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

Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
No 2.CS (10) 2019 9 
Decode-and-Forward vs. Amplify-and-
Forward Scheme in Physical Layer Security 
for Wireless Relay Beamforming Networks 
Nhu Tuan Nguyen 
Abstract— To secure communication from the 
sender to the receiver in wireless networks, 
cryptographic algorithms are usually used to 
encrypt data at the upper layers of a multi-tiered 
transmission model. Another emerging trend in 
the security of data transmitted over wireless 
networks is the physical layer security based on 
beamforming and interference fading 
communication technology and not using 
cryptographic algorithms. This trend has 
attracted increasing concerns from both 
academia and industry. This paper addresses 
how physical layer security can protect secret 
data compare with the traditional cryptographic 
encryption and which is the better cooperative 
relaying scheme with the state of the art 
approached methods in wireless relaying 
beamforming network. 
Tóm tắt— Việc bảo mật truyền thông vô tuyến 
từ nơi gửi đến nơi nhận thường sử dụng các 
thuật toán mật mã để mã hoá dữ liệu tại các tầng 
phía trên trong mô hình phân lớp. Một xu hướng 
khác đang được quan tâm rộng rãi là bảo mật 
tầng vật lý dựa trên kỹ thuật truyền tin 
beamforming và kỹ thuật tương tác fading kênh 
chủ động. Xu hướng này hiện đang được thu hút 
cả trong giới công nghiệp và nghiên cứu. Đóng 
góp của bài báo này là làm rõ khả năng bảo mật 
tầng vật lý và so sách chúng với phương pháp 
bảo mật dùng kỹ thuật mật mã truyền thống. Bài 
báo cũng so sánh hai kỹ thuật chuyển tiếp được 
sử dụng chính trong bảo mật tầng vật lý cho 
mạng vô tuyến chuyển tiếp là Amplify-and-
Forward và Decode-and-Forward. 
Keywords— Physical layer security; DC 
Programming and DCA; Amplify-and-Forward. 
Từ khoá— Bảo mật tầng vật lý; DC 
Programming and DCA; Amplify-and-Forward. 
This manuscript is received on July 18, 2019. It is 
commented on November 20, 2019 and is accepted on 
November 30, 2019 by the first reviewer. It is commented on 
December 15, 2019 and is accepted on December 25, 2019 
by the second reviewer. 
I. INTRODUCTION 
Most of the recent methods of ensuring 
security in the communication system are based 
on cryptography techniques or algorithms to 
encrypt the content of the messages from the 
sender to the receiver. The concept of secrecy 
communication was first proposed in the 
pioneering work from 1949 by Shannon [1], in 
which secrecy communication was investigated 
from the viewpoint of information theory. It 
was proposed therein that the approach termed 
“one-time pad” could achieve the perfect 
secrecy. The traditional communication 
security methods often use cryptographic 
algorithms at the upper layers of multi-layer 
communication models being studied and 
widely applied. Recently, these methods have 
still been considered to be safe in many 
application models. However, the security of 
these cryptographic algorithms often depends 
on the computational complexity of decryption 
without private keys. Therefore, when quantum 
computers are actually applied, this difficulty 
will no longer be a challenge in crypto analysis. 
Another trend for radio network security that 
has been extensively researched lately is 
physical layer security (PLS) without the use of 
cryptographic algorithms and resistance to 
quantum computers. In the recent years, PLS 
has been investigated both as an alternative and 
as a complementary approach to conventional 
cryptographic methods [2,3]. Actually, the 
research on physical layer security was 
pioneered by Dr. Aaron D. Wyner since 1975 
[4]. Wyner has demonstrated that it is possible 
to transmit security information at Cs rate in a 
communication system that has the presence of 
an eavesdropper (Cs ≥ 0). That is the secrecy 
capacity of a discrete memoryless channel was 
the maximum value of the difference between 
the mutual information of the legitimate 
channel and the mutual information of the 
Journal of Science and Technology on Information Security 
10 No 2.CS (10) 2019 
wiretap channel. At that time, Wyner made an 
important assumption in his results that the 
channel between Alice and Eve, called the 
wire-tap channel, had a greater loss than the 
channel from Alice to the legal recipient Bob, 
also known as the main channel. This 
assumption is not easy to guarantee because the 
wire-tap channel is often unchecked. Hence, the 
Wyner's idea was not really interested in the 
following years. 
Over the past decade, with the development 
of wireless communications technology, 
especially multi-antenna communications and 
beamforming techniques, physical layer 
security solutions have been studied widely 
[5,9]. A great effort to increase the achievable 
secrecy rate in physical layer security is 
cooperative nodes networks [3, 9] with act two 
roles are cooperative relaying and cooperative 
jamming (CJ) [10, 12]. In which, the secrecy 
rate value is defined as 
1,
min(log(1 ) log(1 )).s d ej
j K
R SNR SNR
=
= + − + (1) 
Where, SNRd and SNRej are the signal-to-
noise-ratio at the legitimate destination and the 
jth eavesdropper, respectively; K is the number 
of eavesdroppers in system. 
This paper focused on the cooperative 
relaying network with two main relaying 
schemes are Amplify-and-Forward (AF) and 
Decode-and-Forward (DF). This paper presents 
the state-of-the-art cooperative relaying 
networks and the experiments to show detail 
the effects of some techniques and schemes in 
it. These wireless relay beamforming networks 
are modeled as nonconvex optimization 
problems. In which, the solution of these 
optimization problem are the beamforming 
weights of the relay stations, the objective 
function is the value of the secrecy rate of the 
system Rs (bits/symbol). 
We investigate in the case  ... 
constrains [19], then we proposed DCA-AFME 
scheme by applied DCA to solve this problem 
as the following. 
Journal of Science and Technology on Information Security 
14 No 2.CS (10) 2019 
DCA-AFME SCHEME 
Input: Channel coefficients from source to 
relays hs, from relays to destination hd and from 
relays to eavesdroppers Hil, the predefined 
threshold . 
Initialization. Chose a random initial point 0x , 
l=0 
Repeat: l = l+1, calculate xl by solve this 
subproblem: 
𝑚𝑖𝑛
𝒙,𝑡
− (𝑯𝑠𝒙
𝑡−1)†𝒙 + 𝜏𝑡 
𝑠. 𝑡. 𝒙†𝑪𝑘
+𝒙 − 2(𝑪𝑘
−𝒙𝑙−1)†𝒙⟨𝒙 −
𝒙𝑙−1, 2(𝑪𝑘
−𝒙𝑙−1)⟩𝒙 ≤ 1 + (𝒙𝑙−1)†𝑪𝑘
−𝒙𝑙−1 +
2((𝒙𝑙−1)†𝑪𝑘
−𝒙𝑙−1) + 𝑡, ∀𝑘 ∈ 𝜅, 
𝒙†𝑫𝑖𝒙 ≤ 1, ∀𝑖 ∈ 𝑀, 𝑡 ≥ 0 
Until: 
‖𝒙𝑙−𝒙𝑙−1‖
1+‖𝒙𝑙−1‖
≤ 𝜀 or 
|𝑓(𝒙𝑙)−𝑓(𝒙𝑙−1)|
1+|𝑓(𝒙𝑙−1)|
≤ 𝜀 
where 𝑓(𝒙𝑙) = (𝒙𝑙)†𝑯𝑠𝒙
𝑙 
Output: Rs = h(t
l, xl), SNRe, SNRe (2). 
B. The approaches for DF problem 
Null steering 
The authors in [9] focus on the case of Null 
steering beamforming. In which, the signal is 
completely nulled out at all eavesdroppers, then 
the problem (5) addition constraints 
𝐰′𝐡𝑟𝑒𝑗𝐰 = 0𝐾×1 
and rewrite as 
max 
𝒘
(log (
𝜎2 + |∑ ℎ𝑟𝑑,𝑚𝑤𝑚
𝑀
𝑚=1 |
2
𝜎2
)) 
s.t. 𝐰†𝐰 ≤ 𝑃𝑅 
𝐰′𝐡𝑟𝑒𝑗𝐰 = 0𝐾×1. 
 (10) 
Then can be rewritten as 
max
𝒘
 𝐰′𝐇𝑟𝑑𝐰 
s.t. 𝐰†𝐰 ≤ 𝑃𝑅 
𝐰′𝐡𝑟𝑒𝑗𝐰 = 0𝐾×1. 
 (11) 
Where 
𝐇𝑟𝑑 = 𝐡′𝑟𝑑𝐡𝑟𝑑 and 𝐡𝑟𝑑 = [ℎr𝑑,1,  , ℎ𝑟𝑑,𝑀]
𝑇 
By used the equality power constrain 
𝑤†𝑤 = 𝑃𝑅 instead of inequality power 
constrain as 
max
𝐰†𝐰=𝑃𝑅
 𝐰′𝐇𝑟𝑑𝐰 
s.t. 𝐰′𝐡𝑟𝑒𝑗𝐰 = 0𝐾×1. 
 (12) 
The optimization problem (12) has the 
optimal solution given by 
𝒘 =
√𝑃𝑅
‖(𝐈𝑀 − 𝐏𝑟𝑒)𝐡𝑟𝑑‖
(𝐈𝑀 − 𝐏𝑟𝑒)𝐡𝑟𝑑 , 
where 𝐏𝑟𝑒 = 𝐇𝑟𝑒(𝐇𝑟𝑒
† 𝐇𝑟𝑒)
−1
𝐇𝑟𝑒
†
 is the 
orthogonal projection matrix onto the subspace 
spanned by the columns of 𝑯𝒓𝒆. 
3) DC programming and DCA approach 
In [18], we proposed a DC decomposition 
by recall problem (5) with the total power 
constrain as 
𝑚𝑎𝑥
𝒘
𝜎2 + 𝒘†𝑯𝑟𝑑𝒘
𝑚𝑎𝑥𝑗=1..𝐾(𝜎2 + 𝒘†𝑯𝑟𝑒,𝑗𝒘)
𝑠. 𝑡
𝒘†𝒘 ≤ 𝑃𝑅
 (13) 
equivalent to 
𝑚𝑖𝑛
𝒘,𝒕
−
𝜎2 + 𝒘†𝑯𝑟𝑑𝒘
𝑡
s.t. 𝒘†𝒘 ≤ 𝑃𝑅, 𝑡 > 0, 
𝜎2 + 𝒘†𝑯𝑟𝑒,𝑗𝒘 ≤ 𝑡, ∀𝑗 ∈ 𝐾. 
 (14) 
Change to real variables form we have an 
equivalent problem as 
𝑚𝑖𝑛 
𝒙,𝑡
0 −
𝜎2 + 𝒙𝑇𝒁𝒙
𝑡 
𝑠. 𝑡. 𝒙𝑇𝑩𝑗𝒙 ≤ 𝑡 − 𝜎
2, ∀𝑗 ∈ 𝐾 
𝒙𝑇𝒙 ≤ 𝑃𝑅 , 𝑡 ≥ 0 
 (15) 
where 
𝒁 = [
𝑅𝑒(𝑯𝑟𝑑) − 𝐼𝑚(𝑯𝑟𝑑)
𝐼𝑚(𝑯𝑟𝑑) 𝑅𝑒(𝑯𝑟𝑑)
] , 𝑥 = [
𝑅𝑒(𝒘)
𝐼𝑚(𝒘) 
] 
𝑩𝑗 = [
𝑅𝑒( 𝑯𝑟𝑒,𝑗) − 𝐼𝑚( 𝑯𝑟𝑒,𝑗)
𝐼𝑚(𝑯𝑟𝑒,𝑗) 𝑅𝑒(𝑯𝑟𝑒,𝑗)
]
𝑇
. 
Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
No 2.CS (10) 2019 15 
The problem (15) is restated as a standard 
DC program, then we can apply DCA 
algorithm to have DCA-DFME scheme 
following: 
The DCA-DFME scheme [18]: 
Input: The channel coefficient matrix Bj, Z 
Initialization: the random initial points x0, t0>0 
and set l=0, 𝒖0 = (𝑡0, 𝒙0)
Repeat: l=l+1, to calculate 𝒖𝑙 = (𝑡𝑙 , 𝒙𝑙) by 
solving the following subproblem: 
𝑚𝑖𝑛
𝒖=(𝑡,𝒙)
0 − ⟨𝑦𝑙−1, 𝒖⟩
𝑠. 𝑡. 𝒙𝑇𝑩𝑗𝒙 ≤ 𝑡 − 𝜎
2, ∀𝑗 ∈ 𝐾 
𝒙𝑇𝒙 ≤ 𝑃𝑟, 𝑡 > 0,
Until: 
‖𝒖𝑙−𝒖𝑙−1‖
1+‖𝒖𝑙‖
≤ 𝜀
 or 
|𝑓(𝒖𝑙)−𝑓(𝒖𝑙−1)|
1+|𝑓(𝒖𝑙)|
≤ 𝜀 
where 𝑓(𝒖𝑙) =
𝜎2+(𝒙𝑙)
𝑇
𝒁𝒙𝑙
𝑡𝑙
Output: 
𝑅𝑠 = ℎ(𝑡
𝑙 , 𝒙𝑙) = 𝑓(𝒖𝑙), SNRd, SNRe. 
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 
that, the signal received at eavesdroppers is too 
bad then they cannot decode to get the 
messages which send from relays. 
A. Generating experimental datasets: 
We focus on the wireless communication 
model operating under both AF and DF 
schemes with the appearance of multiple 
eavesdropping station as Fig.1 with the two 
cases of number of eavesdropping stations 
used as K = 5 and 7 eavesdroppers; The 
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 
station to the relay station and from the relay 
stations to the destination one and to the 
eavesdroppers with the given configuration 
parameters as above mentioned. These datasets 
are shared for all four methods. 
B. Experimental results 
With the assumption of one-way 
communication system model (considering 
only the direction from source station S to 
receiver D without the opposite direction) as 
illustrated in Fig.2 with the given parameters. 
For each case, 100 independent tests were 
carried out and took the average result for the 
optimal solution value and the signal-to-noise-
ratio received at legitimate destination and 
eavesdroppers for the comparison. The 
experimental results are as follows: 
Fig.2. AF vs. DF in wireless relay 
beamforming network with 5 eavesdroppers 
The optimal solution values: The results 
shown in Fig.2 and Fig.3 reflect the fact that, 
the value of the secrecy rate RS always 
increasing with the number of relay stations. 
Specially, it shown an important thing that, 
the value 𝑅𝑠 has strong increasing when the 
number of relay nodes reached around three 
times of the number of eavesdroppers, after 
that it is lightly increasing. 
Journal of Science and Technology on Information Security 
16 No 2.CS (10) 2019 
Fig.3: AF vs. DF in wireless relay beamforming 
network with 7 eavesdroppers 
The secrecy rate efficiency of DF scheme 
is definitely higher than AF scheme as in 
figures. The gap of DC programming and 
DCA method with SDR method in AF 
network is clear. In contrast, this gap in DF 
network is quite small. 
The maximum value Rs = 5 bits/symbol 
when the number of relay nodes is 40 
respected to the case of DF network and 40 
relays with 5 eavesdroppers (Fig.2). When the 
number of relays equal to the number of 
eavesdroppers then the Rs value down to zero 
for the case of Null steering method as in (12). 
The SNR values: The data in Table 2 
illustrates the SNR values at both destination 
(D) and eavesdroppers (E) as formula (2) and 
(4). It is clearly that, with the optimal 
beamforming weights at the relays, the SNRs 
received at eavesdropper are too small. As 
Wyner’s condition [4] that the wire-tap 
channel had a greater loss than the main 
channel is not difficult to satisfy with the 
beamforming and fading techniques. The SNR 
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 
communication networks. Therefore, the study 
of the security method of physical layers for 
wireless networks is very necessary and really 
being widely concerned around the world. 
According to the information theory, the 
physical layer security problem for the wireless 
network based on Amplify-and-Forward 
scheme is used as the optimal form with the 
goal of increasing the speed of secrecy rate (Rs) 
with a primary constraint on signal source 
power and considering the amplification factor 
at transition stations. This problem has a non-
convex form and is difficult to solve to find a 
globally optimal solution. Some solutions for 
finding solutions to this optimization problem 
are the amplification values of the transition 
stations so that the most optimal security rate 
published recently is often the solution to an 
approximated solution. Therefore, the results 
suggest a new solution method based on the 
study of applying DC programming and DCA 
to solve these difficult problems to find better 
optimal solutions that have shown new and 
scientific features. 
TABLE 2: THE SNR RECEIVED AT D AND E VS. NUMBER OF RELAYS WITH PS = 30 dBm, 5 EAVESDROPPERS. 
Number of Relays 
5 10 15 20 25 30 35 
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 
Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
No 2.CS (10) 2019 17 
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ABOUT THE AUTHOR 
M.Sc Nhu Tuan Nguyen 
Workplace: Vietnam Information 
Security Journal 
Email:nguyennhutuan@bcy.gov.vn 
The education process: received 
the Master of science degree in 
Engineering from Academy of 
Cryptography Technique in 
2007. He is a PhD student in 
Academy of Cryptography Technique. 
Research today: machine learning and data mining 
in cyber security, cloud computing security, 
physical layer security.