2017 3rd IEEE International Conference on Computer and Communications
A Novel Half-Jamming Protocol for Secure Two-Way Relay Systems Using a FullDuplex Jamming Relay
Chensi Zhang, Jianhua Ge, Zeyu Xia, He Wang State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, China e-mail: {cszhang, jhge}@xidian.edu.cn,
[email protected],
[email protected] Abstract —This paper investigates how to improve the physicallayer security for two-way relay systems with the help of a full-duplex relay (FDR). Based on the particularity of two-way relay, a novel FDR-based half-jamming protocol is proposed. In the first time slot, the relay splits a portion of its power to transmit jamming noise against eavesdropping attacks, while simultaneously receiving the sources’ signal by operating in FD mode. In the second time slot, the relay operates in half-duplex mode for broadcasting the overlapped signals from the two sources. Closed-form expression of sum secrecy rate is given. Simulation results has shown that considerable performance gain is achieved compared with no jamming protocol. Keywords —Physical-layer security; two-way relaying; full duplex; half-jamming; power allocation
I. I NTRODUCTION Owing to their abilities to realize diversity gain as well as expand the coverage of wireless networks, cooperative relays have attracted prominent attention. Conventionally, one-way relay (OWR) [1] requires four time slots to complete a bidirectional communication due to half-duplex (HD) [2] mode. As a result, two-way relay (TWR) [3] emerges as a promising approach to mitigate the spectral efficiency loss of OWR by reducing the time overhead to two time slots [4]. Of particular interest is amplify-and-forward (AF)-based TWR (TWR-AF), which is characterized by low-complexity. To further improve the system spectral efficiency, full-duplex (FD) mode has been introduced to TWR-AF [5], [6], which is believed to have double spectral efficiency comparing with HD mode. Due to the opening nature of wireless medium and the broadcast property of physical layer, wireless networks are vulnerable to potential eavesdropping attacks. Therefore, the security of physical-layer has recently gain increasing attention [7]-[9]. Particularly, as a potential technology for 5G networks [10], FD radio has recently been utilized to enhanced PLS and considerable performance gains were achieved [11]-[14]. The goal of [11] is to maximize the achievable secure degrees of freedom by using a FD legitimate receiver for a multi-input multi-output Gaussian wiretap channel. Transmit beamforming for a FD base station was designed in [12] considering both self-interference mitigation. In [13], the power efficient resource allocation algorithm was investigated for secure multiuser wireless communication systems employing a FD
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base station. In [14], fast power allocations were developed to maximize the secrecy capacity for secure communication with FD destination. In this paper, how to improve the PLS for TWR-AF by FD radio is the focus. For TWR-AF, [15] and [16] proposed joint relay and jammer selection schemes, where three nodes are selected for the roles of conventional relay and two jammers, respectively. Following these two studies, [17] introduced game-theoretic power control approach to optimize the benefits of legitimate nodes. However, these works have neglected the particularity of TWR over OWR: the eavesdropper can only access to a overlapped signal from the two sources in each time slot [18],[19]. It has been shown that the jamming process in the second time slot is not necessary. In [19], two nodes were selected, where one for relaying and the other for jamming in the first time slot. In this paper, we adopt a FD relay (FDR) to be responsible for these two duties: relaying and jamming. A novel FDR-based halfjamming protocol is proposed. Specifically, the relay operates in FD mode and allocates a portion of the its power for jamming in the first time slot. The rest of this paper is organized as follows. In Section II, the considered system model is presented. In Section III, we show in detail the proposed FDR-based half-jamming protocol. The simulation results are presented in Section IV. In Section V, we conclude this paper. II. S YSTEM M ODEL Conventionally, a secure HD two-way relay network can be shown as Fig. 2. The network consists of two sources node A and B, one trusted relay R and one passive eavesdropper E. A and B plan to exchange sensitive information with the help of R, while E tries to wiretap the transmission. Both sources operate in half-duplex mode. Let hij denotes the channel gain between node i and j, where i, j ∈ {A, B, R, E}. The transmit power of A, B and R are denoted by PA , PB and PR , respectively. In the first time slot, both A and B transmit their signals to the R, simultaneously. During the second time slot, R broadcasts the superimposed signal after amplifying it with a variable gain G = PR / (PA |hAR |2 + PB |hBR |2 ). The instantaneous signal-to-noise ratios (SNRs) of A and B are
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5
E = log2 1 + ΥE (8) CB BR The secrecy rates of the two one-way channel can be given
% by
( VWWLPHVORW
$
5
D
S E CA = max CA − CA ,0 D
S E = max CB − CB ,0 CB
(9) (10)
The sum secrecy rate is given by S S + CB C S−sum = CA III. FDR- BASED H ALF -JAMMING P ROTOCOL
%
(11)
From (5), in high SNR region, we can observe that ΥE A ≈
(
1st time slot
QGWLPHVORW 'HVLUHGOLQN :LUHWDSOLQN Fig. 1.
Conventional system model for TWR-AF.
given respectively by [19] ΥD A =
PR PB gAR gBR (PR + PA ) gAR + PB gBR
(1)
ΥD B =
PR PA gAR gBR (PR + PB ) gBR + PA gAR
(2)
where gAR = |hAR |2 /N0 , gBR = |hBR |2 /N0 . Then, the capacities of the main channels are given by D CA = log2 1 + ΥD (3) A D D CB = log2 1 + ΥB (4) On the other hand, the total instantaneous received SNR at E can be given by ΥE A =
PB gBE P g +1 A AE 1st time slot
+
PR PB gBR gER P P g g + PR gER + PA gAR + PB gBR R A ER AR
(5)
2nd time slot
ΥE B =
PA gAE PB gBE + 1 1st time slot
+
PR PA gAR gER PR PB gER gBR + PR gER + PA gAR + PB gBR
PB gBE →∞ PA gAE + 1
(6)
2nd time slot
As a result, the capacity from B and A to E are given by E CA = log2 1 + ΥE (7) AR
when gBE gAE (E locates close to B), and vice versa. Obviously, for two-way relaying systems, the overall information leakage is dominated by the first time slot [18]. It has been shown in [19] that only one-time-slot jamming is sufficient. Therefore, the jamming process in the second time slot is not employed in our design. As pointed out in [14], FD radio can be used not only for increased spectral efficiency but also for increased security. This paper focus on the latter. Specifically, FDR is adopted to transmit jamming noise while simultaneously receiving the source signals in the first time slot. As shown in Fig. 2, the power of R is split into two parts with a power splitter factor p. The first part pPR is for jamming and the second part (1 − p)PR is used to forward the sources’ signal. The detail protocol is presented as: FDR-based half-jamming protocol: a) In the first time slot, both A and B simultaneously transmit their signals to R. R helps to degrade the quality of the eavesdropper’s link by operating in FD mode and transmitting jamming noise with power pPR , while it simultaneously receiving the source signals. b) During the second time slot, R first removes its self-interference and then operates in HD mode to broadcast the superimposed signal after amplifying it with a variable gain G = (1 − p) PR / (PA |hAR |2 + PB |hBR |2 ). c) Both A and B can obtain their designed signals by removing their self-interference. The advantage of utilizing full-duplex jamming relay is twofold: i) Since the relay can remove its self-interference, the jamming process have no impact on the two sources. ii) Our design has the characteristic of low-complexity and easy implementation comparing without adopting additional jamming node. The instantaneous signal-to-noise ratios (SNRs) of A and B are rewritten respectively by
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\
%
5
S35 5
( VWWLPHVORW
$
%
5
S 35
[5 \5
$
%
(
(
[
[( \(
QGWLPHVORW 'HVLUHGOLQN
Fig. 3.
Simulation Model.
:LUHWDSOLQN -DPPLQJOLQN Fig. 2.
E(2)
ΥB
Conventional system model for TWR-AF.
ΥD A =
(1 − p)PR PB gAR gBR ((1 − p)PR + PA ) gAR + PB gBR
(12)
ΥD B =
(1 − p)PR PA gAR gBR ((1 − p)PR + PB ) gBR + PA gAR
(13)
For the eavesdroppers, the received signal at E in the first time slot is given by √ √ (1) yER (t) = PA hAE sA (t) + PB hBE sB (t) (14) √ + pPR hER sJ (t) + n1 (t) where sA (t) and sB (t) are the unit power signals transmitted by A and B, respectively, and n1 (t) ∈ CN (0, N0 ) is the additive white Gaussian noise (AWGN) at E. The received SNRs at E in the first time slot are given by E(1)
=
PB gBE PA gAE + pPR gER + 1
(15)
E(1)
=
PA gAE PB gBE + pPR gRE + 1
(16)
ΥA ΥB
In the second time slot, the received signal at E is given by √ √ (2) yRE (t) = hRE G PA hAR sA (t) + PB hBR sB (t) (17) +n2 (t)) + n3 (t) where n2 (t) ∈ CN (0, N0 ) and n3 (t) ∈ CN (0, N0 ) are AWGN at R and E. Then the total instantaneous received SNR at E can be given by E(2)
ΥA
=
(1 − p)PR PB gBR gER (1 − p)PR PA gER gAR + EER
(18)
=
(1 − p)PR PA gAR gER (1 − p)PR PB gER gBR + EER
(19)
where EER = (1 − p)PR gER + PA gAR + PB gBR . As a result, the capacity from B and A to E are given by E CA = log2 1 + ΥE (20) A E = log2 1 + ΥE (21) CB B E(1)
E(2)
E(1)
where ΥE + ΥA and ΥE A = ΥA B = ΥB The sum secrecy rate is given by S S CJS−sum = CA + CB
E(2)
+ ΥB
. (22)
The value of p has significant impact on the system secrecy performance. In this paper, we present a simple strategy to determine p as follows: p = 0, CJS-sum C S-sum (23) p = 0.5, CJS-sum > C S-sum where p = 0 means no jamming process is adopted and p = 0.5 means half of the power of R is utilized for jamming. It is worth remarking that the optimization problem can be further exploited to choose properly the value of p, which is left for future consideration. IV. N UMERICAL R ESULTS In this section, simulation results based on our proposed protocol are presented. Without loss of generality, as shown in Fig. 3 we consider a two-dimensional network topology and let (xi , yi ) denotes the coordinate of node i. Set (xA , yA ) = (−0.5, 0) and (xB , yB ) = (0.5, 0). We assume that the path loss coefficient α = 3 and consider equal power allocation PA = PB = PR = PT /3. Let dij denotes the distance between node i and node j.
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Sum secrecy rate (bps/Hz)
3 Proposed No jamming
2.5 2 1.5 1 0.5 0 0
0.2
0.4
0.6
0.8
1
dR Fig. 4. Sum secrecy rate against dAR with (xR , yR ) = (−0.5 ∼ 0.5, 0), (xE , yE ) = (−0.4, 0) and PT = 15dB.
Fig. 6. Sum secrecy rate against the location of R under no jamming protocol with (xR , yR ) = (−0.5 ∼ 0.5, −0.5 ∼ 0.5) and (xE , yE ) = (−0.4, 0).
Sum secrecy rate (bps/Hz)
7 6
PT = 15dB
5
PT = 10dB
4 3 2 1 0 0.1
Proposed No jamming 0.2
0.3
0.4
0.5
0.6
0.7
0.8
dE Fig. 5. Sum secrecy rate against dAE with (xR , yR ) = (0, 0), (xE , yE ) = (−0.5 ∼ 0.5, 0) and PT = 10, 15dB.
To present the impact of relay’s location, we set (xR , yR ) = (−0.5 ∼ 0.5, 0), (xE , yE ) = (−0.4, 0) and PT = 15dB. That is, E is very close to source A. Fig. 4 plots the sum secrecy rate against dAR under the proposed protocol and no jamming protocol. As shown in Fig. 4, the sum secrecy rate approaches zero without jamming process, and the proposed protocol is well ahead of no jamming protocol, indicating the advantage of our design. To present the impact of eavesdropper’s location, we set (xR , yR ) = (0, 0) and (xE , yE ) = (−0.5 ∼ 0.5, 0). Fig. 5 plots the sum secrecy rate against dAE with PT = 10, 15dB. As shown in Fig. 5, the performance of the proposed algorithm outperforms no jamming protocol when E locates closely to the sources. Furthermore, we can observe that no jamming process is necessary when E locates around the middle of the two sources. To clearly present the effectiveness of the proposed pro-
Fig. 7. Sum secrecy rate against the location of R under the proposed protocol with (xR , yR ) = (−0.5 ∼ 0.5, −0.5 ∼ 0.5) and (xE , yE ) = (−0.4, 0).
tocol, we let R traverses the two-dimensional area. We set (xE , yE ) = (−0.4, 0) and (xR , yR ) = (−0.5 ∼ 0.5, −0.5 ∼ 0.5) and PT = 15dB. Fig. 6 and Fig. 7 plot the sum secrecy rate against the location of R under no jamming protocol and the proposed protocol, respectively. By comparing the two figures, we can observe that the proposed algorithm have not only improved the sum secrecy rate but also enlarged the safe region (C S-sum > 0) to a great extent. V. C ONCLUSION This paper proposes a novel half-jamming protocol based on FD relay for secure two-way relaying networks. Specifically, R helps to degrade the quality of the eavesdropper’s link by operating in FD mode and transmitting jamming while it simultaneously receiving the source signals. The proposed protocol has the advantages of good performance and low complexity. Simulation results indicate that our proposed algorithm is able to bring significant performance gain compared with no
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jamming protocol, and the safe region is enlarged to a great extent. ACKNOWLEDGMENT The authors would like to thank the National Natural Science Foundation of China (61501347), the “111” project (B08038), the Project Funded by China Postdoctoral Science Foundation (2015M580816), and the Fundamental Research Funds for the Central Universities. R EFERENCES [1] G. Kramer, M. Gastpar, P. Gupta, “Cooperative strategies and capacity theorems for relay networks,” , vol. 51, no. 9, pp. 3037–3063, Sep. 2005. [2] B. Rankov and A. Wittneben, “Spectral efficiency protocols for halfduplex fading relay channels,” J , vol. 25, no. 2, pp. 379–389, Feb. 2006. [3] C. S. Zhang, J. H. Ge, J. Li, Y. Rui, and M. Guizani, “A unified approach for calculating outage performance of two-way AF relaying over fading channels,” , vol. 64, no. 3, pp. 1218–1229, Mar. 2015. [4] S.L. Zhang, C.S. Liew and P.P. Lam, “Hot topic: physical-layer network coding,” in , 2006, pp. 358–365 [5] H. Ju, E. Oh, and D. Hong, “Catching resource-devouring worms in nextgeneration wireless relay systems: Two-way relay and full-duplex relay,” , vol. 47, no. 9, pp. 58–65, Sep. 2009. [6] H. Cui, M. Ma, L. Song, and B. Jiao, “Relay selection for two-way full duplex relay networks with amplify-and-forward protocol,” , vol. 13, no. 7, pp. 3768–3777, 2014. [7] A. Mukherjee, S. A. Fakoorian, J. Huang, A. L. Swindlehurst et al., “Principles of physical layer security in multiuser wireless networks: A survey,” & , vol. 16, no. 3, pp. 1550–1573, 2014. [8] J. Zhu, Y. Zou, and B. Zheng. “Physical-Layer Security and Reliability Challenges for Industrial Wireless Sensor Networks,” , vol. 5, 5313–5320, Apr. 2017.
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