is 8K . As 03.5R shown in , the secrecy outage prob OSMSISR wounverge to a fixed value as to heme. Performance analysis and simulation results sh ability of the tran rge ld co the transm smit power S P increases since the selected sin gleantenna jammer nodes introd uce the interference into the sources. It can be also seen that the secrecy outage probability of our proposed relay chatting scheme can convezero as it power S goes to in finity. 5. Conclusions In this paper, a new relay chatting transmission scheme is proposed to enhance secure communications for twoway relay networks. The proposed scheme does not require the knowledge of the eavesdropper’s channel and achieves better performance than the joint relay and jammer selec tion sc P ow that the secrecy outage probability of the proposed scheme goes to zero as the transmit power increases. 0 Copyright © 2013 SciRes. CN
J. XIONG ET AL. Copyright © 2013 SciRes. CN 47 6. Ackn al Journal, Vol. 54, No. 8, 1975, pp. 13551367. 5387305.1975.tb 02040.x owledgements This work was supported in part by the NSFC under Grants 61101096 and 61002032, and the NSF of Hunan Province under Grant 11jj4055. REFERENCES [1] A. D. Wyner, “The Wiretap Channel,” Bell System Tech nic doi:10.1002/j.1 anCheong and M. E. Hellman, “The[2] S. K. LeungY Gaussian Wiretap Channel,” IEEE Transactions on In formation Theory, Vol. 24, No. 4, 1978, pp. 451456. doi:10.1109/TIT.1978.1055917 [3] I. Csiszár and J. Körner, “Broadcast Channels With Con fidential Messages,” IEEE Transactions on Information Theory, Vol. 24, No. 3, 1978, pp. 339348. doi:10.1109/TIT.1978.1055892 [4] F. Oggier and B. Hassibi, “The Secrecy Capacity of The MIMO Wiretap Channel,” IEEE Transactions on Infor mation Theory, Vol. 57, No. 8, 2011, pp. 49614972. 158487 doi:10.1109/TIT.2011.2 heory, Vol. 55, No. 6, 2009, [5] T. Liu and S. Shamai, “A Note on The Secrecy Capacity of The Multiple Antenna Wiretap Channel,” IEEE Transactions on Information T pp. 25472553. doi:10.1109/TIT.2009.2018322 [6] L. Dong, Z. H H. V. Poor, “Im proving Wirelity via Cooperating an, A. P. Petropulu and ess Physical Layer Secur Relays,” IEEE Transactions on Signal Processing, Vol. 58, No. 3, 2010, pp. 18751888. doi:10.1109/TSP.2009.2038412 [7] H. M. Wang, Q. Y. Yin and X. G. Xia, “Improving the Physical Layer Security of Wireless TwoWay Relaying via Analog Network Coding,” Proceedings of IEEE Global Telecommunications Conference (GLOBECOM), Texas, Houston, Dec. 2011. [8] H. M. Wang, Q. Y. Yin and X. G. Xia, “Distributed Beamforming for PhysicalLayer Security of TwoWay Relay Networks,” IEEE Transactions on Signal Process ing, Vol. 60, No. 7, 2012, pp. 35323545. doi:10.1109/TSP.2012.2191543 [9] I. Krikidis, J. S. Thompson and S. McLaughlin, “Relay Selection for Secure Cooperative Networks With Jam ming,” IEEE Transactions on Wireless Communications, Vol. 8, No. 10, 2009, pp. 50035011. doi:10.1109/TWC.2009.090323 , pp. 310320. [10] J. Chen, R. Zhang, L. Song, Z. Han and B. Jiao, “Joint Relay and Jammer Selection for Secure TwoWay Relay Networks,” IEEE Transactions on Information Forensics and Security, Vol. 7, No. 1, Jan. 2012 doi:10.1109/TIFS.2011.2166386 [11] Z. Ding, K. K. Leung, D. L. Goeckel and D. Towsley. “Opportunistic Relaying for Secrecy Communications: Cooperative Jamming vs. Relay Chatting,” IEEE Trans actions on Wireless Communication 2011, pp. 17251729. s, Vol. 10, No. 6, doi: /10.1109/TWC.2011.0 40511.101694 [12] A. Bletsas, A. Khisti, D. P. Reed and A. Lippman, “A Simple Cooperative Diversity Method Based On Network Path Selection,” IEEE Journal Selected in Areas Commu nications, Vol. 24, No. 3, Mar. 2006, pp. 659672. doi:10.1109/JSAC.2005.862417 [13] M. Bloch, J. Barros, M. Rodrigues, and S. McLaughlin, “Wireless Informationtheoretic Security,” IEEE Trans actions on Information Theory, Vol. 54, No. 6, 2008, pp. 25152534. doi:10.1109 /TIT.2008.921908 [14] J. Xiong, K. K. Wong, D. Ma and J. Wei, “A 12.121254 ClosedForm Power Allocation for Minimizing Secrecy Outage Probability for MISO Wiretap Channels via Masked Beamforming,” IEEE Communications Letters, Vol. 16, No. 9, 2012, pp. 14961499. doi:10.1109/LCOMM.2012.0731
