Artificial-Noise-Aided Secure MIMO Full-Duplex Relay ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2579623, IEEE Communications Letters 1

Artificial-Noise-Aided Secure MIMO Full-Duplex Relay Channels with Fixed-Power Transmissions Ahmed El Shafie†, Dusit Niyato⋆ , Naofal Al-Dhahir† †

⋆

Electrical Engineering Dept., University of Texas at Dallas, USA. School of Computer Engineering, Nanyang Technological University (NTU), Singapore.

Abstract—This letter studies the physical-layer security of a full-duplex multiple-input multiple-output relay channel. A legitimate source node (Alice) communicates with her destination node (Bob) through a full-duplex relay node in the presence of a cooperative full-duplex jammer and a potential eavesdropper (Eve). The cooperative jammer is assumed to be a full-duplex node that is solely charged by the ambient radio-frequency transmissions. We investigate the self-energy recycling at the cooperative jammer and derive a sufficient condition for the cooperative jammer to operate as a node with reliable energy supply. Without knowing the eavesdropper’s channel state information at the legitimate nodes, we propose a precoded artificialnoise injection scheme to secure the legitimate transmissions. The numerical results demonstrate that our proposed artificial-noiseaided secure scheme achieves a significant average secrecy rate improvement compared to the case of no cooperative jammer. Index Terms—Energy recycling, full duplex, security.

I. I NTRODUCTION Radio-frequency (RF) energy harvesting is the ability of a wireless node to convert its received RF transmissions into a direct current (DC) electricity. RF energy-harvesting networks have sustainable on-demand power supply from the ambient radio environment [1]. To confuse potential eavesdroppers in a network, artificial noise (AN) injection was proposed in [2]. AN precoding systems assume that the eavesdropper’s channel state information (CSI) is unknown at the legitimate transmitters. Hence, the AN precoder design is based on the legitimate links CSI and the AN vector is typically transmitted orthogonally to the data vectors [3]. The authors of [4] considered the multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) relay channel. Both the source and its destination cooperate in jamming the eavesdropper. The authors assumed that the source and its destination are far away from each other and assume that there is no direct link between them. Unlike [4], we investigate the availability of a full-duplex (FD) relay node and assume the possibility of having an RF energyharvesting cooperative jamming node. The authors of [5] proposed the deployment of an energyharvesting cooperative jammer (CJ) to help a source node in its communication with a legitimate receiver in a multiple-input multiple-output (MIMO) wiretap channel. The jamming signal vector was assumed to be not orthogonal to the desired channel This paper was made possible by NPRP grant number 6-149-2-058 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

vector. Unlike [5], we assume that the CJ is an RF-energy harvester with FD capabilities. The authors in [6] proposed a harvest-and-jam scheme with multi-antenna CJs and a multiantenna amplify-and-forward (AF) half-duplex relay node to improve the legitimate system secrecy rate. However, perfect and imperfect CSI knowledge was assumed at the legitimate system about the eavesdropper’s channel, which is impractical, especially, when the eavesdropper is a passive node. Furthermore, it was assumed in [6] that the legitimate source node, legitimate destination node, and the eavesdropping node are all equipped with single antennas. Moreover, Reference [6] assumed that there is no direct link between the source node and both the legitimate receive node and the potential eavesdropper. In [7], the authors assumed the single-input single-output single-antenna eavesdropper (SISOSE) wiretap channel with single-antenna FD relay node when there is no direct link between the source node and its destination. Unlike [7], we assume that all nodes are equipped with multiple antennas in the presence of a cooperative FD jammer. The contributions of this letter are summarized as follows •

•

•

To the best of our knowledge, this is the first work which investigates the physical (PHY) layer security of an FD relay channel with the aid of an RF energy-harvesting CJ that is solely powered by the ambient RF transmissions. We design a secure scheme with the aid of precoded AN transmissions for an FD relay channel. We design the AN-precoder matrices at the CJ and derive a necessary condition on the number of transmit antennas at the CJ to enable its operation in the network. We derive a sufficient condition for the CJ to become a node with reliable energy supply. Moreover, we investigate the impact of the self-interference channel on the recycled energy at the CJ’s receiver and the transmit signal from nearby nodes (i.e. source and relay nodes). Moreover, unlike [6], we incorporate the energy consumption due to signal processing at the CJ in our analysis.

Notation: Unless otherwise stated, lower and upper case bold letters denote vectors and matrices, respectively. The matrix IN denotes the identity matrix whose size is N × N . CM×N denotes the set of all complex matrices of size M ×N . (·)∗ denotes Hermitian (i.e. complex-conjugate transpose) operation. The function min{·, ·} (max{·, ·}) returns the minimum (maximum) among the values in the brackets. E{·} denotes

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statistical expectation. 0 denotes the all-zero matrix/vector and its size is understood from the context. Trace{·} denotes the sum of the diagonal elements of the matrix in the brackets. II. M AIN A SSUMPTIONS AND P ROPOSED S CHEME We consider a wireless network composed of one source node (Alice), one eavesdropper (Eve), one cooperative FD jammer, one FD relay, and one destination (Bob). All nodes are equipped with multiple antennas. The number of antennas at Alice, Eve, and Bob are denoted by NA , NE , and NB , respectively. We assume a general scenario of a completely cooperative set of eavesdroppers (i.e. an eavesdropper with multiple antennas can be viewed as NE colluding singleantenna eavesdroppers) in the presence of a CJ which harvests its energy from the ambient RF transmissions. Time is partitioned into equal-size slots. Alice is always backlogged with data to transmit. We assume that Alice is located far away from both Bob and Eve; hence, there are no direct links between Alice and any of them. Moreover, the relay, the CJ, Bob and Eve are in the same cluster (i.e. they are in the transmission range of each other). In addition, we assume that Alice, the relay and the CJ are in the same cluster [6]. We adopt the similar assumptions as in, e.g., [6]. The CJ must be in the same cluster of the relay and Alice so that it can harvest more energy by overhearing both Alice and the relay transmissions. 1) CJ’s Model: The CJ is assumed to be equipped with RF energy harvesting capability and is solely charged by the ambient RF transmissions from nearby nodes. The CJ is assumed to be an FD node in the sense that it can harvest energy and transmit an AN signal at the same time. Hence, it can recycle the energy transmitted from its transmit RF chain to its RF-to-DC conversion circuits through the loop-back channel.1 Since energy is critical for the CJ to operate properly, we do not need to suppress the self-interference caused by the concurrent operation of the transmit RF chain and the receive RF chain. Hence, the design of the CJ’s transceiver is simpler than the conventional transceiver design.2 We assume that the CJ’s energy is stored in a battery, the energy level of which is denoted by BJ . Since the CJ is an FD node, we assume that it has NJt transmit antennas and NJr receive antennas which are assigned permanently for the transmission of AN signals and reception of energy signals, respectively. 2) Relay’s Model: The FD relay is used for data transmission and reception. Hence, the self-interference can degrade the achievable data rate at the relay node. The relay decodes and forwards Alice’s data. Since the relay is an FD node, it has NRt transmit antennas and NRr receive antennas. 3) Channel Model: Each link follows a flat block-fading channel which is corrupted by an additive white Gaussian noise (AWGN) vector. We assume that the channel coefficient 1 This

actually represents the so-called self-energy recycling (loop energy) [1]. In particular, the energy used for AN transmission can be harvested by the CJ’s receive RF chain and reused in addition to the other RF energy harvested from the ambient transmissions of the nearby nodes. 2 Conventionally, the implementation of the transceiver of an FD node that receives information requires a complex analog and/or digital interferencecancelation schemes. However, in our assumed CJ’s design, we do not need to suppress the self-interference. On the contrary, we exploit the self-interference to recycle most of the transmitted energy by the CJ.

of the link connecting Antenna nk at (k ∈ {1, 2, . . . , Nn }) at Node n and Antenna mℓ (ℓ ∈ {1, 2, . . . , Nm }) at Node m, denoted by hnk ,mℓ , is independent and identically distributed (i.i.d.) from one slot time to another with zero mean and vari2 ance σn,m . Furthermore, the channels are spatially independent. We denote Alice, Bob, the relay, the jammer, and Eve by A, B, R, J, and E, respectively. The channel matrix between Node n ∈ {A, R, J} and Node m ∈ {A, B, R, J, E} is Hn,m . We assume that Eve knows all the channel coefficients of the links between CJ/the relay and her receiver and the links between CJ/the relay and Bob. Hence, she perfectly knows the data and AN precoders used at the relay and the jammer, which represents the best-case scenario for Eve and enables her to decode the relay data reliably.3 The AWGN at receiving node m is assumed to have a zero mean and a variance of κm Watts/Hz. Each legitimate node knows perfectly the channels connecting it with the intended receiver in a given time slot. Fixed-power transmissions are assumed. The average transmit power level of Node n is Pn Watts, n ∈ {A, R, J}. The energy dissipated in operating the transmit RF chain at the CJ, i.e., the signal processing power consumption in the CJ’s transmit circuit caused by filters, frequency synthesizer, etc, is Pp < Pn power units.4 For the CJ to transmit an AN vector, it needs Pp T energy units to operate its circuits for T seconds and PJ T energy units for its precoded-AN signals transmission. Hence, the CJ’s battery must have at least PJ T +Pp T energy units for the relay to transmit an AN vector in a given time slot. 4) Proposed AN-Aided Secure Scheme: To increase the probability of secure transmission (i.e. decrease Eve’s decoding ability), we assume a precoded AN vector transmissions by a CJ node. The AN vector is designed in a way that it is canceled at the desired receivers. Hence, Eve (the undesired receiver) will suffer from interference signals transmitted by the CJ node. Our proposed scheme is summarized as follows. Alice transmits data to the relay. At the same time, the relay decodes the data and retransmits it to Bob, and the CJ transmits an AN vector to confuse Eve when its battery has at least PJ T +Pp T energy units. Since there is no direct link between Alice and Eve, Eve only eavesdrops the relay’s transmissions. III. DATA AND AN P RECODING M ATRICES D ESIGN AND N ODE R ATES In this section, we design the data precoders and filters for the relay and Alice and the AN precoder for the CJ. The AN precoder matrix is designed such that the AN vector is canceled simultaneously at both the relay and Bob. Let us denote by IJ the state of the jamming activity of the CJ. If the CJ has sufficient energy, i.e., the CJ’s battery level BJ ≥ PJ + Pp , then IJ = 1. If BJ < PJ + Pp , then IJ = 0. A. Data and AN Precoding Matrices Design By assuming a processing delay at the relay, the received signal vector at the relay’s receiver is given by yR = HA,R PA xA +HR,R PR xR +IJ HJ,R PJ zJ +nR

(1)

3 Eve can obtain the CSI through channel estimation and overhearing the channel feedback from Bob to both the relay and the CJ. 4 The processing power is typically lower than the transmission power.



where yR ∈ CNRr ×1 is the received observation vector at the relay, xA ∈ CNA,R ×1 is the data vector transmitted by Alice, NA,R ≤ min{NA , NRr } is the number of data streams transmitted by Alice, xR ∈ CNR,B ×1 is the data vector transmitted by the relay, NR,B ≤ min{NRt , NB } is the number of data streams transmitted by the relay, HR,R is the residual self-interference matrix at the relay after the self-interference cancellation, PR ∈ CNRt ×NR,B is the data precoder matrix at the relay, PJ is the used AN precoding matrix at the CJ, zJ is the AN vector, and nR ∈ CNRr ×1 is the AWGN vector at the relay. Assuming a filter matrix C∗R at the relay, the condition to cancel the CJ’s AN vector at the relay’s receiver is C∗R HJ,R PJ = 0.

(2)

−1

The received signal vector at Bob is given by yB = HR,B PR xR + IJ HJ,B PJ zJ + nB .

HR,B , ΣR,B is the singular values diagonal matrix, and the columns of VR,B are the right singular vectors of HR,B . Hence, the data precoder PR is the NR,B columns of VR,B corresponding to the largest NR,B non-zero singular values, and the receive filter CB is the NR,B columns of UR,B corresponding to the largest NR,B non-zero singular values. For MIMO systems with equal power allocation, the covariance matrix of the data vector transmitted by Node n to Node m is pn INn,m = (Pn /Nn,m )INn,m where pn = Pn /Nn,m . Since the relay suffers from self-interference due to its own transmission, the relay uses a whitening filter to whiten the self-interference-plus-noise signal followed by a linear receive filter based on the SVD of the equivalent channel matrix. The covariance matrix of HR,R PR xR + nR in (1) is QR = pR HR,R PR (HR,R PR )∗ + κR INRr . The relay applies

(3)

∗ . the whitening filter QR 2 followed by a receive filter WR Hence, the receive signal vector at the relay becomes −1

Assuming a filter matrix vector at Bob, we have

C∗B

at Bob, to cancel the CJ’s AN

(9)

−1

C∗B HJ,B PJ = 0.

(4)

To cancel the AN at both the relay node and Bob, conditions (2) and (4) must be satisfied simultaneously. Hence, WJ∗ PJ =

−1

∗ ∗ ∗ ˜R WR QR 2 yR = WR QR 2 HA,R PA xA + WR n

C∗R HJ,R PJ = 0. ∗ CB HJ,B

(5)

Since the size of C∗R HJ,R is NA,R × NJt and C∗B HJ,B is NR,B × NJt , the null space existence condition is NJt > NA,R + NR,B .

(6)

The dimension of PJ is thus NJt × (NJt − (NA,R + NR,B )). Remark 1. If NJt ≤ NA,R + NR,B , the CJ cannot transmit a jamming signal concurrently with data transmissions since there is no null space for matrix WJ∗ in (5). Hence, the CJ remains silent. Accordingly, a necessary condition for the CJ’s operation in the network is that the CJ should have at least NA,R + NR,B + 1 transmit antennas.

(7)

where nE ∈ CNE ×1 is the AWGN vector at Eve. The received signal vector at the CJ is given by yJ = HA,J PA xA + HR,J PR xR + IJ HJ,J PJ zJ + nJ

B. Node Rates and Secrecy Rate The achievable rate at the relay node is ∗ −1 ˜ A,R PA H ˜ A,R PA RR RA,R = log2 det INRr +pA H

where pA =

PA NA,R ,

1

−1 ∗ −1 RR = QR 2 pR HR,R PR (HR,R PR )∗ +κR W INRr QR 2 . (11)

The achievable rate at Bob is

where pR =

PR NR,B .

where nJ ∈ CNJr ×1 is the AWGN vector at the CJ, HA,J PA xA is the received signal vector at the CJ’s receiver from Alice data vector transmission, HR,J PR xR is the received signal vector at the CJ’s receiver from the relay data vector transmission, and HJ,J PJ zJ is the self-interference signal vector at the CJ. To maximize the signal-to-noise ratio (SNR) at Bob, the relay and Bob use the singular value decomposition (SVD) for the channel matrix HR,B to design the data precoder matrix ∗ , and receive filter matrix. Let HR,B = UR,B ΣR,B VR,B where the columns of UR,B are the left singular vectors of

(12)

The achievable rate at Eve is thus

−1 J RIR,E = log2 det INE +pR HR,E PR (HR,E PR )∗ RE

(8)

(10)

˜ A,R = Q− 2 HA,R and H R

pR RR,B = log2 det INB + HR,B PR (HR,B PR)∗ κB W

The received signal vector at Eve is given by yE = HR,E PR xR + IJ HJ,E PJ zJ + nE

˜ R = QR 2 (HR,R PR xR + IJ HJ,R PJ zJ + nR ). where n −1 ∗ ∗ Let CR = WR QR 2 denote the overall receive filter at the relay. From (5), C∗R HJ,R PJ = 0. Hence, ∗ ˜ WR nR = C∗R (HR,R PR xR + nR ) + IJ C∗R HJ,R PJ zJ = ∗ ∗ ˜ R is an AWGN n CR (HR,R PR xR +nR ). Accordingly, WR vector. The signal-to-interference-plus-noise ratio (SINR) is maximized at the relay’s receiver when Alice and the relay use −1 the SVD of the equivalent channel QR 2 HA,R in designing the ∗ data precoder matrix PA and receive filter matrix WR .

(13)

with RE = κE W INE + IJ pJ HJ,E PJ (HJ,E PJ )∗ where PJ pJ = NJ −(NA,R +NR,B ) is the power of an AN symbol and t NJt −(NA,R +NR,B ) is the number of symbols per AN vector. The end-to-end rate of the legitimate system is given by RA,B = min{RA,R , RR,B }.

(14)

The system secrecy rate is given by J J RIA,B,sec = (RA,B − RIR,E )+

(15)

where (·)+ = max{·, 0}. The average system secrecy rate is E{RA,B,sec } = Pr{BJ < PJ + Pp }E{R0A,B,sec } + Pr{BJ ≥ PJ + Pp }E{R1A,B,sec }.

(16)


This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2016.2579623, IEEE Communications Letters N =1, N =4

C. CJ’s Battery In the following, we derive the condition for the CJ to become a node with reliable energy supply and is able to jam Eve in every time slot. We show that when the CJ’s battery reaches the state that {BJ ≥ (PJ + Pp )T } and the energy 2 conversion efficiency, denoted by ζ, is ζ = 1 and both σJ,J 2 5 and σA,J are not less than 1, it will build up with time. From (8), the harvested energy at the CJ in a given time slot is given by EH = ζT Trace {E{yJ yJ∗ }} = pA Trace {HA,J PA (HA,J PA )∗ }

+ IJ pJ Trace {HJ,J PJ (HJ,J PJ )∗ } + pR Trace {HR,J PR (HR,J PR )∗ } + NJr κJ W ζT. (17)

From (17), the energy harvested in a given time slot is a function of the channel matrices between the transmitting nodes and the CJ. 2 2 2 Lemma 1. When ζ = 1 and σA,J , σR,J , σJ,J ≥ 1, the CJ’s battery state increases with time. 2 2 2 Proof. When ζ = σA,J = σR,J = σJ,J = 1, the average harvested energy at the CJ’s receiver is

E{EH } = T NJr (PA +PR +PJ +κJ W )

(18)

Assuming that BJ (t) ≥ (PJ + Pp )T , the battery state at the CJ will evolve as E{BJ (t + 1)} = E{BJ (t)}−(PJ +Pp )T (19) +T NJr PA +PR +PJ +κJ W > E{BJ (t)}

where BJ (t+1) is the CJ’s battery state at time t+1 and the last inequality follows from the fact that Pp < Pn , n ∈ {A, R, J}. Hence, the battery state increases with time which is beneficial since we need the CJ’s battery to be saturated with energy. IV. N UMERICAL S IMULATIONS We simulate the considered wireless network. The fading channels are assumed to be complex circularly-symmetric Gaussian random variables with zero mean and unit variance. The parameters used to obtain the results in Figure 1 are: κR = κB = κE = κ, PA /(κW ) = 15 dB, PR /(κW ) = 10 dB, PJ /(κW ) = 20 dB, Pp /(κW ) = 2 dB, ζ = 1, NRt = NRr = 3, NA,R = min{NA , NRr }, NR,B = min{NRt , NB }, NJr = 3, 2 2 2 NJt = NA,R + NR,B + 2, σA,R = σR,B = 1, σJ,J = 0.7, 2 2 σR,R = 0.6, and σR,E = 0.8. Figure 1 shows the gain of our proposed scheme in terms of the average system secrecy rate. As the number of transmit antennas, NA , increases, the average secrecy rate increases. The saturations are due to the fact that the rates are limited by the minimum number of transmit and receive antennas. The figure also shows the impact of increasing the number of receive antennas at Bob. When NB = NE = 4, the average secrecy rate at NA = 9 is 4.2 bits/sec/Hz. On the other hand, when NB = 5 and NE = 4, the average secrecy rate is 5.3 bits/sec/Hz. Hence, the average secrecy rate gain is 26%. Moreover, the figure 5 We emphasize that the analysis in our letter is not restricted by the assumption of ζ = 1. Please refer to Eqns. (16) and (17).

Average secrecy rate [bits/sec/Hz]

E

12

N =4, N =5

10

N =N =4

E E

4

B B

B

No jammer N =N =4

8

E

B

6 4 2 0

2

4

6

8

10

12

14

16

18

20

NA

Fig. 1. Average secrecy rate versus NA for different values of NE and NB .

demonstrates the average secrecy rate gain due to the presence of an RF energy-harvesting CJ. Without a CJ, the maximum average secrecy rate is 1.1 bits/sec/Hz. For the same antenna configuration (i.e. NE = NB = 4), the CJ helps in achieving an average secrecy rate of 4.2 bits/sec/Hz. Hence, the gain of the cooperative jamming is 282%. This reveals the significant gain of the CJ, which requires no external energy supply. Finally, the figure demonstrates the impact of the number of receive antennas at Eve. When NE = 1 and NB = 4, the average secrecy rate at NA = 9 is 9.65 bits/sec/Hz. On the other hand, when NE = 4, NB = 4 and NA = 9, the average secrecy rate is 4.2 bits/sec/Hz. Thus, the average secrecy rate loss due to increasing the number of antennas at Eve from NE = 1 to NE = 4 is 56%. V. C ONCLUSIONS We analyzed the PHY-layer security of an FD relay wireless network in the presence of an RF energy-harvesting CJ. We proposed an AN-aided secure transmission scheme in which an RF energy-harvesting jammer cooperatively confounds Eve by generating AN signals. In our proposed AN-aided scheme, the CJ transmits AN vectors in a way such that the interference is completely canceled at both the relay and Bob. We derived the condition on the CJ to operate as a node with reliable energy supply. Self-energy recycling at the CJ and self-interference at the relay were considered in our analysis. We showed that the CJ’s battery level increases with time under certain system parameters. Our numerical results demonstrated the secrecy rate benefits of the CJ, number of transmit antennas at Alice, number of receive antennas at Bob, and the negative impact of increasing the number of antennas at Eve. R EFERENCES [1] A. El Shafie and N. Al-Dhahir, “Secure communications in the presence of a buffer-aided wireless-powered relay with self-energy recycling,” IEEE Wireless Commun. Lett., vol. 5, no. 1, pp. 32–35, Feb 2016. [2] S. Goel and R. Negi, “Guaranteeing secrecy using artificial noise,” IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2180–2189, 2008. [3] Z. Chu, K. Cumanan, Z. Ding, M. Johnston, and S. Y. Le Goff, “Secrecy rate optimizations for a MIMO secrecy channel with a cooperative jammer,” IEEE Trans. Veh. Tech., vol. 64, no. 5, pp. 1833–1847, 2015. [4] J. Huang and A. L. Swindlehurst, “Cooperative jamming for secure communications in MIMO relay networks,” IEEE Trans. Sig. Process., vol. 59, no. 10, pp. 4871–4884, Oct 2011. [5] A. Mukherjee and J. Huang, “Deploying multi-antenna energy-harvesting cooperative jammers in the MIMO wiretap channel,” in IEEE ASILOMAR, 2012, pp. 1886–1890. [6] H. Xing, K.-K. Wong, Z. Chu, and A. Nallanathan, “To harvest and jam: A paradigm of self-sustaining friendly jammers for secure AF relaying,” IEEE Trans. Sig. Process., vol. 63, no. 24, pp. 6616–6631, Dec 2015. [7] G. Chen, Y. Gong, P. Xiao, and J. A. Chambers, “Physical layer network security in the full-duplex relay system,” IEEE Trans. Inf. Forensics Security, vol. 10, no. 3, pp. 574–583, 2015.
