Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals

Nội dung text: Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals

1. REV Journal on Electronics and Communications, Vol. 10, No. 3–4, July–December, 2020 85 Regular Article Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals Chan Dai Truyen Thai1, Vo Nguyen Quoc Bao2, De-Thu Huynh3 1 Vietnamese-German University (VGU), Vietnam 2 Posts and Telecommunications Institute of Technology (PTIT), Ho Chi Minh City, Vietnam 3 Ho Chi Minh City University of Economics and Finance (UEF), Vietnam Correspondence: Chan Dai Truyen Thai, chan.ttd@vgu.edu.vn Communication: received 28 November 2020, revised 31 December 2020, accepted 14 January 2021 Online publication: 16 April 2021, Digital Object Identifier: 10.21553/rev-jec.260 The associate editor coordinating the review of this article and recommending it for publication was Prof. Dang The Ngoc. Abstract– Active attacking in physical-layer security has not been significantly studied while potentially causing serious consequences for the legitimate networks. In this paper, we propose a novel method to estimate and remove the jamming signals from multiple multi-antenna jammers in a two-way relay network with multi-antenna legitimate and relay nodes. We carefully consider the signals in the time slots in order to exploit the repetition of the signals and design the transmitted signals which can work in different cases. The numerical results show that the secrecy rate at the legitimate nodes of the proposed scheme is higher than that of the conventional method when considering the affect of transmit signal-to-noise ratio (SNR); the number antennas at the legitimate and relay nodes; normalized distance between one legitimate node and the relay; and the vertical coordinate of the relay. Keywords– Eavesdropper, jamming, physical-layer security, reactive, untrusted relay. 1 Introduction solving for a point-to-point wireless network however the full description is given for the case of only two Physical-layer security has been extensively researched antennas and one jammer [5]. Karlsson et al. designed for about two decades. A great number of results and an optimal scheme to jam a pair of single-antenna techniques have been created. The view on the mali- transmitter and receiver with a direct transmission [6]. cious agents have also changed, become more diverse, In a game-theoretic and multi-antenna scenario in [7], and upgraded over time [1–3]. Generally, the mali- the eavesdropper can choose either eavesdropping and cious agents can be classified into two main categories: jamming the legitimate nodes in a direct transmission. passive and active attacks. The former refers to those A few other works considered on jamming attacking nodes only listening to or overhearing signals, trying in VANETS [8], flying Ad Hoc networks [9], jamming to extract the most information from them, and using attacking in cognitive radio networks with Stackelberg it for malicious purposes including analysis while the Game [10]. later can emit attacking signals. In an efficient way of using energy, while passive Eavesdroppers and untrusted relays/cooperators can attackers try to maximally receive information, active be considered as passive attackers [1]. The eavesdrop- attackers try to maximally hinder the transmissions pers stay completely in the “dark” and are generally of the legitimate [11, 12]. Two examples of actively assumed to be unknown by the legitimate nodes in attacking is jamming and forwarding garbled informa- terms of positions and channel gains. In the majority of tion [13]. Basically, there are three modes of jamming cases, the distribution of those variables are assumed as follows. to be known by the legitimate nodes. The untrusted cooperative nodes will honestly help/cooperate with • Constant jamming: the jammers always transmit the legitimate nodes in a way that the secrecy rate jamming signals [14]. is maximized. However, in the meantime, they try • Random jamming: the jammers only transmit in to extract as much information as possible from the random time slots with a certain probability [15]. received/overheard signals and use it for malicious • Reactive jamming: only when the jammers detect purposes. Other trustworthy levels/trust degrees can an active transmission from the legitimate nodes, also be defined to consider a finer resolution of mali- they transmit. However, we assume that due to ciousness [4]. the delay of the detection, the jammers only start Even though the active attacking topics has not been the jamming transmission one time slot after the extensively researched, there are a number of works legitimate nodes start their transmission [16]. in this area. Yan et al. proposed a scheme to remove In each jamming mode, the jammers can transmit one the jamming signals by variable elimination in equation of two signal types as follows. 1859-378X–2020-3403 â 2020 REV
2. 86 REV Journal on Electronics and Communications, Vol. 10, No. 3–4, July–December, 2020 • Fixed signal: each jammer always transmit the Jammers same signal. • Varied signal: each jammer transmit a different signal in every time slot. 1 1 1 In this paper, we propose a novel scheme to estimate R,1 � �R,2 �R,3 and remove the jamming signals in a two-way relay network with multi-antenna legitimate, relaying, and 1 1 A B jamming nodes. The two-way relay network is con- A � R � B sidered because this network model is very popular in practice, e.g., a wireless user is downloading from Figure 1. The network model. Transmissions in the first and second and uploading to a server [17]. To the best of our frames are represented by solid and dashed arrows, respectively. knowledge, this is the first work on such a topic. We consider constant and reactive fixed-signal jamming. The numerical results show that the performance of the two phases. There are m and m time slots in the first proposed scheme in both modes is better than that of 1 2 and second phases, respectively. The designed scheme the conventional scheme. will depend on the comparison between these numbers The rest of the paper is organized as follows. Sec- and l. The channel matrices from A and B to R in slot i tion 2 describes the system model used in the pa- of phase i are denoted by HiP,i and HiP,i, respectively. per. Section 3 presents the proposed and conventional P A B schemes in the constant jamming mode. From the result The channel matrices from the k-th jammer to A, B, iP,i iP,i of this section, we discuss and deduce the result for and R in slot i of phase iP are denoted by GA,k, GB,k , the reactive jamming mode, and present in Section 4. iP,i and GR,k, respectively. The noise in time slot i of phase The numerical results are presented and analyzed in iP,i iP ∈ {1, 2} at node iN ∈ {R, B} is denoted by z . We Section 5 and the conclusion is drawn in Section 6. iN denote 1 ì n vectors with all entries of 1 and 0 by 1n and 0n, respectively; element i and elements i1 to i2 of vector a by [a] and a by [a]i2 , respectively; element 2 System Model i i1 (i, j), column j, and row i of matrix A by [A]i,j, [A](:,j) 2.1 General System Model and [A](i,:), respectively; and the determinant of matrix In this part, we describe the general model for both A by |A| = det(A). Assume we can write A = {[A]i,j}. conventional and proposed schemes. A and B, which In slot i of phase 1, A and B transmit the i-th elements are referred here to as legitimate nodes, want to send of xA and xB, respectively. The received signal at R is information signal vectors xA and xB, respectively, to given by each other as shown in Figure 1. However, due to a K large distance or a bad faded channel between them, 1,i = 1,i i + 1,i i + 1,i 1,i + 1,i yR HA uAxA HB uBxB ∑ GR,kxJ,k zR (1) there is not a reliable channel for them to exchange the k=1 information and they must rely on the help of relay R. where 1 ≤ i ≤ m1; uA and uA are corresponding There are K actively attacking nodes which transmit 1,i 1,i precoding vectors. H u xi + H u xi is referred to jamming signals to make interference to the transmis- A A A B B B as the mixed information signal. In slot j of phase 2, R sions of A, B, and R. We assume that A, B, and R do i ji precodes y1, with matrix B ∈ CnRìnR and transmit it not have information about all jamming signals and all R B to A and B. The received signal at B is given by channels from the jammers to them but know which m1 K jamming mode and signal type are used. Nodes A, B, j j† ji j j j y2, = H2, B y1,i + G2, x2, + z2, R, and Jk are equipped with n, n, nR, and nJ antennas, B B ∑ B R ∑ B,k J,k B respectively. To focus on estimating and cancelling the i=1 k=1 † m1 † m1 jamming signals, we assume that the channels between 2,j ji 1,i i 2,j ji 1,i i = HB ∑ BBHA uAxA + HB ∑ BBHB uBxB A (B) and R are known among these nodes so that the i=1 i=1 m1 K needed information signals are successfully detected. j† ji +H2, B G1,i x1,i The channels are fixed in a coherence time of l time B ∑ B ∑ R,k J,k i=1 k=1 slots and change between such periods. Therefore all † m1 K + 2,j ji 1,i + 2,j 2,j + 2,j precoding vectors and matrices can be calculated at A, HB ∑ BBzR ∑ GB,kxJ,k zB B, and R. i=1 k=1 (2) i where 1 ≤ j ≤ m2. Since xB, channels, precoding vectors 2.2 System Model for the Proposed Scheme and matrices are available at B, it can remove the second 2,j In this part, we describe the system model and term in yB . The achieved signal then given by common scheme for the proposed scheme in both con- m1 m1 2,j 2,j† ji 1,i i 2,j† ji 1,i stant and reactive jamming modes. In order to analyze y˜ B = HB ∑ BBHA uAxA + HB ∑ BBgR the characteristics of different scenarios and classify i=1 i=1 m1 (3) them, we first describe the general transmission scheme 2,j† ji 1,i 2,j 2,j +HB ∑ BBzR + gB + zB , which is organized in frames. Each frame consists of i=1
3. C. D. T. Thai et al.: Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals 87 1,i = K 1,i 1,i 2,j = K 2,j 2,j where gR ∑k=1 GR,kxJ,k, and gB ∑k=1 GB,kxJ,k. We of the jamming components is the rate of the one, of the 1,i 2,j two factors, channels and signals, which varies faster. refer gR and gB to as jamming components of the first 2,j In addition, the faster the factors vary, the more difficult and second phases, respectively; and G1,i , G , x1,i, R,k B,k J,k it is for us to estimate the jamming components. In this 2,j xJ,k as jamming factors. Generally, there are methods to paper, we consider all three jamming modes with both i ≥ = decode needed information signal xA as follows. signal types and coherence time l 2 since with l 1, • i the jamming components vary the fastest and there is B decodes xA treating all jamming components as noise. This method gives a low performance, not enough information to estimate them. Furthermore, especially when the jamming powers are high or l ≥ 2 is reasonable and usually assumed for wireless the channels from the jammers to B are good. cooperative/relaying networks. • B estimates all jamming components first, cancels The jamming signal from each jammer is always the 2,j i same and that from the k-th jammer is given by them iny ˜ B , and decodes xA. This is impossible since B does not achieve enough signals to de- ( 2,j aJ,k, when jamming, code the needed signals. To demonstrate this, we x1,i = x = (4) J,k J,k 0 , when not jamming. consider two cases as follows in the most general nJ scenario in which all channels and jamming signals In case all jammers transmit with the same signal, change every time slot. aJ,k = aJ, ∀k. However, as we will try to decode and – Estimating each jamming component in factors: 1,i 2,i cancel jamming component gR and gB as a whole, not B first needs to estimate all (m1 + m2)KnJ the individual jamming signals from jammers, that the   1,i 2,j jamming signals from different jammers are the same jamming signals xJ,k, xJ,k in two phases; all or not is not important. However, we assume that in a m1KnJnR channels from the jammers to R in time slot all jammers transmit jamming signals or all phase 1; all m2KnJn channels from the jammers jammers do not transmit jamming signals. The case in to B in phase 2. However, B achieves only m2n 2,j signals in vectory ˜ while m n is much smaller which some jammers transmit while others do not in a B 2 time slot is not considered in this section. To improve than (m1 + m2)KnJ + m1KnJnR + m2KnJn. – Estimating each jamming component as a whole: the average rate, we design that the coherence time fits we reduce the number of variables to be esti- into each phase, i.e., each of the two phases consists of mated by only estimating each component as l time slots. In this section, we consider only two cases:  2,j all jammers transmit in a time slot with probability p ; a whole g1,i or g and does not need to es- J R B and no jammer transmits, with probability 1 − pJ.  1,i 2,j 1,i 2,j timate each factor inside GR,k, GB,k, xJ,k, xJ,k . In this case, B has m1nR + m2n + m1 signals 1,i to decode, including m1nR signals in all gR , 3 Constant Jamming 2,i m2n signals in all gB , and m1 signals in xA. However, again m2n is also much smaller than 3.1 Conventional Scheme m n + m n + m . 1 R 2 1 In this scheme, we assume that all jamming signals • We design the transmission scheme and the pre- cannot be estimated and removed, therefore R, A, and coding matrices so as in phase 1, R can estimate B will treat them as noise. In return, they use all time each jamming component as a whole or in factors, slots for transmitting information signals instead of cancel them, amplify and forward a jamming-free sacrificing one for estimating the jamming components. version of the mixed information signal to A and The scheme is performed every two time slots and does B in phase 2; and in phase 2, A and B can estimate not depend on the coherence time. The noise vectors each jamming component as a whole or in factors, at node R and B are respectively denoted by z and cancel them, and decode the information signal. In R zB below. In the first slot, the received signal at R is this paper, we use this third method and explain given by about it in more details below. 1 1 The way we design the scheme depends on which yR = HAuAxA + HBuBxB + gR + zR. (5) jamming mode and jamming signal type are used as The transmitted signal by R in the second slot is well as how long the coherence time is. In fact, jam- 1,i 2,j given by ming components gR and gB depend on the chan-    2,j 1 nels G1,i , G2,i and jamming signals x1,i, x . The x = √ y R,k R,k J,k J,k R α R channels are decided by the surrounding environment 1 (6) = √ (H1 u x + H1 u x + g + z ) while the jamming signals are decided by the jammers. α A A A B B B R R Jamming signals may vary slower than the channels with a short-enough coherence time and, e.g., constant where h i † † jamming strategy with fixed signals. On the other hand, † † 1 1 † 1 1 α = E yRyR = uAHA HAuA + uBHB HBuB jamming signals may vary faster than the channels K (7) with a long-enough coherence time and, e.g., reactive † 2 + ∑ pJ,ktr{GR,kGR,k} + nRσ . jamming strategy with varied signals. The varying rate k=1
4. 88 REV Journal on Electronics and Communications, Vol. 10, No. 3–4, July–December, 2020 1 j The received signal at B is given by where 2 ≤ j ≤ l, to remove gR and transmits xR, which is free of jamming signals and given by 1 2† 1 1 yB = √ H (H uAxA + H uBxB + gR + zR) B A B j 1 α x = √ y˜ i K (8) R α R + G a + z . (19) ∑ B,k J,k B 1  1 i 1 i i 1  = = √ H u x + H u x + z − z k 1 α A A A B B B R R After the known component is removed, the signal is where given by h † i α = E y yR 1 2† 1 1 R y˜ B = √ H (H uAxA + gR + z ) (20) α B A R † 1† 1 † 1† 1 2 = u H H uA + u H H uB + 2nRσ . K (9) A A A B B B + ∑ GB,kaJ,k + zB. k=1 ji The MAR at B is given by (10) at the beginning of the In section 2.2, we have used precoding matrix BB for next page where subscript “C” refer to the conventional the transmitted signal from R. This can be used for a scheme. Similarly, the MAR at A is given by (11) at general view of the readers. However, optimizing this i i matrix can lead to very complicated content which may the beginning of the next page. R estimates xA and xB with MARs respectively given by (12) and (13) at the require a lot of other works. Therefore, in this paper we ji = ì beginning of the next page. The secrecy MARS is then assume BB InR which is a nR nR eye matrix. The given by received signal at B is given by + +  A A-R   B B-R  j 1 2† 1 i 1 i 1,i 1,1 r = r − r + r − r . (14) y = √ H (H uAx + H uBx + z − z ) C-Co C-Co C-Co C-Co C-Co B α B A A B B R R K (21) 2 j + ∑ GB,kaJ,k + zB. 3.2 Proposed Scheme k=1 The jammers always jam with the same signals there- B also uses similar technique used by R in (18) to fore, we design such that in first time slot of each phase remove the jamming component by calculating of the first frame, the transmitter does not transmit j 1 1 2† 1 i 1 i any signal. The intended receiver thus receives only y − y = √ HB (HAuAxA + HBuBxB B B α (22) the jamming signals and noise. It needs to estimate the j +z1,i − z1,1) + z − z1 . jamming signals and use them to cancel their contri- R R B B bution in the received signals in the next time slots. 1 i Since HB, uB, and xB are known at B, it removes the Since the channels are fixed in each phase, we replace second term in (22) and gets superscripts i and j of H and u by 1 and 2, respectively. 1 † √ 2 1 i 1,i 1,1 j 1 In the first time slot of the first phase, A and B y˜ B = HB (HAuAxA + zR − zR ) + zB − zB. (23) transmit no signal so the signal received at R is given by α 1 1 yR = gR + zR (15) Since there two phases each with l time slots and K 1 where gR , ∑k=1 GR,kaJ,k. For simplicity, in this paper the first time slot in each phase is used to calibrate the we use Zero Forcing to estimate the jamming compo- jamming component, the scheme can only transfer l − 1. 1 1 * nent as gˆ R = yR. In the i-th time slot of the first phase, messages from A to B. The maximum achievable rate 2 ≤ i ≤ l, A and B transmit their respective information (MAR) at B is given by signals so the signal received at R is given by † 1† 2 2† 1 ! l − 1 u H H H H uA yi = H1 u xi + H1 u xi + g + zi (16) rB = log 1 + A A B B A (24) R A A A B B B R R P-Co 2l 2 2 2 2† 2 2σ tr{HBHB } + 2αnσ where 2 ≤ i ≤ l. In the first time slot of the second phase, R does not transmit any signals so that B receives where subscripts “P” and “Co” refer to the proposed only the jamming signals and noise given by scheme and constant jamming, respectively. Similarly, A can remove the jamming component and known K 1 2 1 term [18]. The MAR at A is therefore given by yB = GB,kaJ,k + zB. (17) ∑ † † ! k=1 l − 1 u† H1 H2 H2 H1 u rA = log 1 + B B A A B B . In the j-th time slot of the second phase, R calculates P-Co 2l 2 2 2 2† 2 2σ tr{HAHA } + 2αnσ i i 1,i 1 (25) y˜ = y − gR = y − y R R R R (18) 1 i 1 i i 1 R estimates xi and xi with the MARs respectively = HAuAxA + HBuBxB + zR − zR, A B given by * 1 1 † ! If MMSE is used, gˆ R = ΛRyR where ΛR is a diagonal matrix in † 1 1 h i 2 l − 1 u H H u K 1 B-R A A A A ∑ G [pJ,k ]i = + k=1 R,k i rP-Co log2 1 † , (26) which element (i, i) is given by ΛR[i, i] = h i 2 . 2l † 1 1 2 K 1 2 u H H u + 2σ ∑ G [p k ]i +σ B B B B k=1 R,k i J,
5. C. D. T. Thai et al.: Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals 89 † 1† 2 2† 1 ! 1 u H H H H uA rB = log 1 + A A B B A . (10) C-Co 2 2 K { † 2 2† } + 2 { 2 2† } + K { † } + 2 ∑k=1 pJ,ktr GR,kHBHB GR,k σ tr HBHB α ∑k=1 pJ,ktr GB,kGB,k αnσ † 1† 2 2† 1 ! 1 u H H H H uB rA = log 1 + B B A A B . (11) C-Co 2 2 K { † 2 2† } + 2 { 2 2† } + K { † } + 2 ∑k=1 pJ,ktr GR,kHAHA GR,k σ tr HAHA α ∑k=1 pJ,ktr GA,kGA,k αnσ † 1† 1 ! 1 u H H uA rB-R = log 1 + A A A , (12) C-Co 2 2 † 1† 1 + K { † } + 2 uBHB HBuB ∑k=1 pJ,ktr GR,kGR,k nRσ † 1† 1 ! 1 u H H uB rA-R = log 1 + B B B . (13) C-Co 2 2 † 1† 1 + K { † } + 2 uAHA HAuA ∑k=1 pJ,ktr GR,kGR,k nRσ † 1† 1 ! l − 1 u H H uB A and B repeat their transmissions in the first slot. rA-R = log 1 + B B B . (27) P-Co 2l 2 † 1† 1 2 Since this slot is jammed, R use the mixed information uAHA HAuA + 2σ signal estimated in the first slot to cancel its contri- The secrecy rate is therefore given by bution in the received signal in the second slot and + +  A A-R   B B-R  estimate the jamming component. In slot i, 3 ≤ i ≤ l, rP-Co = rP-Co − rP-Co + rP-Co − rP-Co . (28) i−1 i−1 A and B transmit information signals xA and xB , respectively. R easily removes the jamming component. 4 Reactive Jamming The second phase is conducted in a similar way and finally l − 1 pairs of information signals are delivered In reactive jamming, the jammers only jam when detect- to the receivers. Obviously, the secrecy sum-rate of this ing that the legitimate nodes are transmitting. When case is the same as in constant jamming. Consequently, the legitimate nodes stop transmitting, they also stop in section Numerical Results we do not distinguish jamming. However, it takes a short period of time these two jamming modes for both conventional and for them to detect a transmission. So in this period, proposed schemes. the legitimate receivers can receive and decode their needed information signals in a jamming-free way. In 5 Numerical Results this paper, we assume that this period is equal to one time slot [5]. In this section, we present several numerical results to show the superiority of the proposed scheme to 4.1 Conventional Scheme the conventional scheme in many scenarios. In the first scenario, we consider three antennas at all nodes In the first time slot of the conventional scheme, the including three jammers. The powers at a non-jamming legitimate and relaying nodes enjoy a jamming-free slot. node (A, B, and R) and a jamming node are 1 and However, from the second slot, they are continuously † 0.02 , respectively. All A-R, B-R, Jk-A, Jk-B, and Jk-R jammed. Therefore, if we consider a very large time channels are circular complex Gaussian with mean of 0 scale, the affect of the first slot is insignificant. Note and variance of 1. Since in this paper, we focus on the that the time scale we mention here is not related to the estimation and removal of the jamming signals rather coherence time since the working of the conventional than on optimization of precoding vectors, we choose scheme does not depend on the coherence time as long these precoding vectors as corresponding vectors 1. as it is at least two time slots. As a result, we almost Figure 2 shows the maximum achievable sum-rate can approximate the secrecy rate of the conventional of the proposed and conventional schemes as the SNR scheme in reactive jamming mode to that in constant is varied with different coherence times of l time slots. jamming mode. Note that the performance of the conventional does not depend on the coherence time as A-R and B-R channels 4.2 Proposed Scheme †We choose a low jamming power in order to show relative The proposed scheme is designed as follows. In the comparison between the proposed and conventional schemes. As first slot of the first phase, A and B simultaneously the performance of the proposed scheme does not depend on the 1 1 jamming power since all jamming signals are estimated and removed. transmit xA and xB, respectively. R receives the mixed The factors to deteriorate its performance is double noises as shown information signal jamming-free. In the second slot, in (24) and (25).
6. 90 REV Journal on Electronics and Communications, Vol. 10, No. 3–4, July–December, 2020 6 3 C P, l = 2 5 P, l = 6 2.5 P, l = 10 4 2 3 1.5 2 1 C 1 0.5 P, l = 2 Secrecy rate (bits/channel use) Secrecy rate (bits/channel use) P, l = 6 P, l = 10 0 0 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 Transmit SNR (dB) Number of antennas at the relay Figure 2. The proposed scheme (P) in different coherence times, (l Figure 4. The effect of the number of antennas at the relay on the time slots). The performance of the conventional scheme (C) does secrecy rate at SNR = 15 dB. not depend on l. 3 3 C P, l = 2 2.5 2.5 P, l = 6 P, l = 10 2 2 1.5 1.5 1 1 C 0.5 P, l = 2 0.5 Secrecy rate (bits/channel use) Secrecy rate (bits/channel use) P, l = 6 P, l = 10 0 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Relay's horizontal coordinate (r ) Number of antennas at A and B X Figure 3. The effect of the number of antennas at A and B on the Figure 5. The affect of the relay’s horizontal coordinate, rX, on the secrecy rate at SNR = 15 dB. secrecy rate. in both time slots of the scheme are perfectly known at relay can reduce the affect of the jamming signals more A, B, and R even though they are different between two effectively, however, at the same time, it also increases time slots. In the proposed scheme, A, B, and R sacrifice its decoding rate therefore the secrecy rate is finally one time slot in each coherence time to estimate the decreased since the leaked rate is larger. jamming components which change every coherence To analyze the affect of the positions of the nodes time. At higher SNR regime, the proposed scheme is to the performance of the schemes, we consider the better and surpass the conventional scheme more and scenario where the all channel gains are given by − 3 more since the double noises get less effective. In the d 2 h in which d is the physical distance between the meantime, it also improves with the coherence time considered transmitter and receiver, 3 is the power path since with a long coherence time the sacrificed time loss coefficient in the non-line of sight wireless module, slot becomes insignificant. and h is the circular complex Gaussian random variable Figure 3 shows the effect of the number of antennas with 0 mean and 1 variance (as described in Section at A and B on the secrecy rate at SNR of 15 dB. 2). A, Jk, R, and B are respectively located at (0, 1), The performance of the conventional scheme increases (1,1), (rX, 1), and (2, 1) positions. The SNR is fixed at faster than that of the proposed scheme since the former 15 dB. The affect of the relay’s horizontal coordinate is affected by the interference (jamming signals) whose on the secrecy rate is shown in Figure 5. As with effect can be reduced by a larger number of receiving other two-way relay scenarios, the performance of the antennas while the latter is affected by the noise whose proposed scheme maximizes at the middle since all effect can be increased. When the number of antennas at jamming signals are removed. However, as they are not R is increased as shown in Figure 4, the performance of removed in the conventional scheme, its performance the proposed scheme also increases but not rapidly. The minimizes here.
7. C. D. T. Thai et al.: Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals 91 3 References C P, l = 2 [1] A. Mukherjee, S. Fakoorian, J. Huang, and A. Swindle- 2.5 P, l = 6 hurst, “Principles of physical layer security in multiuser P, l = 10 wireless networks: A survey,” IEEE Communications Sur- 2 veys & Tutorials, vol. 16, no. 3, pp. 1550–1573, Feb. 2014. [2] Y. Wu, A. Khisti, C. Xiao, G. Caire, K. Wong, and X. Gao, 1.5 “A survey of physical layer security techniques for 5G wireless networks and challenges ahead,” IEEE Journal on Selected Areas in Communications 1 , vol. 36, no. 4, pp. 679–695, Apr. 2018. [3] T. Lv, H. Gao, and S. Yang, “Secrecy transmit beamform- 0.5 Secrecy rate (bits/channel use) ing for heterogeneous networks,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 6, pp. 1154–1170, 0 Jun. 2015. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 [4] J. Y. Ryu, J. Lee, and T. Q. S. Quek, “Confidential co- Relay's vertical coordinate (r ) Y operative communication with trust degree of potential eavesdroppers,” IEEE Transactions on Wireless Communi- Figure 6. The affect of the relay’s vertical coordinate, rY, on the secrecy cations, vol. 15, no. 6, pp. 3823–3836, 2016. rate. [5] Q. Yan, H. Zeng, T. Jiang, M. Li, W. Lou, and Y. T. Hou, “Jamming resilient communication using MIMO interference cancellation,” IEEE Transactions on Informa- A, Jk, and B are kept at the same positions as in tion Forensics and Security, vol. 11, no. 7, pp. 1486–1499, Figure 5. However, the relay (1, rY) moves from (1, Jul. 2016. 0) to (1, 2), i.e., on the line perpendicular to the line [6] M. Karlsson, E. Bjửrnson, and E. G. Larsson, “Jamming a connection A and B positions. This means that the affect TDD point-to-point link using reciprocity-based MIMO,” IEEE Transactions on Information Forensics and Security, of the position change is weaker therefore the the curve vol. 12, no. 12, pp. 2957–2970, 2017. near the maxima are more rounded than in the previous [7] A. Mukherjee and A. L. Swindlehurst, “Jamming games case. We can find the maxima of the performance of the in the mimo wiretap channel with an active eavesdrop- per,” IEEE Transactions on Signal Processing, vol. 61, no. 1, conventional scheme near rY = 0.3 and rY = 1.7. These two maximum values are symmetrical across the line of pp. 82–91, 2013. [8] L. Xiao, X. Lu, D. Xu, Y. Tang, L. Wang, and W. Zhuang, rY = 1. At these maxima, there is a balance between the “UAV relay in VANETs against smart jamming with negative affect of the jammers and the positive affect of reinforcement learning,” IEEE Transactions on Vehicular the optimal position of the relay which both culminate Technology, vol. 67, no. 5, pp. 4087–4097, 2018. [9] C. Pu, “Jamming-resilient multipath routing protocol for at rY = 1. flying Ad Hoc networks,” IEEE Access, vol. 6, pp. 68 472– 68 486, 2018. 6 Conclusion [10] L. Xiao, T. Chen, J. Liu, and H. Dai, “Anti-jamming transmission stackelberg game with observation errors,” IEEE Communications Letters, vol. 19, no. 6, pp. 949–952, In this paper, we have considered a two-way relay 2015. network with multi-antenna legitimate, relaying, and [11] L. Li, A. P. Petropulu, and Z. Chen, “MIMO secret jamming nodes. We proposed a novel scheme to es- communications against an active eavesdropper,” IEEE timate and eliminate the jamming signals in case of Transactions on Information Forensics and Security, vol. 12, constant and reactive jamming modes. The numerical no. 10, pp. 2387–2401, Oct. 2017. [12] S. Vahidian, S. Hatamnia, and B. Champagne, “On the results showed that the secrecy rate of the proposed security analysis of a cooperative incremental relaying scheme is larger than that of the conventional scheme. protocol in the presence of an active eavesdropper,” IEEE The superiority of the proposed scheme increases with Access, vol. 7, pp. 181 812–181 828, Sep. 2019. the coherence time. Generally, the performance of the [13] T. Lv, Y. Yin, Y. Lu, S. Yang, E. Liu, and G. Clapworthy, conventional scheme is affected by interference and “Physical detection of misbehavior in relay systems with unreliable channel state information,” IEEE Journal on therefore significantly improved by a larger number Selected Areas in Communications, vol. 36, no. 7, pp. 1517– of antennas at A and B. Meanwhile, that of the pro- 1530, Jul. 2018. posed scheme is affected by doubled and amplified [14] H. Pirayesh, P. K. Sangdeh, and H. Zeng, “Securing noise due to the process of eliminating jamming signals ZigBee communications against constant jamming attack and therefore slightly improved by a larger number of using neural network,” IEEE Internet of Things Journal, vol. 8, no. 6, pp. 4957 – 4968, 2021. antennas at A and B. The larger number of antennas at [15] K. Panyim, T. Hayajneh, P. Krishnamurthy, and D. Tip- the relay helps to reduce the effect of the jamming but per, “On limited-range strategic/random jamming at- also increases the leaked rate. The optimal position of tacks in wireless ad hoc networks,” in Proceedings of the the relay is achieved at the midpoint between A and B IEEE 34th Conference on Local Computer Networks, 2009, as in other relay networks. pp. 922–929. [16] M. Spuhler, D. Giustiniano, V. Lenders, M. Wilhelm, and J. B. Schmitt, “Detection of reactive jamming in DSSS- Acknowledgment based wireless communications,” IEEE Transactions on Wireless Communications, vol. 13, no. 3, pp. 1593–1603, 2014. This study was funded by Scientific Research Project [17] C. Zhang, J. Ge, J. Li, F. Gong, and H. Ding, “Complexity- B2019-VGU-05, Ministry of Education and Training aware relay selection for 5G large-scale secure two-way (MOET) of Vietnam. relay systems,” IEEE Transactions on Vehicular Technology,
8. 92 REV Journal on Electronics and Communications, Vol. 10, No. 3–4, July–December, 2020 vol. 66, no. 6, pp. 5461–5465, 2017. Vo Nguyen Quoc Bao (SMIEEE) is an asso- [18] D. Tse and P. Viswanath, “Fundamentals of wireless ciate professor of Wireless Communications communications,” Cambridge Univ. Pr., 2005. at Posts and Telecommunications Institute of Technology (PTIT), Vietnam. He is currently serving as the Dean of Faculty of Telecom- munications and the Director of the Wireless Communication Laboratory (WCOMM). His Chan Dai Truyen Thai received the B.S. research interests include wireless communi- degree from Posts and Telecommunications cations and information theory with current Institute of Technology (PTIT), Ho Chi Minh emphasis on MIMO systems, cooperative and City, Vietnam; the M.Sc. degree from Korea cognitive communications, physical layer se- Advanced Institute of Science and Technol- curity, and energy harvesting. He is the Technical Editor in Chief of ogy (KAIST), Daejeon, South Korea; and the REV Journal on Electronics and Communications. He is also serving Ph.D. degree from Aalborg University, Den- as an Associate Editor of EURASIP Journal on Wireless Commu- mark, in 2003, 2008, and 2012, respectively. nications and Networking, an Editor of Transactions on Emerging He was with IFSTTAR, LEOST, Villeneuve Telecommunications Technologies (Wiley ETT), and VNU Journal of d’Ascq, France; with Singapore University of Computer Science and Communication Engineering. He served as a Technology and Design (SUTD); and is now Technical Program co-chair for ATC (2013, 2014, 2018), NAFOSTED- the Academic Coordinator cum Senior Lecturer of the Electrical and NICS (2014, 2015, 2016), REV-ECIT (2015, 2017), ComManTel (2014, Computer Engineering (ECE) Study Program, Vietnamese-German 2015), and SigComTel (2017, 2018). He is a Member of the Executive University (VGU). His research interests include cooperative com- Board of the Radio-Electronics Association of Vietnam (REV) and munications, vehicle-to-vehicle communications, communication for the Electronics Information and Communications Association Ho Chi high-speed vehicles, security in wireless communications, and secu- Minh City (EIC). He is currently serving as vice chair of the Viet- rity in smart grid. nam National Foundation for Science and Technology Development (NAFOSTED) scientific Committee in Information Technology and Computer Science (2017-2019). De-Thu Huynh received the Ph.D. degree in Computer Science from Huazhong Uni- versity of Science and Technology, China in 2015. He is working as a lecturer and re- searcher in the Faculty of Information Tech- nology at Ho Chi Minh City University of Economics and Finance, Vietnam. His current research interests were in the areas of Wire- less Sensor Networks, Wireless Body Area Networks, Device-to-Device Communications, Internet of Things, and Network Security.