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Channel Path-Loss Measurement and Modeling in Wireless Data Network (IEEE 802.11n) Using Artificial Neural Network

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Careful network planning has become increasingly critical with the rising deployment, coverage, and congestion of wireless local area networks (WLANs).This paper investigates and determine the Path-loss exponent value for the ubiquitous wireless local area network at the Federal University Oye-Ekiti for the line of sight and non-line of sight (N-LOS). Aside this, the paper also models the wireless network using artificial neural network (ANN) technology by training some neurons based on data collected from a drive-test. The proposed ANN model performed with accuracy and is offered as a simple, yet strong predictive model for network planning – having both speed and accuracy. Results show, that for the area under study, Oye Campus has a higher standard deviation of 5.76dBm as against ikole Campus with 1.44dBm, this is because of dense vegetation at Oye Campus. In view of this, the paper provides a predictive site survey for rapid wireless Access point deployment.
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EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 1
AbstractCareful network planning has become
increasingly critical with the rising deployment, coverage, and
congestion of wireless local area networks (WLANs). This
paper investigates and determine the Path-loss exponent value
for the ubiquitous wireless local area network at the Federal
University Oye-Ekiti for the line of sight and non-line of sight
(N-LOS). Aside this, the paper also models the wireless
network using artificial neural network (ANN) technology by
training some neurons based on data collected from a drive-
test.
The proposed ANN model performed with accuracy and is
offered as a simple, yet strong predictive model for network
planning having both speed and accuracy. Results show, that
for the area under study, Oye Campus has a higher standard
deviation of 5.76dBm as against ikole Campus with 1.44dBm,
this is because of dense vegetation at Oye Campus.
In view of this, the paper provides a predictive site survey
for rapid wireless Access point deployment.
Index TermsArtificial Neural Network, N-LOS, Path Loss,
Propagation Model.
I. INTRODUCTION
Path Loss is difference in dB between transmitted signal
and received signal strength at a location. Network
Engineers mostly used path loss model as a mathematical
tool to determine received signal strength at a given point.
The problem of predicting propagation loss between two
points may be seen as a function of several inputs and a
single output. The inputs contain information about the
transmitter and receiver locations, surrounding buildings,
frequency, etc. while the output gives the propagation loss
for those inputs. From this point of view, research in
propagation loss modeling consists of finding both the
inputs and the function that best approximate the
propagation loss. The various models that have been
proposed can be classified as empirical or deterministic
model. Empirical models like ITU, TGn, SUI and Okumura-
Hata[12]-[13], [17], [20] are based on received signal
measurement within a given environment. The Empirical
models are computationally efficient but may not be very
accurate in different environment. Deterministic models like
geometric theory of wave, ray-tracing [8][9] technology is
very accurate but requires extensive computational time and
Published on February 27 , 2020.
O. Y. Olajide, Department of Electrical/Electronic Engineering, Federal
University of Technology Akure, Nigeria.
(e-mail: yoolasoji@futa.edu.ng)
Y. M. Samson, ICT UNIT, Federal University Oye-Ekiti, Nigeria.
(e-mail: samson.yerima@fuoye.edu.ng)
detailed information of the environment.
The introduction of Machine learning techniques has
helped in solving complex problems in our everyday life,
this can be exploited for path loss predictions in given
propagation environments. Artificial Neural Network
(ANN) is an adaptive statistical tool that models the
biological nervous system to solve regression problems. The
capability of ANNs to model complex nonlinear functional
relationships provides an opportunity to combine the gains
of empirical and deterministic models and also to provide
better computational efficiency. ANN has high processing
speed and can process large volume of data, has the
flexibility to adapt to different environments and can be
trained to perform well in environments similar to where the
training data are collected. The basic features of the ANN
are for it to be able to create its own internal model of
behavior of radio waves by observing the measured data,
measured data have inherent behavior of the network from
where it was collected, as such the measured data are needed
for the creation of ANN model. The feed-forward neural
networks [4], [5] are very well suited for prediction purposes
because they do not allow any feedback from the output
(field strength or path loss) to the input. ANN can be used
to model the mathematical function of Pathloss of a given
environment.
II. RELATED LITERATURE
A. Stanford University Interim (SUI) Model [2], [21]
The 802.16 IEEE group, jointly with the Stanford
University, carried out an extensive work with the aim to
develop a channel model for WiMAX applications in
suburban environments. The model is formulated to operate
based on an operating frequency above 1900MHz and a cell
radius of 0.1km to 8km, base station antenna height 10m to
80m, and receiver antenna height of 1m to 10m. This model
is divided into three categories of terrains namely A, B, C.
The terrain category A is associated with maximum path
loss, and densely populated region. Moderate path loss is
captured in terrain category B. The terrain category C is
associated with minimum path loss and flat terrain with light
tree densities.
The basic path loss expression of The SUI model with
correction factors is presented as:
!"#$%&'()*+!"
,
#
#!
-
%.$%.%%/000000121"000000
(1)
Channel Path-Loss Measurement and Modeling in
Wireless Data Network (IEEE 802.11n) Using Artificial
Neural Network
Olasoji Y. Olajide and Yerima M. Samson
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 2
where
10
is the distance between BS and receiving antenna
(m),
1"&&
is the reference distance 100 (m),
.$&&
is the frequency
correction factor for frequency above 2 GHz,
.%
is the
correction factor for receiving antenna height (m),
/000
is the
correction for shadowing (dB), and
00(
is the path loss
exponent. The random variables are taken through a
statistical procedure as the path loss exponent γ and the
weak fading standard deviation s is defined. The log
normally distributed factor
/
, for shadow fading because of
trees and other clutter on a propagations path and its value is
between 8.2 dB and 10.6 dB.
The parameter A is defined as:
$#3')*+!"
,
'(#!
)
-
0000000000
(2)
The frequency correction factor
.$
and the correction for
receiver antenna height
.%
for the model are expressed in:
.$#45')*+!"
,
$
*"""
- (3)
For terrain type A and B
.%#6&'57)*+!"
,
%"
*"""
- (4)
for terrain type C
.%#63')*+!"
,
%"
*"""
- (5)
Where
80
is the operating frequency (MHz),
9+
is the
receiver antenna height (m)
For the above correction factors this model is extensively
used for the path loss prediction of all three types of terrain
in rural, urban and suburban environments.
B. IEEE 802.11 TGn channel model
The TGn channel model was conceived for systems with
4x4 MIMO, and are based on the Kronecker channel
correlation model assumption. According to the IEEE
802.11 TGn channel model, the PL can be modeled by the
free space PL for
:;:"
, and by a one-slope model with
exponent 3.5 for
:2:"
. The TGn model predicts a
breakpoint of 5m for ‘Small environment’ (type of
environment ‘C’) and a breakpoint of 10m for ‘Large
environment’ (type of environment ‘D’).
<=
>
:
?
#<=,-./01:@:"00000000000000000
(6)
<=
>
:
?
#<=,23
>
:"
?
%AB)*+!"
,
0
0!
-
:2:"0
(7)
where d is the transmit-receive separation distance in m. the
standard deviations of log-normal (Gaussian in dB) shadow
fading were found to be in the 3-14 dB range.
PLLOS(d)= Free path loss
C. COST 231 Walfish-Ikegami (W-I) Model [17], [20],
[15]
This model is a combination of J. Walfish and F. Ikegami
models. This model is considered as the most appropriate
model for rural and suburban environments which have
regular building height. Among other models like the Hata
model, COST 231 W-I model gives a more precise path
loss. This is as a result of the additional parameters
introduced which characterized the different environments.
It distinguishes different terrain with different proposed
parameters. The equation of the proposed model is
expressed in:
For LOS condition
!"456&#C354%34)*+!"
>
1
?
%03')*+!">8?
(8)
And for NLOS condition
!"!"#$ #
$
"%&' %"()& %"*&+ &'()**+),-.*-./*0+,+),-.
"%&'&*********************"()& %"*&+ 12 *
(9)
"%&' #34567%428(9,- :;<%428(9,-:=<>0*?@A*')AA*0B-CA*8(00
"+78
is the roof top to street diffraction
"98#
is the multi-screen diffraction loss
Fig. 1. Diffraction angle and urban scenario [15]
"+78 #
D
6&45E6&')*+!"
>
F
?
%&')*+!"
>
8
?
%
3')*+!"
>
G99
?
%":+;H 9+::$ 299
'
(10)
where
":+; #
D
6&'%'5ABCI0000000000000000000000000'@I;AB
35B%'5'JB
>
I6AB
?
00000000000000AB@I;BB
C6'5&&C
>
I6BB
?
00000000000000BB@I;E' 0
(11)
Note that
G99#9+::$ 699G9<=8> #9<=8> 69+::$
(12)
The multi-screen diffraction loss is
!!"# " !$"%# $&%&''(
(
)
*
# $)%&''(
(
+
*
, - %&''(
(
+
*
, .- %&''((/*
(13)
"<8%#
K
6&7)*+!"
>
&%G9<=8>
?
H 9<=8> 29+::$
'H00000000000000000000000000000000000000000000000009<=8> @9+::$0
(14)
D.#
E
76*************************************F/.&0 GF(11%
76H25IJF/.&0****************;K257*LM;*F/.&0 NF(11%
76H25IJF/.&0
O
+
-23
P
;1257*LM;*F/.&0 NF(11%
(15)
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 3
L##
D
&7H 9<=8> 29+::$
&76&B
,
?%#$%&
%#$%&
-
H000009<=8> @9+::$
(16)
For suburban or medium size cities with moderate tree
density
L$#6C%'5J
,
$
@*A 6&
- (17)
And for metropolitan urban
L$#6C%&5B
,
$
@*A 6&
- (18)
where
10
is the distance between transmitter and receiver antenna
(m)
8
is the frequency (GHz)
M0
is the building to building distance (m)
F0
is the street width (m)
I0
is the street orientation angel with respect to direct
radio path (degree)
D. ITU Model [10], [17], [19], [12]
The International Telecommunication Union Radio
communication (ITU-R) is a semi empirical path loss model
that can be employed in different environment comprising
indoor, outdoor, vehicular and pedestrian. The applicable
operational frequency is 900MHz 6GHz and the equations
for the line of sight (LOS) and non-LOS (NLOS) path loss
are;
!B/4561#&7)*+!">8C?%N)*+!">1?637
(19)
!B/D4561#3')*+!">8C?%N)*+!">1?%"8>OE?637
(20)
Where;
8C
= carrier frequency in MHz N= Power Loss
Coefficient d= Tx-Rx distance in meters
Lf= wall penetration loss
OE#
the number of walls
E. Calculation of distance power loss coefficient
The distance power loss coefficient, N is the quantity that
expresses the loss of signal power with distance. This
coefficient is an empirical one. Some values are provided in
Table I.
TABLE I: [12]
Frequency
band
Residential area
Office
area
Commercial
area
900 MHz
N/A
33
20
1.21.3 GHz
N/A
32
22
1.82.0 GHz
28
30
22
4 GHz
N/A
28
22
5.2 GHz
30 (apartment), 28
(house)
31
N/A
5.8 GHz
N/A
24
N/A
6.0 GHz
N/A
22
17
F. Calculation of floor penetration loss factor
The floor penetration loss factor is an empirical constant
dependent on the number of floors the waves need to
penetrate. Some values are tabulated in Table II.
TABLE II: [12]
III. DATA COLLECTION METHOD AND ANALYSIS
Pathloss model prediction for wireless data network
requires practical data from the field measurement.
Received signal strength were measured at various distances
from the transmitter at the ISM band frequency of
2400MHz. A drive test tools for data collection includes a
laptop equipped with communication Network/Protocol
Analyser (metageek insider 4 software) and GPS receiver to
measure the longitude and latitude of the received signal.
The average transmitted power from the transmitter is 28
dBm. Results obtained was plot in MATLAB.
Designing ANN models follows a number of systemic
procedures. In general, there are five basic steps: (1) data
collection, (2) data preprocessing, (3) Network Building, (4)
training and (5) model performance test as shown below.
Fig. 2. Basic flow for ANN Model Designing
The work presented in this paper is modeled using
McCulloch-Pitts model. The MATLAB [1][3][5] tools
contain the Neural Network Toolbox [4] for designing,
implementing, visualizing and simulating neural networks.
It also provides comprehensive support for many proven
network paradigms, as well as graphical user interfaces
(GUIs) that enable the user to design and manage neural
networks in a very simple way.
Fig. 3. McCullouch-Pitts Model of ANN
Y=F(P
>F+QR+%S?
+
+F!
) (21)
p = (p1, …, pr) is the input column-vector
W = (w1, …, wr) is the weight row-vector
F=the transfer function
The bias b can be treated as a weight whose input is
always 1.
Data Collection Preprocessing Building
Network
Trainin
g
Networ
k
Testing
Network
Number
of floors
Residential
area
Office area
Commercial
area
1
N/A
9
N/A
2
N/A
19
N/A
3
N/A
24
N/A
n
4n
15+4(n-1)
6 + 3(n-1)
1
N/A
16
N/A
1
N/A
22 (1 floor), 28
(2 floors)
N/A
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 4
IV. PATHLOSS MEASUREMENT AND RESULTS
The path loss measurement was taken at the Ikole and
Oye campus of the Federal University Oye-Ekiti Ekiti State
Nigeria. The two campuses consist of structures and foliage.
The measurements were done at the ISM band frequency
2.4GHz. The transmitter used is the ZoneFlex_9.7 802.11n
Outdoor Access Point [6]. The receiver equipment included
a laptop, equipped with LB LINK™ BL-WN150 WLAN
USB adapter card and inSSIDer Wi-Fi network
scanner/protocol analyzer. The receiver was moved around
the campus for the received power in dBm and the
longitude/latitude position of the receiver was recorded.
Haversine formula was used to calculate the distance
between the transmitter and the receiver given the
longitude/latitude.
This work concentrated on the received radio signal
needed for the path loss analysis of the coverage area. The
path loss includes signal attenuation with signal fading
between the transmitter and the receiver, while the channel
consists of structures and foliage. It is to be noted that while
conducting the drive test other WiFi AP acted as
interference to the received signal.
Fig. 4. Google Earth view of Oye campus
Fig. 5. Google Earth view of Ikole Campus
TABLE III: AP POSITION IKOLE CAMPUS
AP NAME
LONGITUDE
LATITUDE
MechaEng AP
5 29’ 38.20”E
7 48’ 27.65”N
Civil Eng AP
5 29’ 35.98”E
7 48’ 27.63”N
Dean Eng AP
5 29’ 37.11”E
7 48’ 26.72”N
Dean Agric AP
5 29’ 49.41”E
7 48’ 13.72”N
TABLE IV: AP POSITION OYE CAMPUS
AP NAME
LONGITUDE
LATITUDE
ICT New AP
5 18’ 42.75”E
7 46’ 34.70”N
Fac of sci AP
5 18’ 55.58”E
7 46’ 37.24”N
Theater AP
5 18’ 59.73”E
7 46’ 35.96”N
Science1 AP
5 18’ 15.78”E
7 46’ 37.14”N
Science2 AP
5 18’ 55.28”E
7 46’ 36.96”N
The measured received power in both campuses are
plotted in Fig. 6, while the path loss are plotted in Fig. 7. By
observing the path loss values, it was clear that the path loss
deviation has less value at Ikole campus than Oye campus,
this is due to less foliage and structures at Ikole campus than
Oye campus as seen in the Google Earth view map.
Fig. 6. Measured Received Power
Fig. 7. Path Loss Using Measured Data
Fig. 8. Path Loss include one Slope Model
A. Determination of Power exponent and log-normal
variation
Average Transmitted power from the AP datashet,
Pt=28dBm.
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 5
Average received power from the AP d0=1m,
!+#6&&1MT
,
0U#!76!+#AE1MT
(22)
Using the one slope model to determine the power
exponent
(
Let
0!*#+,
(
)
*
".1-
(
)/2
*
, 1.
(
)/2
*
" $
(
)/2
*
#345678'(
9
#
#!
:
# ;/
(23)
VG#0
zero-mean Gaussian distributed random variable
(in dBm) with standard deviation
W
(also in dBm)
minimum mean square error (MMSE) equation for the
dBm power measurements is
X
>
(
?
#
P Y
Z9>=8H+>#
>
1;
?
6Z9:#>B
>
1;
?[
*
I
;F!
(24)
Q
:
R
<
#
ST
U*0.&4(0+
:
;5
<
H:D
:
;VW
<
%X2RYZ[,-
\
;5
;-
]
<
^
6
7
58,
Q
:
R
<
#
_`
U*0.&4(0+
:
;5
<
HD
:
;VW
<
HX2RYZ[,-
O
+!
+"
Pa
6
7
58,
(25)
MMSE occur at
0J/K1
0K #'
(#
L
MN'&$%("&)
/
#*
1
OP
/
#Q9
1
R
+
*,-
L
M!"B:S-!
T
)*
)!
U
R
+
*,-
(26)
Ikole campus
n=93,
P
\Z9>=8H+>#
>
1;
?
]
I
;F!
=summation of PL=7681.5,
P
\&'^_`!"
,
#*
#!
-
]
I
;F! #1a/bcOde0/fTTcba_O#
1330.013
(#>J47&5B6EAgAE?
&AA'5'&A #A5'B
Oye campus
n=184, P
\Z9>=8H+>#
>
1;
?
]
I
;F!
=summation of PL=15631
P
\&'^_`!"
,
#*
#!
-
]
I
;F! #1a/bcOde0/fTTcba_O#
2756.47
(#>&B4A&6&7CgAE?
3JB45CJ #A5'4
The log-normal variation or shadow fading is giving by
VG#&
O
hY
Z9>=8H+>#
>
1;
?
6Z9:#>B
>
1;
?[
*
I
;F!
Ikole Campus
b9#X
M
Sc
U*0.&4(0+
:
;5
<
HU*1+0'
:
;5
<d
6: #XeX56I
e3 #4&2f
7
58,
Standard deviation σ =i
VG
=j
35'4
= 1.44
01MT
Oye Campus
b9#X
M
Sc
U*0.&4(0+
:
;5
<
HU*1+0'
:
;5
<d
6: #
7
58, fXX654g
XI6 #33543
Standard deviation σ =i
VG
=j
AA53A
= 5.76
01MT
TABLE V: RESULT OBTAINED
Freq
(Ghz)
Locatio
n
<
(=>?*
PL
Expon
ent
σ
(dBm)
Tx-Rx
Distance(m)
2.4
Ikole
39
3.05
1.44
1-100
2.4
Oye
39
3.06
5.76
1-100
V. ANN MODELING AND RESULTS COMPARISON WITH THE
FOUR EXISTING MODELS
IEEE802.11n is a fixed wireless network, therefore the
ANN model presented in this paper has the following
parameters: distance between WiFi AP and the receiver,
carrier frequency, height of the WiFi AP and height of the
receiver. Set of path loss data recorded at distances between
transmitter and receiver were used in the training of the
neurons. Levenberg-Marquardt (trainlm) algorithm was used
to train the network, this algorithm is generally faster than
the others and very ideal for the network model. During the
training phase the characteristics of the network were
modified by this iterative algorithm until a minimum error is
obtained, that is the error between the network (predicted)
output and the desired (measured) output is minimized.
Observations were made during the training process. It was
observed that different results were obtained each time the
network was trained. This is as a result of different initial
weight and bias values, and different divisions of measured
data into training, validation and test sets, thus it is possible
that different artificial neural structures trained on the same
problem can generate different outputs for the same input.
Another observation noted was that network sensitivity
depends on the number of neurons in the hidden layer.
When the number is few it leads to underfitting but when the
number is too many it causes overfitting, the number of
hidden layers was varied during training until the desired
result was obtained. To achieve the modeling of the network
using McCulloch-pitts model, two hidden layer of size five
(5) was obtained as the best representation of the network.
Fig. 9. Training the ANN
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 6
Fig. 10. Result Performance
The various weights and bias are given below:
IW{1,1}- WEIGHT TO LAYER 1 FROM INPUT 1
-7.0587
-8.3286
-7.5125
-5.7149
6.440
IW{2,1}-WEIGHT TO LAYER
1.4840
-1.1689
1.8698
1.2639
1.3860
0.6068
-2.3206
-0.8896
-0.6184
-0.9326
1.4892
1.0294
-0.3789
0.0312
-2.1822
-1.2016
-0.5139
0.4895
2.5840
-0.0674
0.6244
0.4632
1.1968
0.2990
1.0982
IW{3,1}-WEIGHT TO LAYER
0.5657
0.9578
1.7526
0.2508
0.9772
B{1}- BIAS TO LAYER 1
6.9731
2.6584
0.6378
-3.2609
7.8763
B{2}- BIAS TO LAYER 2
-1.7008
-0.7874
0.1788
-1.2809
2.2889
B{3}- BIAS TO LAYER 3
[-0.23941]
From the ANN analysis the proposed mathematical
function for the wireless data network Path loss is given
!"#'54&kA6'57Jk'6'577kV6'5J4k*%75Ck%$
(27)
where
$#&'()*+!"
l
./)!01
2
m
%3C
(28)
k#
/
#OVA
1
WX
(29)
!"0
represent the channel modeling of the wireless data
network in mathematical function, where:
(
= the Path Loss coefficients of the environment (3.05-
3.06)
8C
= ISM band frequency (2.4GHz to 2.5GHz)
1
= distance between the Tx and Rx
The model proposed is to be site-general, the radio
transmission loss is characterized by both an average
transmission loss and its associated shadow fading statistics.
The model proposed in this research accounts for the loss
through multiple floors to allow for such characteristics as
frequency reuse between floors. The distance power loss
coefficients include an implicit allowance for transmission
through walls and over and through obstacles, and for other
loss mechanisms likely to be encountered within a single
floor of a building.
Fig. 11. Comparison of proposed ANN Model with Industry Standard
VI. DISCUSSION
From Fig. 11, the proposed ANN model matches closer
with the average drive test data as compared to other
models, the zero-mean Gaussian distribution is within the
range of 2.06-33.32 dBm, while standard deviation ranges
from 1.44dBm to 5.76dBm and the path loss exponent
ranges from 3.05-3.06. it was observed from Fig 11 that the
ITU model has the highest value of Path loss at 2400 MHz.
compared to other models in the same environment, this is
as a result of the floor penetration loss factor given in Table
V for the number of floors between Access Point and the
receiver. It was also observed that at a distance less than
70m the pathloss is approximately linearly depended on the
distance, above 70m fading and signal attenuation
drastically affect the Pathloss. This result shows that for a
good signal connection in wireless data connection distance
between Tx and Rx should be less than 70m. From this
observation, it could be concluded that the ANN model is
statistically a better model compared to others and can be
used as a better estimator of path loss for university
campuses in Nigeria
VII. CONCLUSION
The research goal was to analyze the behavior of
propagation channel, determine the Path loss exponent and
to model the channel using ANN for wireless data
communication systems operation at ISM 2.4GHz. Based on
several drive tests conducted. A mathematical model was
formulated which could be used in the deployment of WiFi
AP due to its adaptive nature. The propose ANN new model
explains the relationship between the path-loss coefficient,
the distance between Tx-Rx and the frequency, together
produces a novel framework that describe the Path Loss. It
provides the basis for the realization of wireless data
communication under complicated environment with
complex utilizing of the spectrum resource. The ANN model
can be used for regular IoT deployment, VOIP, and robotics
operating in the ISM band 2.4GHz frequency. As a future
work, it is intended that the path loss model for
IEEE802.11ac with frequency band of 5GHz will be
examined.
EJECE, European Journal of Electrical and Computer Engineering
Vol. 4, No. 1, February 2020
DOI: http://dx.doi.org/10.24018/ejece.2020.4.1.157 7
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Olasoji Y. Olajide (PhD) is with the Department of
Electrical/Electronic Engineering, Federal University
of Technology Akure, Nigeria (e-mail:
yoolasoji@futa.edu.ng).
Yerima Musa Samson is with the ICT UNIT,
Federal University Oye-Ekiti, Nigeria (e-mail:
samson.yerima@fuoye.edu.ng.
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