Security for two-way untrusted relay against constant and reactive jamming with fixed signals

tect- 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).
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.
C. D. T. Thai et al.: Security for Two-Way Untrusted Relay against Constant and Reactive Jamming with Fixed Signals 91
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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.