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2796 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 4, APRIL 2022
Weighted Voting in Physical Layer Authentication
for Industrial Wireless Edge Networks
Feiyi Xie , Zhibo Pang , Senior Member, IEEE, Hong Wen , Senior Member, IEEE,
Wenxin Lei , Graduate Student Member, IEEE, and Xinchen Xu
Abstract—Edge computing (EC) is an essential compo-
nent of large-scale intelligent manufacturing systems for
Industry 4.0, which promises to provide a preprocessing
platform for the massive data generated by the terminals
and guarantee lower delay and more security compared
to directly processing data in cloud computing. Neverthe-
less, access authentication is a crucial security issue of
current EC systems, and, thus, this article presents a so-
lution to enhance the access classification accuracy by
exploiting the physical layer information. Our method em-
ploys a weighted voting scheme for channel state infor-
mation based authentication using a single sample which
includes sample segmentation, grouping, and weighted
voting and finally achieves the fast and low complexity
secure-access requirement of the EC system without in-
creasing the individual devices’ sample size and compu-
tational complexity. Experimental results utilizing public
datasets and field-measured datasets demonstrate that the
proposed weighted voting method has higher accuracy and
robustness than existing methods.
Index Terms—Channel state information (CSI), industrial
wireless networks, physical layer authentication, weighted
voting.
I. INTRODUCTION
THE fourth industrial revolution (Industry 4.0) is an intelli-
gent era that utilizes information technology to promote
industrial change [1]. It employs the cyber–physical system
to digitize and intellectualize the supply, manufacturing, and
Manuscript received July 11, 2021; revised July 26, 2021 and Au-
gust 3, 2021; accepted August 4, 2021. Date of publication August
10, 2021; date of current version December 27, 2021. This work was
supported in part by the National Key R and D Program of China
under Grant 2018YFB0904900 and Grant 2018YFB0904905 and in
part by the Swedish Foundation for Strategic Research (SSF) under
Project APR20-0023. Paper no. TII-21-2919. (Corresponding author:
Hong Wen.)
Feiyi Xie is with the National Key Laboratory of Science and Technol-
ogy on Communications, University of Electronic Science and Technol-
ogy of China, Chengdu 610054, China (e-mail: helloyuiki@foxmail.com).
Zhibo Pang is with the Department of Automation Technology, ABB
Corporate Research Sweden, 72226 Vasteras, Sweden, and also with
the Department of Intelligent Systems, Royal Institute of Technology
(KTH), 11428 Stockholm, Sweden (e-mail: pang.zhibo@se.abb.com).
Hong Wen, Wenxin Lei, and Xinchen Xu are with the School of Aero-
nautics and Astronautics, University of Electronic Science and Technol-
ogy of China, Chengdu 610054, China (e-mail: sunlike@uestc.edu.cn;
leiwenxin@std.uestc.edu.cn; uestcxxc@outlook.com).
Color versions of one or more figures in this article are available at
https://doi.org/10.1109/TII.2021.3103780.
Digital Object Identifier 10.1109/TII.2021.3103780
sales information in production and finally achieves a more
agile, efficient, and personalized product supply [2]. Smart
manufacturing has enabled most factory devices to perform
intelligent computational processing and data storage functions.
Thus, edge computing (EC) was created to serve these smart
devices, addressing specific problems such as excessive network
response time, delayed response, and network congestion [3].
Through EC integration, data processing capacity is pushed to
the edge of network equipment, thus relieving the pressure on
the centralized control system [4].
Nevertheless, EC involves a large amount of data communi-
cation between the devices and terminals, which could suffer
from cyber-attacks exploiting security breaches in the internal–
external factory environment [5], [6]. Attackers can compromise
the data communications between legitimate parties of intelli-
gent devices in a factory, thereby jeopardizing the proper oper-
ation and cooperation between devices [7], [8]. Consequently,
secure data communications across the various smart devices
are of critical importance [9], [10]. An elegant solution to these
challenges is the devices resisting the insecure public networks’
attack and cleaning the data when the network receives them
from the unauthenticated or partly authenticated terminals [11].
For such a purpose, cryptography-based secure mechanisms
are utilized to encrypt or decrypt the data and authenticate
the transmission data and terminals’ access. However, such
cryptography-based secure mechanisms impose a significant
computational burden, which is undesirable for many computing
resource-constrained industrial devices.
Due to the open propagation nature of the wireless channel,
attackers might be able to access the local industrial wireless
network even without entering the building and probing the
wires, which is termed probing-free attacks. By taking advantage
of wireless channel characteristics, channel authentication is
well-suited for industrial scenarios where the computing power
of terminals and consoles is not equal. Channel state information
(CSI) based physical layer authentication focuses on different
routes to pass the authentication process to enhance the security
of a wireless network [12]. Since the CSI varies from different
channels, CSI-based physical layer authentication can identify
senders from different locations. The traditional threshold-based
authentication method is the most commonly used [13]. At the
same time, the accuracy could not always be satisfied. Machine
learning and deep learning significantly improved the authen-
tication result. Meanwhile, the requirements for the computing
and storage property of the device are also raised [14].
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XIE et al.: WEIGHTED VOTING IN PHYSICAL LAYER AUTHENTICATION FOR INDUSTRIAL WIRELESS EDGE NETWORKS 2797
Intelligent scenarios in Industry 4.0 have higher requirements
for real-time processing and precision, imposing shorter training
and classification time for the authentication classifier and a
higher accuracy rate. Nevertheless, these requirements are con-
tradictory without presupposing any increase of the classifier
device computing power [15]. A solution can be benefiting from
the vast number of terminals in the industrial environment, which
constitute a substantial intelligent EC system and realize some
cooperative decision-making algorithms that require multiple
smart devices to work together [16].
Cooperative decisions can help groups of agents make de-
cisions using a voting methodology and ultimately improving
accuracy without increasing the computational burden on a
single device [17]. Further, weighted voting allows agents to
join existing coalitions, which offers higher performance over
the voting memory on both types of memory sets [18]. Current
research highlights that the weighted voting strategy outper-
forms simple voting, reduces voting time, and improves deci-
sion efficiency. For example, Liang’s [19] experiment proved
that weighted voting can further improve the classification per-
formance compared with plurality voting. Recently, weighted
voting is widely used in various fields ranging from political
and economic organizations to neuroscience, threshold logic,
reliability theory, and distributed systems [20], [21].
A few researchers applied cooperative decisions or voting in
the field of access authentication. Existing solutions involve a
mutual entity authentication protocol using biometrics to ensure
voter eligibility and digital signatures for ballot authentication in
an untrustworthy environment [22]. Additionally, the media pre-
sented a mobile terminal voting system to solve the problems of
traditional voting and e-voting, which provided higher efficiency
compared to the existing schemes in the network environment.
Sridharan provided to voters during the registration process a
secret voting password acting as an authentication mechanism,
enabling voters to cast their votes and their captured biometrics.
However, all current schemes need multiple voters, such as
biosignatures, mobile terminals, or password voting machines.
It should be noted, though, that in some cases, it is challenging to
have so many voters, making it impossible to increase accuracy
while exploiting a cooperative decision. However, commonly,
data are not fully exploited, providing the opportunity to exploit
the entire dataset and ultimately solve the reduced voter problem.
Hence, this article proposes a cooperative decision scheme
using only a single sample. Specifically, the sample is divided
into groups where each group acts as a voter, similarly to a
machine learning classification scheme where each group is used
as a training set to train a subclassifier. This strategy affords
to establish several subclassifiers, which during the classifi-
cation step, samples are divided as the training samples, and
the corresponding subclassifier classifies each group. Finally,
the subclassifiers provide their results to make the cooperative
decision.
The significant contributions of this article can be summarized
as follows.
1) An enhancement of authentication that neglects the require-
ment of multiple receiving devices. Indeed, a single device can
complete the decision via the data it received, while it makes full
use of every data sample point and improves the classification
accuracy.
2) Our field-measured experiments demonstrated the supe-
riority of our method in terms of accuracy and robustness in
industrial scenarios against current techniques, including our
previous method.
The rest of this article is organized as follows. Section II in-
troduces the background of the theories and algorithms involved
in this article. The theories of our novel grouping and weighted
voting schemes are proposed in Section III. Section IV presents
the industrial scenario experiment. Finally, Section V concludes
this article.
II. BACKGROUND
A. CSI-Based Physical Layer Authentication
CSI-based physical layer access authentication focuses on
different routes to pass the authentication process [23], [24]. CSI
refers to the propagation properties of a wireless communication
link, which describes the decay factors of a signal on each
transmission path, such as power attenuation, multipath decay,
Doppler frequency shift, etc. CSI is divided into statistical CSI
and transient CSI, including the type of decay distribution,
statistical average delay, Rician factor, and spatial correlation.
CSI used in this article is the estimated channel response matrix
ˆ
H, which is the instantaneous CSI estimated using the frequency
guide. Generally, in the multi-input multioutput (MIMO) system
Y=HX+N(1)
where Xand Yrepresent the input and output matrices or vectors
of the system, respectively. His the actual CSI, NCN(0,R
N)
is the system noise, and RNis the noise covariance matrix.
Channel estimation is generally performed using least squares
(LS) based on training symbols. It is done by minimizing the cost
function Yp−ˆ
HpXp. Setting the gradient of the loss to zero and
solving for ˆ
Hp, the channel matrix can be estimated as follows:
ˆ
HLS =(XH
pXp)−1XH
pYp=X−1
pYp(2)
where Xpis the frequency matrix consisting of known
frequency-guided sequences, Ypis the received signal matrix,
and (·)Hdenotes the Hermitian transpose.
LS estimation is widely used in channel estimation because it
is relatively simple to calculate and does not require statistical
characteristics of the system or statistical characteristics of the
channel noise.
Generally, the CSI matrix estimate for an M×NMIMO
system can be partitioned according to the transmitting and
receiving antennas as follows:
ˆ
H=⎡
⎢
⎢
⎢
⎣
ˆ
h11
ˆ
h12 ···
ˆ
h1N
ˆ
h21
ˆ
h22 ···
ˆ
h2N
.
.
..
.
..
.
.
ˆ
hM1
ˆ
hM2···
ˆ
hMN
⎤
⎥
⎥
⎥
⎦
(3)
where
ˆ
hmn represents the channel estimate of the mth receiving
antenna to the nth transmitting antenna. If it is an orthogonal
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2798 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 4, APRIL 2022
frequency division multiplex system and has Psubcarriers, then
each estimate vector has Pelements
ˆ
hmn =[
ˆ
h1,ˆ
h2,...,ˆ
hP].(4)
1) Threshold-Based Authentication: Conventional access
authentication is generally based on a threshold decision, with
standard test statistics such as Euclidean distance and correlation
coefficient. Physical layer access authentication is achieved by
the difference between the state information of the channel to
be authenticated and the state information of a known legitimate
channel
ΛF=diff(ˆ
Hu,ˆ
HA)=
ˆ
Hu−ˆ
HA
F≷η(5)
Λρ=diff(ˆ
Hu,ˆ
HA)= cov( ˆ
Hu,ˆ
HA)
var( ˆ
Hu)var( ˆ
HA)
≷η(6)
where ˆ
HAand ˆ
Hurepresent the physical channel information
for known legal node and unknown node, respectively. Λrepre-
sents their test statistics, and ηrepresents the threshold.
2) Machine Learning Based Authentication: Several innova-
tive research in channel authentication has been proposed in
the last few years. A new unified cryptographic authentica-
tion protocol to solve the channel authentication and device
interaction problems caused by device heterogeneity and inde-
pendent development [25]. Liu [26] proposed a wireless link
signature, a physical layer authentication mechanism using the
unique wireless channel characteristics between transmitter and
receiver to provide wireless channel authentication. Meanwhile,
make good use of wireless channel information. For example, by
making the system channel adaptive when designing a system,
authentication performance could be improved.
They commonly use machine learning or neural network
based classification algorithms for authentication. It is trained
using a large number of previously known CSI XTand the
corresponding label I(supervised learning) to obtain a classifier,
which is used to authenticate the anonymous CSI. Training set
TR=ˆ
HT
I=ˆ
H1
1,..., ˆ
HL1
1,..., ˆ
H1
K,..., ˆ
HLK
K
I1, ..., I
1..., I
K, ...,I
K(7)
where ˆ
H1
k,..., ˆ
Hk
Lkdenotes the CSI at node kand Ikdenotes
its corresponding label.
Since both of the above methods require that the channel ma-
trix be transformed into (or viewed as) a 1-D vector, traditional
methods generally reduce 2-D matrices to 1-D using minima,
maxima, averages, or concatenation, where minima and maxima
methods are not commonly used [27]. Jiseok [27] typically
expanded the channel matrix ˆ
Hin (3) to a one-dimensional
vector in the simulation
ˆ
HDr =fc(ˆ
H)=ˆ
h11,...,
ˆ
h1N,...,
ˆ
hM1,...,
ˆ
hMN .(8)
For ease of differentiation, the classification algorithm using
this method is named direct classification in this article.
Pan [28] chose to reduce the dimensionality by averaging
over the MIMO CSI matrix. In this method, each column of
the matrix is integrated. This classification algorithm is named
Fig. 1. CSI-based authentication in industrial edge computing.
averaged classification
ˆ
HAv =mean(ˆ
H)=M
1
ˆ
hm1,
M
1
ˆ
hm2, ... ,
M
1
ˆ
hmN .(9)
Ken [29] got better authentication results by using downsam-
pling first and then concatenation, which is named downsampled
classification
ˆ
HDs =sp(ˆ
H)=d
ˆ
h11,...,d
ˆ
h1N,...,d
ˆ
hM1,...,d
ˆ
hMN
(10)
where d
ˆ
hmn presents the downsampling of
ˆ
hmn in (4). Denote
the downsampling factor by S, then
d
ˆ
hmn =sp(
ˆ
hmn)=[
ˆ
h1,ˆ
hS,...,ˆ
hN·S](11)
where N=P/Srepresents the largest integer that does not
exceed Pwhen multiplied by S.
The above classification algorithms are shown in Fig. 2.Be-
cause integration and downsampling both compress the channel
matrix into a one-dimensional vector, they could not make
full use of the information in the channel matrix. This article
considers the use of multiuser collaborative decision-making
to exploit most of this information, which will be discussed in
Section III.
B. Weighted Voting
Voting is widely used in coalition formation, which can help
groups of agents to make decisions using the methodology of
voting. And the weighted voting mechanism has been proposed
that allows agents to join existing coalitions.
In Valdovinos’ paper [30], it is suggested that the weights
should be added to each classifier based on their performance,
named average distance weight. The purpose of this dynamic
weighting process is to reward a single classifier with the nearest
neighbor of the input pattern (by assigning the most considerable
weight)
w(Dj)=n
i=1di
dj
.(12)
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XIE et al.: WEIGHTED VOTING IN PHYSICAL LAYER AUTHENTICATION FOR INDUSTRIAL WIRELESS EDGE NETWORKS 2799
Fig. 2. Classification methods compared. (a) Direct Classification [29].
(b) Averaged Classification [30]. (c) Downsampled Classification [31]. (d)
Equal Voting. (e) Weighted Voting (this work).
The basic principle behind this weight is that in the given input
pattern classification, the classifier closest to X may correspond
to the classifier with the highest accuracy.
In Lau’s paper [31], a more detailed method is given, in which
the weight is calculated as
w=(conx)×y
e=1Ce
y(13)
where the conxrepresents the contribution of each member
of the coalition that works together toward a shared goal in
the coalition. Cerepresents the agent’s criteria, who proposes
the joining coalition request to coalition registration agent and
coalition leader, being evaluated. yrepresents the number of
criteria to be accounted.
When making a decision, the total vote and the number of wyes
and wno should be calculated. The ideal termination condition
is when the total votes reached the predefined quota minimum
vote required to pass or fail the voting session. The decision is
if
n
x=1
wx/2>ηwin
if
n
x=1
wx/2<ηlose (14)
where ηis the minimum number of required voters [31].
III. METHODS
Given its high accuracy and intelligence, machine learning is
used as a decision algorithm to get higher performance.
A. Sample Segmentation
In the MIMO system, multiple antennas receive the identi-
cal transmitting antennas’ information from different positions,
which can be regarded as observing the same object from dif-
ferent directions. In this case, it is not the optimal solution to
classify the channel matrix of all receiving antennas into one
sample.
In this article, the channel matrix obtained by each receiving
antenna is considered as a separate sample. In the training of
machine learning, a series of channel matrices obtained by
one receiving antenna are regarded as one sample set, called
subsample set. For the M×Nmatrix ˆ
Hin (3)
ˆ
H=ˆ
H1;ˆ
H2;··· ;ˆ
HM(15)
where
ˆ
H1=ˆ
h11,
ˆ
h12,...,
ˆ
h1N
ˆ
H2=[
ˆ
h21,
ˆ
h22,...,
ˆ
h2N
.
.
.
ˆ
HM=[
ˆ
hM1,
ˆ
hM2,...,
ˆ
hMN.(16)
Correspondingly, the training set in (7) is delivered as
TR=[Tr1;Tr2;··· ;TrM](17)
where
Tr
1=ˆ
HT1
IT1=H1
11··· HLK
1K
I1··· IK
Tr
2=ˆ
HT2
IT2=H1
21··· HLK
2K
I1··· IK
.
.
.
Tr
M=ˆ
HTM
ITM=H1
M1··· HLK
MK
I1··· IK.
(18)
In this way, multiple subsample sets can be obtained (the
number is equal to receiving antennas). Each subsample set
is trained separately to get each subclassifier. For example, as
shown in Fig. 4, the channel matrix obtained by eight antennas
can be divided into eight subsample sets and trained separately
to get eight subclassifiers.
The unknown channel matrix is divided into several sub-
samples according to the receiving antennas, and then the sub-
classifiers of the corresponding antennas are used to get each
classification result. Finally, the decision is made according to
the classification results of all the subclassifiers.
B. Sample Grouping
Downsampling can reduce the data size of the sample, which
can present a better classification result compared with the other
downscaling methods. So, downsampling, separate classifying,
and then a cooperative decision are considered. Set the sampling
interval to S, only 1/S elements of the original data are used for
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2800 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 4, APRIL 2022
Fig. 3. Grouping and weighted voting based classification flow.
Fig. 4. 8×8 CSI matrix
ˆ
H(converted to 2-D form) and the grouping of a SISO CSI vector.
identification. It is possible to downsample the original data in
different ways to get a group of downsampled data. This process
is named grouping.
The system flow of this algorithm is shown in Fig. 3. Through
grouping, several training sets are obtained. Accordingly, mul-
tiple voters can be provided for the next voting step.
In particular, if S|N, the grouping algorithm of a single-input
single-output (SISO) CSI vector can be shown in the box of
Fig. 4. Different part of the vector is used repeatedly to get S
groups of data. By processing the remainder of the MIMO CSI
matrix in the same way, multiple groups of different downsam-
pled data can be obtained. For the M×Nmatrix ˆ
Hin (3), the
grouping process g(ˆ
H)can be expressed as
g(ˆ
H)=[G1;G2;...;GS](19)
where
G1=⎡
⎢
⎣
G1.
ˆ
h11 ··· G1.
ˆ
h1N
.
.
..
.
.
G1.
ˆ
hM1··· G1.
ˆ
hMN
⎤
⎥
⎦
G2=⎡
⎢
⎣
G2.
ˆ
h11 ··· G2.
ˆ
h1N
.
.
..
.
.
G2.
ˆ
hM1··· G2.
ˆ
hMN
⎤
⎥
⎦
.
.
.
GS=⎡
⎢
⎣
GS.
ˆ
h11 ··· GS.
ˆ
h1N
.
.
..
.
.
GS.
ˆ
hM1··· GS.
ˆ
hMN
⎤
⎥
⎦(20)
where G1.
ˆ
hmn,G
2.
ˆ
hmn,...,G
S.
ˆ
hmn represents the grouping
result of
ˆ
hmn in (4)
g(
ˆ
hmn)=[G1.
ˆ
hmn;G2.
ˆ
hmn;...;GS.
ˆ
hmn](21)
where the grouping is a form of downsampling that starts with
different elements of
ˆ
hmn
G1.
ˆ
hmn =[
ˆ
h1,ˆ
h1+S,...,ˆ
hP−S+1]
G2.
ˆ
hmn =[
ˆ
h2,ˆ
h2+S,...,ˆ
hP−S+2]
.
.
.
GS.
ˆ
hmn =[
ˆ
hS,ˆ
h2S,...,ˆ
hP].(22)
C. Weighted Voting
Voting is an effective cooperative decision, which can con-
sider all subclassifiers’ results and come to an agreement quickly
and efficiently. In an ideal situation, the voters are uncorrelated
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XIE et al.: WEIGHTED VOTING IN PHYSICAL LAYER AUTHENTICATION FOR INDUSTRIAL WIRELESS EDGE NETWORKS 2801
and utterly random according to the accuracy rate. When the
classification accuracy is higher than 50%, voting can improve
the classification accuracy. And the more the voters, the better
the result (as shown in Fig. 3).
Frequently, there is a wide variation in the classification
accuracy of different subclassifiers. A simple and effective way
to solve this problem is to give weight to each voter. In this
case, there is previous validation accuracy before test classifica-
tion. Without severe overfitting, there is no significant disparity
between the validation classification accuracy and the test. In
this article, the accuracy of verification is used as the reference
for the weight of each subclassifier. Then the weight of each
classifier is
wv=1
1−Av
(23)
where Avrefers to the accuracy of verification during training.
Normalize to ensure the total weight value is 1
wi=wvi
n
k=1wk
(24)
where nrepresents the total number of subclassifiers, and 1
kn.
The result of weighted voting is
RF=
S
i=1
Ri·wi≷η. (25)
Riis the classification result of each subclassifier (generally true
is 1, false is –1, and η=0), wiis the weight of each subclassifier,
RFrepresents the final decision (−1RF1). If RF>0,
then the final decision is true or the decision is false. Because of
the weight value, it is almost impossible to get RF=0.
However, weighted voting raises the total computational com-
plexity. Task allocation through EC can effectively reduce the
computational burden on individual devices [32].
IV. SIMULATION
A. Dataset Acquisition
All simulation results presented in this section were using
the data in NIST library. The CSI of mobile communication in
NIST data AAP lantD_2GH z_TX1_vpol_run3_pp is used
for simulation experiment, which is collected on the move.
The sampling path and center sampling points are illustrated
in Fig. 5(a). Five hundred points are taken before and after
each central sampling point, i.e., there are 1000 samples in
a set. A frequency-domain example of its CSI is shown in
Fig. 5(b). The classifier used in this simulation is support
vector machine (SVM). An example of subclassification accu-
racy of its segments is shown in Fig. 5(c), which points out
that there is a significant disparity between the classification
accuracy of different segments. The subclassifiers with low
accuracy play a negative role in the subsequent voting deci-
sions, reducing the accuracy. Weighted voting may therefore be
useful here.
The methods of weighted voting and direct classification,
downsampled classification, averaged classification, and equal
Fig. 5. Simulation result using the NIST steamship plant dataset. (a)
Sampling paths and central sampling points in the steamship plant of
NIST dataset. (b) The frequency domain example of CSI of a NIST data
sample and its segmentation. (c) Sub classifier validation and weight
determination. (d) Classification accuracy around each central sampling
points using the NIST dataset.
Fig. 6. Determination results for each subclassifier and the decision
results using equal voting and weighted voting. (a) Sub classification
result of every point. (b) Equal Voting result. (c) Weighted Voting result.
voting are compared, illustrated in Fig. 5(d). The abscissa repre-
sents the classification results of this group of data and the next
adjacent group data.
_
B. Simulation Comparison
The results of all decisions for every subclassifier are shown
in Fig. 6(a). The first 500 points are true, while the rest of 500
are false.
Note that subclassifiers 3, 4, 13, and 14 have made mistakes
from point 200 to 400 majority, which leads to several wrong
decisions in this part [as shown in Fig. 6(b)].
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2802 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 4, APRIL 2022
TABLE I
OVERALL RESULT OF DIFFERENT METHODS USING NIST DATASET
TABLE II
CSI COEFFICIENTS
With weighted voting, classifiers with low identification accu-
racy have lower weight, which will not have a significant impact
on the decision result. It reduces wrong decision to a certain
extent.
The classification results of the data for validation of the
overall cooperative decision and the comparison methods are
filled in Table I, which presents the weighted voting has a better
result in this test.
V. E XPERIMENT
The results presented in Section V-C are using the public
datasets of our previous experiment [28], and then an actual
experiment in a factory scene using 8 ×8 MIMO was added in
Section V-D.
A. Experiment Platform
In this experiment, several Universal Software Radio Periph-
erals (USRP) are used as the senders and receivers to build an
actual communication link. The USRP is a wireless transceiver
module with a series of functions such as baseband signal
processing, clock synchronization, D/A, and A/D conversion.
A single X310 model USRP has two half-duplex channels, each
with one transmitting antenna and one receiving antenna, as
shown in Fig. 7, of which the parameters are set as shown in
Table III.
By cascading multiple USRPs and synchronizing them with
an external clock source, a multiantenna array can be formed. A
base station in this experiment has four USRPs and an external
clock source, shown in Fig. 7, which are linked to the host
computer via the peripheral component interconnect (PCI) bus.
All the USRP hardware are controlled by the host computer’s
software platform, LabVIEW, to receive and send data. The
specific parameters of this experiment are shown in Table II.
The CSI matrices were estimated by LabVIEW embedded
program using LS. The scale of the matrix is 8 ×8×128 matrix.
Then it is grouped into eight submatrices, which are 8 ×8×16,
and eventually expand into 1-D vectors with 1024 elements.
Gaussian SVM was used as the machine learning classifier,
Fig. 7. USRP base station: 8 ×8 MIMO antennas array.
of which the kernel scale σ=10. Voting and decision were
performed by the simulation software. The number of voters is
8, and the threshold η=0.
B. Experiment Design
To simulate the real industrial scenario, we arranged the exper-
iment in a university workshop for precision engineering intern-
ships. The size of the factory workshop is 48.3×38.8×6.5 m,
in which most are metal production equipment, and a small
number of wooden desks and chairs were prevented. Four USRP
base stations are used in this experiment, and three of them, base
stations 1, 3, and 4 (TX1, TX3, and TX4) act as the senders. Base
station 2 (RX2), which has eight receiving antennas, works as
the receiver.
The planar graph of the factory and the experiment is shown
in Fig. 8. Rx2 is fixed in position 2. The transmitter moves at
the speed of 1m/s in the No.1, No.3, and No.4 areas. The size
of each motion acquisition area is 1 ×6 m. The distances from
each center of motion acquisition areas to position 2 are 10.4,
8.4, and 14m, respectively. Fig. 9 is when we were collecting
data at each place.
In each experiment, the transmitter transmits 300 frames of
data to the receiver. After three times of transmission, select 800
available data, of which 400 data are used as training data, and
400 are for the test.
C. Experiment on the Public Data Set
The previous experiment has collected a series of data, which
are transmitted by four antennas USRP base station [28]. In
Pan’s paper, they compressed the data to 128 by integrating. In
this experiment, each sample has 500 points, and SVM is used
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XIE et al.: WEIGHTED VOTING IN PHYSICAL LAYER AUTHENTICATION FOR INDUSTRIAL WIRELESS EDGE NETWORKS 2803
Fig. 8. Planar graph of the industrial experiment environment.
Fig. 9. Real industrial experiment scenario.
as the classifier. Fig. 10 illustrated the classification results of
these methods, which shows that the accuracy of grouping with
weight voting is generally higher than that of other algorithms.
Specifically, the classification error rate of grouped weighted
voting reaches 5.1%, while the error rate of direct classification
is only 16.1%. The averaged classification of Pan has a similar
result to direct classification, of which the error rate is 16.3%.
The error rate of the proposed method in this article is reduced
by 13.1% and 13.4% compared with the above two methods,
respectively. Grouped weighted voting showed a slight improve-
ment over downsampling classification, with a 1.3% reduction
of error rate over 6.4% of the downsampling method. Compared
with the existing three methods, the relative reduction ratios are
Fig. 10. Classification accuracy of public industrial MIMO data.
Fig. 11. ROC curve of public industrial MIMO data.
61.1%, 68.7%, and 20.3%, which proves that grouped weighted
voting successfully reduces the classification error rate.
Considering the stability, the variance of the results of grouped
weighted voting is 2.43 ×10−3. The variances of direct clas-
sification and averaged classification reached 9.5 ×10−3and
9.95 ×10−3, while the variance of downsampled classification
is 3.34 ×10−3. Compared with these three methods, the vari-
ance of grouped weighted voting is reduced by 74.4%, 75.6%,
and 27.2%. Therefore, grouped weighted voting has a smaller
variance and better classification stability.
The receiver operating characteristic (ROC) curves of aver-
aged classification and grouped weighted voting are illustrated
in Fig. 11, which shows that grouped weighted voting is bet-
ter and more stable. Especially, in low classification accuracy,
when classifying positions 1 and 4, grouped weighted voting
has apparent advantages over direct classification and averaged
classification. The difference in the area under ROC curve
(AUC) between the two curves is 0.15. The ROC curves for
grouped weighted voting and downsampled classification are
relatively close in most cases, while in Position: legal 3, illegal 4,
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2804 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 18, NO. 4, APRIL 2022
Fig. 12. Classification accuracy of new experimental industrial MIMO
data.
grouped weighted voting shows advantages over downsampled
classification.
D. Experiment on the New Industrial Data Set
We recently repeated the experiment to prevent contingency.
In comparison, the transmitting base stations used 8 ×8MIMO
USRP group. The classification accuracy is illustrated in Fig. 12,
which shows a similar result to that of the public data.
The classification error rate of grouped weighted voting
reaches 6.5%, and the error rate of direct classification is 21.5%.
The error rate of averaged classification is 21.8%, while that of
downsampled classification is 7.9%. Compared with the existing
three methods, the absolute reduction ratios of grouped weighted
voting are 15%, 15.3%, and 1.4%, and the relative reduction
ratios are 69.8%, 70.2%, and 17.7%. From the perspective of
accuracy, the conclusion of the new experiment is similar to that
of the experiment on the public data set.
The results’ variances of direct classification, averaged classi-
fication, and downsampled classification are 1.85 ×10−2,2.32
×10−2, and 2.18 ×10−3. The variance of grouped weighted
voting falls to 1.65 ×10−3, which shows a relative decrease
of 91.1%, 92.3%, and 24.3%. Consequently, the stability of
grouped weighted voting has a significant improvement over
the existing methods.
Meanwhile, the ROC curves, illustrated in Fig. 13, also sup-
port it. In Position: legal 4–illegal 1, the difference in AUC is
0.06, which proves that weighted voting is superior to the other
three methods (not as significant as the previous experiment,
though). Focusing on the first group, when authenticating po-
sitions 1 and 3, direct classification and averaged classification
have almost no classification ability, while grouped weighted
voting still shows nice performance. It indicates that the grouped
weighted voting has better robustness.
E. Experiment of Execution Time
Theoretically, the time complexity of an SVM is proportional
to the square of a sample feature dimension. The feature di-
mension in averaged classification, downsampled classification,
equal voting, and weighted voting is reduced to 1/8 of the original
sample by integration, downsampling, or grouping; hence, the
Fig. 13. ROC curve of new experimental industrial MIMO data.
TABLE III
PARAMETER CONFIGURATION OF USRP-BASED MIMO SYSTEM
TABLE IV
EXECUTION TIME OF DIFFERENT METHODS USING PUBLIC DATA SET AND
NEW DATA SET
single time complexity for them is 1/64 of direct classification.
Further, since equal voting and weighted voting need to perform
training and classification of eight sets of samples, the time
complexity is eight times that of averaged classification and
downsampled classification.
A single-threaded Intel i7-4790 processor was used to test
the training and classification times of each method. As it is
difficult to maintain complete consistency in the use of hardware
and software, resulting in fluctuating test results, this experiment
uses the average value of ten tests. The execution times of each
method using the public data set and new data set are located in
Table IV.
The training time of the public data set illustrated that av-
eraged classification and downsampled classification have the
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XIE et al.: WEIGHTED VOTING IN PHYSICAL LAYER AUTHENTICATION FOR INDUSTRIAL WIRELESS EDGE NETWORKS 2805
shortest time. Direct classification takes approximately ten times
longer to execute than the first two methods. The training times
of equal voting and weighted voting are about five times that
of averaged classification and downsampled classification. The
execution time is less than the time complexity in theory because
other steps in the experiment also take up time (e.g., initialization
of the SVM, data loading, classifier output, etc.).
The execution time of the remaining experiment shows a
similar result with the training of the public data set. Direct
classification takes about 9–27 times longer than averaged clas-
sification and downsampled classification. The execution times
of equal voting and weighted voting are about 5–8 times as long
as averaged classification and downsampled classification.
Although the execution time of weighted voting becomes
significantly longer, this tradeoff of execution time for accuracy
is acceptable considering that it can be trained offline and the
classification time is relatively short. Further, the execution time
of weighted voting could be reduced by using parallel processing
of CPUs or cooperative training in EC, which is a promising
future topic.
VI. CONCLUSION
This article is focused on the cooperative decision of wireless
channel access authentication, which successfully gets rid of the
limitation of the requirement for multiple receiving devices to
make a unified decision. Using the proposed method, a single
device can be used for an entire voting decision. Meanwhile,
it makes full use of every sample point of the received data to
improve the classification accuracy. Moreover, it is suitable for
the EC system, which makes full use of the EC and network
resources and finally reduces the running time.
Weighted voting of simple lines or simple parts can improve
the classification result with a curve that is below the ideal
case but in line with the trend. When sampling is much better
than other methods, sampling voting and sampling weighted
voting can be considered, which can improve the classification
accuracy to some extent. Users should balance the accuracy
and the calculation complexity. In an EC system with massive
intelligent terminals, reasonable assignment of classifying tasks
can significantly improve operation efficiency, make full use of
computing resources, and save classification time.
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Feiyi Xie received the B.Eng. degree in elec-
tronic science and technology from the Bei-
jing University of Posts and Telecommunications
(BUPT), Beijing, China, in 2012, and the Ph.D.
degree in communication and information sys-
tems from the University of Electronic Science
and Technology of China (UESTC), Chengdu,
China, in 2021.
He is currently engaged in the study of physi-
cal layer security and edge computing. His main
research interests include wireless and mobile
communications.
Zhibo Pang (Senior Member, IEEE) received
the MBA degree in innovation and growth from
the University of Turku, Turku, Finland, in 2012,
and the Ph.D. degree in electronic and computer
systems from the Royal Institute of Technology
(KTH), Stockholm, Sweden, in 2013.
He is currently a Senior Principal Scien-
tist with ABB Corporate Research Sweden,
Västeras, Sweden, an Adjunct Professor with
the University of Sydney, Sydney, Australia, and
an Affiliated Faculty with the Royal Institute of
Technology (KTH).
Dr. Pang is a Co-Chair of the Technical Committee on Industrial Infor-
matics. He is an Associate Editor for IEEE TRANSACTIONS ON INDUSTRIAL
INFORMATICS, IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS,
and IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN INDUSTRIAL
ELECTRONICS. He was an Invited Speaker at the Gordon Research
Conference on Advanced Health Informatics (AHI2018), General Chair
of IEEE ES2017, and General Co-Chair of IEEE WFCS2021. He was
awarded the “2016 Inventor of the Year Award” and “2018 Inventor of
the Year Award” by ABB Corporate Research Sweden.
Hong Wen (Senior Member, IEEE) received the
Ph.D. degree in communication and computer
engineering from Southwest Jiaotong Univer-
sity, Chengdu, China, in 2004.
She was an Associate Professor with the
National Key Laboratory of Science and
Technology on Communications, University of
Electronic Science and Technology of China
(UESTC), Chengdu. From 2008 to 2009, she
was a Visiting Scholar and a Postdoctoral Fellow
with the ECE Department, University of Water-
loo, Waterloo, ON, Canada. She is currently a Professor with UESTC.
Her current main research interests include wireless communication
systems security.
Wenxin Lei (Graduate Student Member, IEEE)
is currently working toward the Ph.D. degree in
control science and engineering with the School
of Aeronautics and Astronautics, University of
Electronic Science and Technology of China,
Chengdu, China.
His current research interests include wire-
less communication security, edge computing
systems and architecture, edge computing se-
curity, and situational awareness security.
Xinchen Xu is currently working toward the
Ph.D. degree in control science and engineering
with the School of Aeronautics and Astronau-
tics, University of Electronic Science and Tech-
nology of China, Chengdu, China.
His current research interests include edge
computing and Docker technology.
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