Decode - and - forward vs. amplify - andforward scheme in physical layer security for wireless relay beamforming networks

in general. x,t t (9) 
 Recalled that the problem (6) has form of s.., txT B x t − 2  j K
Quadratically Constrained Quadratic Program j
 xxT Pt, 0.
(QCQP) with nonconvex objective function and R 
nonconvex constraints. It is difficult to find the 
global optimal solution of that problem by Where: 
solving directly in general. The existing method 
 Re(R) − Im( R) Re( w) 
proposed in [18] is to find suboptimal solution Z ==rd rd , x
by Semi-definite Relaxation (SDR) method as 
 Im(Rrd) Re( R rd ) Im( w) 
following. T 
 † Re(RRre,, j )− Im( rej )
 By defined U = uu and considering B = .
 j ImR Re R
relaxation on rank one symmetric positive ( re,, j) ( re j )
semi-definite (PSD) constraint (rank(U) = 1), 
the optimization program (6) can be written as The problem (9) is actually a general DC 
 program at the objective function and first K 
 †
 푡 푒(풉푠풉푠 ∗ 푼) 
 푼 constrains [19], then we proposed DCA-AFME 
 (7) scheme by applied DCA to solve this problem 
 푠. 푡. 푡 푒(푪 ∗ 푼) ≤ 1, ∈ 휅 as the following. 
 푡 푒(푫푖 ∗ 푼) ≤ 1, 푖 ∈ 
 As the objective function and all constraints 
in (7) are convex, this problem can be solved 
by CVX optimization tool. Once problem (7) is 
solved, we can find the corresponding optimal 
u and thereby w by applying eigenvalue 
decompression on matrix U. 
 2) DC programming and DCA Solution 
 In [16], we proposed to apply DC 
programming and DCA to solve the problem 
(6). By define 
 2
 + 1 − |𝜌푖, | , 푖 |𝜌푖, | ≤ 1
 𝜌 = { 
 0, 푒푙푠푒
 2
 − |𝜌푖, | − 1, 푖 |𝜌푖, | ≥ 1
 𝜌 = { 
 0, 푒푙푠푒
 No 2.CS (10) 2019 13 
 Journal of Science and Technology on Information Security 
DCA-AFME SCHEME By used the equality power constrain 
 †
Input: Channel coefficients from source to 푤 푤 = 푃푅 instead of inequality power 
 constrain as 
relays hs, from relays to destination hd and from 
relays to eavesdroppers Hil, the predefined max 퐰′퐇 퐰 
 퐰†퐰=푃
threshold . 푅
 (12) 
 0 s.t. 퐰′퐡 퐰 = 0 . 
Initialization. Chose a random initial point x , 푒푗 퐾×1
l=0 
 l The optimization problem (12) has the 
Repeat: l = l+1, calculate x by solve this optimal solution given by 
subproblem: 
 푡−1 † √푃푅
 푖푛 − (푯푠풙 ) 풙 + 휏푡 풘 = (퐈 − 퐏 )퐡 , 
 풙,푡 푒 
 ‖(퐈 − 퐏 푒)퐡 ‖
 푠. 푡. 풙†푪+풙 − 2(푪−풙푙−1)†풙⟨풙 −
 −1
 푙−1 − 푙−1 푙−1 † − 푙−1 † †
 풙 , 2(푪 풙 )⟩풙 ≤ 1 + (풙 ) 푪 풙 + where 퐏 푒 = 퐇 푒(퐇 푒퐇 푒) 퐇 푒 is the 
 푙−1 † − 푙−1 , 
 2((풙 ) 푪 풙 ) + 푡, ∀ ∈ 휅 orthogonal projection matrix onto the subspace 
 풙†푫 풙 ≤ 1, ∀푖 ∈ , 푡 ≥ 0 
 푖 spanned by the columns of 푯 . 
Until: 풓풆
 ‖풙푙−풙푙−1‖ | (풙푙)− (풙푙−1)| 3) DC programming and DCA approach 
 ≤ 휀 or ≤ 휀 
 1+‖풙푙−1‖ 1+| (풙푙−1)| In [18], we proposed a DC decomposition 
 푙 푙 † 푙
 where (풙 ) = (풙 ) 푯푠풙 by recall problem (5) with the total power 
 l l constrain as 
Output: Rs = h(t , x ), SNRe, SNRe (2). 
 2 †
 𝜎 + 풘 푯 풘 
 B. The approaches for DF problem 
 풘 (𝜎2 + 풘†푯 풘)
 Null steering 푗=1..퐾 푒,푗 (13) 
 The authors in [9] focus on the case of Null †
 푠. 푡 풘 풘 ≤ 푃푅
steering beamforming. In which, the signal is 
completely nulled out at all eavesdroppers, then equivalent to 
the problem (5) addition constraints 𝜎2 + 풘†푯 풘 
 퐰′퐡 푒 퐰 = 0퐾×1 푖푛 −
 푗 풘,풕 푡 (14) 
 †
and rewrite as s.t. 풘 풘 ≤ 푃푅, 푡 > 0, 
 2
 2 2 †
 𝜎 + |∑ =1 ℎ , 푤 | 𝜎 + 풘 푯 풘 ≤ 푡, ∀푗 ∈ 퐾. 
 max (log ( )) 푒,푗
 풘 𝜎2 
 Change to real variables form we have an 
 (10) 
 † equivalent problem as 
 s.t. 퐰 퐰 ≤ 푃푅 
 𝜎2 + 풙 풁풙 
 퐰′퐡 퐰 = 0 . 푖푛 0 −
 푒푗 퐾×1 풙,푡 푡
 (15) 
 2
 Then can be rewritten as 푠. 푡. 풙 푗풙 ≤ 푡 − 𝜎 , ∀푗 ∈ 퐾 
 max 퐰′퐇 퐰 
 풘 풙 풙 ≤ 푃푅, 푡 ≥ 0 
 † (11) 
 s.t. 퐰 퐰 ≤ 푃푅 where 
 푅푒(푯 ) − (푯 ) 푅푒(풘)
 퐰′퐡 푒푗 퐰 = 0퐾×1. 풁 = [ ] , = [ ] 
 (푯 ) 푅푒(푯 ) (풘) 
 Where 푅푒( 푯 푒,푗) − ( 푯 푒,푗)
 = [ ] . 
 푗
 퐇 = 퐡′ 퐡 and 퐡 = [ℎr ,1,  , ℎ , ] (푯 푒,푗) 푅푒(푯 푒,푗)
 14 No 2.CS (10) 2019 
 Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
 The problem (15) is restated as a standard station to the relay station and from the relay 
DC program, then we can apply DCA stations to the destination one and to the 
algorithm to have DCA-DFME scheme eavesdroppers with the given configuration 
following: parameters as above mentioned. These datasets 
 are shared for all four methods. 
The DCA-DFME scheme [18]: 
 B. Experimental results 
Input: The channel coefficient matrix Bj, Z 
Initialization: the random initial points x0, t0>0 With the assumption of one-way 
 communication system model (considering 
and set l=0, 풖0 = (푡0, 풙0)
 only the direction from source station S to 
 푙 푙 푙
Repeat: l=l+1, to calculate 풖 = (푡 , 풙 ) by receiver D without the opposite direction) as 
solving the following subproblem: illustrated in Fig.2 with the given parameters. 
 푖푛 0 − ⟨ 푙−1, 풖⟩ For each case, 100 independent tests were 
 풖=(푡,풙) 
 2 carried out and took the average result for the 
 푠. 푡. 풙 푗풙 ≤ 푡 − 𝜎 , ∀푗 ∈ 퐾 optimal solution value and the signal-to-noise-
 풙 풙 ≤ 푃 , 푡 > 0, ratio received at legitimate destination and 
 ‖풖푙−풖푙−1‖ | (풖푙)− (풖푙−1)| eavesdroppers for the comparison. The 
Until: ≤ 휀 or ≤ 휀 
 1+‖풖푙‖ 1+| (풖푙)| experimental results are as follows: 
 𝜎2+ 풙푙 풁풙푙
 where (풖푙) = ( )
 푡푙
Output: 푅 = ℎ(푡푙, 풙푙) = (풖푙), SNR , SNR . 
 푠 d e
 V. EXPERIMENT AND RESULTS 
 This section presents the experimental 
results and evaluation of all four proposed 
methods in part IV. We compare the quality of 
AF scheme to DF scheme in wireless relying 
network from the perspectives of the values of 
secrecy rate. It shows that, DF scheme has 
better secrecy performance than AF scheme. In 
the rest of this section, we also describe 
received signal-to-noise-ratio at destination and 
eavesdroppers. From this viewpoint, it is clear 
 Fig.2. AF vs. DF in wireless relay 
that, the signal received at eavesdroppers is too 
 beamforming network with 5 eavesdroppers 
bad then they cannot decode to get the 
messages which send from relays. The optimal solution values: The results 
A. Generating experimental datasets: shown in Fig.2 and Fig.3 reflect the fact that, 
 the value of the secrecy rate RS always 
 We focus on the wireless communication increasing with the number of relay stations. 
model operating under both AF and DF Specially, it shown an important thing that, 
schemes with the appearance of multiple 
 the value 푅푠 has strong increasing when the 
eavesdropping station as Fig.1 with the two number of relay nodes reached around three 
cases of number of eavesdropping stations times of the number of eavesdroppers, after 
used as K = 5 and 7 eavesdroppers; The that it is lightly increasing. 
relay nodes variable from 5 to 40 nodes; the 
power consumption P = 30 dBm. Assuming 
a one-way communication system, these 
channel coefficients are randomly generated 
according to the Gaussian distribution and 
are known in advance. 
 For each case, we generated 100 datasets of 
channel coefficient values from the source 
 No 2.CS (10) 2019 15 
 Journal of Science and Technology on Information Security 
 values at eavesdroppers in the Null steering 
 case as in the Tables 2 is suitable with the 
 constrain of this system model (11). When the 
 number of relays and eavesdroppers are 
 equally, these SNRs become to similar then 
 the Rs values down to zero (1) as in Fig.2 and 
 Fig.3. 
 IV. CONCLUSION 
 With the emergence of 5G communication 
 networks and the powerful development of IoT 
 networks, wireless communication networks 
 are gradually replacing fiber optic 
 Fig.3: AF vs. DF in wireless relay beamforming communication networks. Therefore, the study 
 network with 7 eavesdroppers 
 of the security method of physical layers for 
 The secrecy rate efficiency of DF scheme wireless networks is very necessary and really 
is definitely higher than AF scheme as in being widely concerned around the world. 
figures. The gap of DC programming and 
 According to the information theory, the 
DCA method with SDR method in AF 
 physical layer security problem for the wireless 
network is clear. In contrast, this gap in DF 
 network based on Amplify-and-Forward 
network is quite small. 
 scheme is used as the optimal form with the 
 The maximum value Rs = 5 bits/symbol goal of increasing the speed of secrecy rate (Rs) 
when the number of relay nodes is 40 with a primary constraint on signal source 
respected to the case of DF network and 40 power and considering the amplification factor 
relays with 5 eavesdroppers (Fig.2). When the at transition stations. This problem has a non-
number of relays equal to the number of convex form and is difficult to solve to find a 
eavesdroppers then the Rs value down to zero globally optimal solution. Some solutions for 
for the case of Null steering method as in (12). finding solutions to this optimization problem 
 The SNR values: The data in Table 2 are the amplification values of the transition 
illustrates the SNR values at both destination stations so that the most optimal security rate 
(D) and eavesdroppers (E) as formula (2) and published recently is often the solution to an 
(4). It is clearly that, with the optimal approximated solution. Therefore, the results 
beamforming weights at the relays, the SNRs suggest a new solution method based on the 
received at eavesdropper are too small. As study of applying DC programming and DCA 
Wyner’s condition [4] that the wire-tap to solve these difficult problems to find better 
channel had a greater loss than the main optimal solutions that have shown new and 
channel is not difficult to satisfy with the scientific features. 
beamforming and fading techniques. The SNR 
TABLE 2: THE SNR RECEIVED AT D AND E VS. NUMBER OF RELAYS WITH PS = 30 dBm, 5 EAVESDROPPERS. 
 5 10 15 20 25 30 35 
Number of Relays 
SNR D E D E D E D E D E D E D E 
DCA_AF 9.4 0.31 70.4 0.30 172.1 0.31 260.3 0.32 325.4 0.32 451.2 0.33 534.8 0.33 
SDR_AF 3.0 0.43 25.1 0.46 77.5 0.58 105.9 0.51 140.7 0.50 220.2 0.50 252.1 0.53 
DCA_DF 60.4 2.46 165.5 0.03 296.4 0.01 473.7 0.00 589.3 0.00 741.7 0.00 880.7 0.00 
SDR_DF 30.3 37.5 157.9 0.00 292.2 0.00 470.5 0.00 587.0 0.00 740.0 0.00 879.3 0.00 
 16 No 2.CS (10) 2019 
 Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
 REFERENCE [13]. O. G. Aliu, A. Imran, M. A. Imran, and B. Evans, 
 “A Survey of Self Organisation in Future Cellular 
[1]. C. E. Shannon, “Communication theory of secrecy Networks,” IEEE Commun. Surv. Tutor., vol. 15, 
 systems,” Bell Syst. Tech. J., vol. 28, no. 4, pp. no. 1, pp. 336–361, First 2013. 
 656–715, Oct. 1949, [14]. F. I. Kandah, O. Nichols, and Li Yang, “Efficient 
[2]. G. de Meulenaer, F. Gosset, F.-X. Standaert, and key management for Big Data gathering in 
 O. Pereira, “On the Energy Cost of dynamic sensor networks,” in 2017 International 
 Communication and Cryptography in Wireless Conference on Computing, Networking and 
 Sensor Networks,” in 2008 IEEE International Communications (ICNC), 2017, pp. 667–671, doi: 
 Conference on Wireless and Mobile Computing, 10.1109/ICCNC.2017.7876209. 
 Networking and Communications, 2008, pp. 580– [15]. Physical Layer Security: Bounds, Codes and 
 585, doi: 10.1109/WiMob.2008.16. Protocols (João Barros) - Part 2 
[3]. D. Wang, B. Bai, W. Zhao, and Z. Han, “A Survey (SPCodingSchool). 
 of Optimization Approaches for Wireless Physical [16]. N. N. Tuan and D. V. Son, “DC Programming and 
 Layer Security,” ArXiv190107955 Cs Math, Jan. DCA for Enhancing Physical Layer Security in 
 2019. Amplify-and-Forward Relay Beamforming 
[4]. A. D. Wyner, “The Wire-Tap Channel,” Bell Syst. Networks Based on the SNR Approach,” in 
 Tech. J., vol. 54, no. 8, pp. 1355–1387, Oct. 1975, Advanced Computational Methods for Knowledge 
 doi: 10.1002/j.1538-7305.1975.tb02040.x. Engineering, vol. 629, N.-T. Le, T. van Do, N. T. 
[5]. I. Csiszar and J. Korner, “Broadcast channels with Nguyen, and H. A. L. Thi, Eds. Cham: Springer 
 confidential messages,” IEEE Trans. Inf. Theory, International Publishing, 2018, pp. 23–33. 
 vol. 24, no. 3, pp. 339–348, May 1978. [17]. S. Sarma, S. Agnihotri, and J. Kuri, “Secure 
[6]. F. Jameel, S. Wyne, G. Kaddoum, and T. Q. Communication in Amplify-and-Forward 
 Duong, “A Comprehensive Survey on Cooperative Networks with Multiple Eavesdroppers: Decoding 
 Relaying and Jamming Strategies for Physical with SNR Thresholds,” Wirel. Pers. Commun., 
 Layer Security,” IEEE Commun. Surv. Tutor., vol. vol. 85, no. 4, pp. 1945–1956, Dec. 2015. 
 21, no. 3, pp. 2734–2771, 2019, doi: [18]. N. N. Tuan and T. T. Thuy, “Physical Layer 
 10.1109/COMST.2018.2865607. Security Cognitive Decode-and-Forward Relay 
[7]. Tạp chí An toàn thông tin, “Bảo mật dữ liệu tầng Beamforming Network with Multiple 
 vật lý trong mạng truyền tin không dây: Những ý Eavesdroppers,” in Intelligent Information and 
 tưởng đầu tiên và hướng nghiên cứu hiện nay”, Database Systems, vol. 11432, N. T. Nguyen, F. L. 
  Gaol, T.-P. Hong, and B. Trawiński, Eds. Cham: 
 viet-cua-101779. [Accessed: 15-Feb-2020]. Springer International Publishing, 2019, pp. 254–
[8]. X. Chen, D. W. K. Ng, W. H. Gerstacker, and H.- 263. 
 H. Chen, “A Survey on Multiple-Antenna [19]. H. A. Le Thi, V. N. Huynh, and T. P. Dinh, “DC 
 Techniques for Physical Layer Security,” IEEE Programming and DCA for General DC 
 Commun. Surv. Tutor., vol. 19, no. 2, pp. 1027– Programs,” in Advanced Computational Methods 
 1053, Secondquarter 2017. for Knowledge Engineering, Cham, 2014, pp. 15–
[9]. L. Dong, Z. Han, A. P. Petropulu, and H. V. Poor, 35, doi: 10.1007/978-3-319-06569-4_2. 
 “Improving Wireless Physical Layer Security via 
 Cooperating Relays,” IEEE Trans. Signal Process., ABOUT THE AUTHOR 
 vol. 58, no. 3, pp. 1875–1888, Mar. 2010, doi: 
 M.Sc Nhu Tuan Nguyen 
 10.1109/TSP.2009.2038412. 
[10]. Y.-W. P. Hong, P.-C. Lan, and C.-C. J. Kuo, Workplace: Vietnam Information 
 “Enhancing Physical-Layer Secrecy in Security Journal 
 Multiantenna Wireless Systems: An Overview of Email:nguyennhutuan@bcy.gov.vn 
 Signal Processing Approaches,” IEEE Signal 
 The education process: received 
 Process. Mag., vol. 30, no. 5, pp. 29–40, Sep. 
 the Master of science degree in 
 2013, doi: 10.1109/MSP.2013.2256953. 
 Engineering from Academy of 
[11]. A. Mukherjee, S. A. A. Fakoorian, J. Huang, and Cryptography Technique in 
 A. L. Swindlehurst, “Principles of Physical Layer 2007. He is a PhD student in 
 Security in Multiuser Wireless Networks: A Academy of Cryptography Technique. 
 Survey,” IEEE Commun. Surv. Tutor., vol. 16, no. 
 3, pp. 1550–1573, 2014. Research today: machine learning and data mining 
 in cyber security, cloud computing security, 
[12]. H.-M. Wang and X.-G. Xia, “Enhancing wireless 
 physical layer security. 
 secrecy via cooperation: signal design and 
 optimization,” IEEE Commun. Mag., vol. 53, no. 
 12, pp. 47–53, Dec. 2015, doi: 
 10.1109/MCOM.2015.7355565. 
 No 2.CS (10) 2019 17