EVALUATION OF WIRELESS SENSOR NETWORK CLUSTER HEAD SELECTION FOR DIFFERENT PROPAGATION ENVIRONMENTS BASED ON LEE PATH LOSS MODEL AND K-MEANS ALGORITHM

Abstract

In this paper, the evaluation of wireless sensor network (WSN) cluster head selection for different propagation environments based on Lee path loss model and K-means algorithm is presented. A set of 50 WSN nodes distributed randomly over an area of 3000 m by 3000 m with the base station located in the middle of the area , at the coordinate of x = 1500 m and y = 1500 m. The X and y coordinates of each of the 50 WSN nodes were generated using Matlab software random number generators function. The coordinate geometry formula for distance, d between two points with coordinates, (1 , 1) and (2 , 2) is used to compute the distance from each of the nodes to the base station and then the distances were used to compute the path loss and hence the received signal strength (RSS) for each of the nodes. The computation was conducted for the three different propagation environments, as specified in the Lee model, namely, the urban , the suburban and the rural or open area. Based on RSS (-60 dBm ≤ RSS ≤-90 dBm), candidate cluster heads were selected for the urban , the suburban and the rural or open area. Afterwards, the K-means clustering algorithm was used to select the cluster heads from the candidate cluster heads. The results show that for the urban area, only 4 nodes were selected as cluster heads ; the node with a received signal strength of-60.8 dBm had the highest number of 17 slave nodes clustered around it whereas, the node with a received signal strength of-91.7 dBm had the lowest number of 10 slave nodes clustered around it. Also, for the open or rural area, 12 nodes were selected as cluster heads; the node with a received signal strength of-60.1 dBm had the highest number of 13 slave nodes clustered around it whereas, the several cluster head nodes with received signal strength lower than-60.1dBm had the lowest number of 2 slave nodes clustered around them. In all, the results showed that the urban area had the highest path loss, the lowest RSS value and the lowest number of cluster heads selected by the K-means algorithm. On the other hand, the open or rural area had the lowest path loss, the highest RSS value and the l highest number of cluster heads selected by the K-means algorithm. Keywords-K-means algorithm, Lee path loss model, wireless sensor network, sensor device, propagation loss, received signal strength.

Full text

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EVALUATION OF WIRELESS SENSOR NETWORK CLUSTER HEAD SELECTION FOR
DIFFERENT PROPAGATION ENVIRONMENTS BASED ON LEE PATH LOSS MODEL AND
K-MEANS ALGORITHM
Wali Samuel1
Department of Electrical/Electronic
and Computer Engineering
University of Uyo
samwalliuy@yahoo.com
Ozuomba, Simeon2
Department of Electrical/Electronic
and Computer Engineering
University of Uyo
simeonoz@yahoomail.com
simeonozuomba@uniuyo.edu.ng
Philip M. Asuquo3
Department of Electrical/Electronic
and Computer Engineering
University of Uyo
Abstract— In this paper, the evaluation of wireless sensor
network (WSN) cluster head selection for different
propagation environments based on Lee path loss model
and K-means algorithm is presented. A set of 50 WSN
nodes distributed randomly over an area of 3000 m by
3000 m with the base station located in the middle of the
area , at the coordinate of x = 1500 m and y = 1500 m. The
X and y coordinates of each of the 50 WSN nodes were
generated using Matlab software random number
generators function. The coordinate geometry
formula for distance, d between two points with
coordinates,󰇛 󰇜and 󰇛 󰇜 is used to compute
the distance from each of the nodes to the base station and
then the distances were used to compute the path loss and
hence the received signal strength (RSS) for each of the
nodes. The computation was conducted for the three
different propagation environments, as specified in the Lee
model, namely, the urban , the suburban and the rural or
open area. Based on RSS (-60 dBm ≤ RSS ≤ -90 dBm),
candidate cluster heads were selected for the urban , the
suburban and the rural or open area. Afterwards, the K-
means clustering algorithm was used to select the cluster
heads from the candidate cluster heads. The results show
that for the urban area, only 4 nodes were selected as
cluster heads ; the node with a received signal strength of -
60.8 dBm had the highest number of 17 slave nodes
clustered around it whereas, the node with a received signal
strength of -91.7 dBm had the lowest number of 10 slave
nodes clustered around it. Also, for the open or rural area,
12 nodes were selected as cluster heads; the node with a
received signal strength of -60.1 dBm had the highest
number of 13 slave nodes clustered around it whereas, the
several cluster head nodes with received signal strength
lower than -60.1dBm had the lowest number of 2 slave
nodes clustered around them. In all, the results showed that
the urban area had the highest path loss, the lowest RSS
value and the lowest number of cluster heads selected by
the K-means algorithm. On the other hand, the open or rural
area had the lowest path loss, the highest RSS value and the
l highest number of cluster heads selected by the K-means
algorithm.
Keywords— K-means algorithm, Lee path loss
model, wireless sensor network, sensor device,
propagation loss, received signal strength.
1.0 Introduction
Wireless sensor networks (WSNs) are very useful
technology for smart city and other contemporary
applications [1,2,3,4,5,6,7,8]. In WSNs, resource limited
sensor devices are used to collect data from the
environment and to transmit the data to remote locations.
[9,10,11,12,13,14]. One of the key challenges of WSN is
the power limitations of the sensor devices which tends to
lime the WSN lifetime [15,16,17,18,19,20]. As such, effort
is always made in WSN to adopt energy efficient
approaches that will enhance WSN life time. One of such
energy efficient approach is device-to-device
communication which utilizes clustering mechanism to
select appropriate set of WSN nodes as cluster head heads
which aggregates the data from the other nodes in the
network and relay them through the base station or gateway
to their respective destination
[21,22,23,24,25,26,27,28,29,30,31].
In any case, the transmission energy demand depends
among other things on the distance [32,33,34,35,36] of the
nodes from the base station as well as path loss [37,38,
39,40,41,42,43,44] which depends on the environmental
factors. Accordingly, in this paper, the effect of propagation
environment on the cluster head selection by K-means
algorithm is studied [45,46,47,48]. The study is based on
the received signal strength (RSS) computed using Lee path
loss model [49,50] and link budget formula. The
computation was carried out for three different propagation
environments, as specified in the Lee model. A common
RSS range of values were used for cluster head selection in
the three propagation environment. The actual computation
was conducted using the Matlab tools for K-means
algorithm. Key analytical expression are presented along
with requisite data and discussion of findings.
2. Methodology
The papers presents a study of cluster head selection in a
wireless sensor network for different propagation
environment based on Lee path loss model K-means
clustering algorithm. The study considers a set of 50 sensor
network nodes distributed randomly over an area of 3000 m
by 3000 m. The Base station in the network is located in the
middle of the area and it has the coordinate of x = 1500 m
and y = 1500 m. The X and y coordinates of each of the 50
WSN nodes are generated using Matlab software random
number generators function and they are shown in Figure 1.
The coordinate geometry formula for distance, d
between two points with coordinates,󰇛 󰇜and
󰇛 󰇜 is used to compute the distance from each of the
nodes to the base station, where;

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  󰇛󰇜󰇛󰇜 (1)
Figure 1; Coordinate positions of the 50 WSN nodes and the base station at the center (1500 m, 1500 m)
The received signal strength (RSS) at each of the nodes is
estimated using link budget formula where the path loss
was estimated using Lee path loss model for three different
propagation environments, namely, the urban area, the
suburban area and rural area. The propagation loss
according to Lee path loss model is given as follows;
󰇛󰇜  󰇛󰇜󰇛󰇜  󰇛󰇜󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜 (2)
Where
f is the centre frequency f in MHz;
d = path length in km;
= antenna height of the base station;
 = antenna height of the mobile station;
The values of n and Po for the Lee path loss model are
given in Table 1 for the various propagation environments.
Table 1 The value of n and Po for the Lee path loss model
The RSS is dBm according to link budget formula is given
as;
RSS = PT + GT + GR – 󰇛󰇜
(3)
Where PT = transmitter power, GT = transmitter antenna
gain and GR = receiver antenna gain. Based on Lee model
and the values of Po and n in Table 1, the RSS was
computed for the open rural area, the suburban area and the
urban area. The RSS values obtained were then used in
Matlab for K-means based cluster head selection from the
50 WSN nodes. The cluster head selection was first based
on a set rang of RSS values for the candidate nodes that can
be eligible to serve as cluster heads. Specifically, in this
paper, the receiver sensitivity is assumed to be -110 dBm
and the range of values of RSS for used nodes for selecting
candidate cluster heads is -60 dBm ≤ RSS ≤ -90 dBm. The
same range of values of RSS was used for the three
different propagation environments, namely, the open rural
area, the suburban area and the urban area.
3. Simulation and Results
The results of the devices or nodes selected as candidate
cluster heads for the urban area based on the set range of
value for RSS (-60 dBm ≤ RSS ≤ -90 dBm) are given in
Table 2 and Figure 2. Similar results of the devices or
nodes selected as candidate cluster heads for the suburban
is shown in Table 3 and Figure 3 while the results for the
open or rural area is shown in Table 4 and Figure 3. In all,
based on the selected range of values for RSS, there are 12
candidate nodes in the urban area, 19 candidate nodes in the

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suburban area and 39 candidate nodes in the open or rural area.
Table 2 The results of the devices or nodes selected as candidate cluster heads for the urban area based on the set range of
value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
S/N
Device Number
x-coordinate (m)
y-coordinate (m)
d (km)
Lee Path Loss For
Urban (dB)
RSSI For
Urban (dB)
1
1
1043.1
1602.2
1.2287
101.7
-91.7
2
2
449.99
269.85
0.2355
70.8
-60.8
3
4
786.44
408.88
0.3006
75.4
-65.4
4
7
728.36
569.13
0.2386
71.1
-61.1
5
10
1077.7
164.92
0.6678
90.3
-80.3
6
19
810.81
1.5671
0.5874
87.9
-77.9
7
26
1190.4
683.53
0.7144
91.6
-81.6
8
33
982.7
740.2
0.5392
86.3
-76.3
9
35
1315.9
250.45
0.8532
94.9
-84.9
10
45
599.59
50.949
0.46
83.3
-73.3
11
46
1220.9
362.58
0.7339
92.1
-82.1
12
50
955.57
628.22
0.4733
83.9
-73.9
Figure 2 The results of the devices or nodes selected as candidate cluster heads (red square dots) for the urban area based on
the set range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
Table 3 The results of the devices or nodes selected as candidate cluster heads for the suburban area based on the set range of
value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500
y-coordinate (m) for the urban area
x-coordinate (m)
y-coordinate (m) y-coordinate of CH candidate devices (m)

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S/N
Device
Number
x-coordinate (m)
y-coordinate (m)
d (km)
Lee Path Loss
For Suburban
(dB)
RSSI For
Suburban (dB)
1
1
1043.1
1602.2
1.2287
98.3
-83.3
2
3
1758.3
335.12
1.2691
98.9
-83.9
3
5
133.36
2036
1.5792
102.5
-87.5
4
8
1327.2
1485
1.2863
99.1
-84.1
5
9
2063.4
442.82
1.5644
102.4
-87.4
6
10
1077.7
164.92
0.6678
88.1
-73.1
7
12
1184.1
1681.7
1.3654
100.1
-85.1
8
15
1326.9
1748.4
1.4974
101.6
-86.6
9
19
810.81
1.5671
0.5874
86
-71
10
24
1173.5
1438.6
1.1552
97.3
-82.3
11
26
1190.4
683.53
0.7144
89.3
-74.3
12
29
1132.2
1724
1.3776
100.2
-85.2
13
33
982.7
740.2
0.5392
84.6
-69.6
14
35
1315.9
250.45
0.8532
92.2
-77.2
15
38
501.76
2189.3
1.6893
103.6
-88.6
16
44
464.26
1740.3
1.2408
98.5
-83.5
17
45
599.59
50.949
0.46
81.9
-66.9
18
46
1220.9
362.58
0.7339
89.7
-74.7
19
50
955.57
628.22
0.4733
82.4
-67.4
Figure 3 The results of the devices or nodes selected as candidate cluster heads (red square dots) for the suburban area based
on the set range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500
y-coordinate (m) for the Suburban area
x-coordinate (m)
x-coordinate (m) y-coordinate of CH candidate devices (m)

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Table 4 The results of the devices or nodes selected as candidate cluster heads for the open or rural area based on the set range
of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
S/N
Device
Number
x-coordinate (m)
y-coordinate (m)
d (km)
Lee Path Loss For
Rural/Open (dB)
RSSI For
Rural/Open (dB)
1
1
1043.1
1602.2
1.2287
75.7
-60.7
2
3
1758.3
335.12
1.2691
76
-61
3
5
133.36
2036
1.5792
77.8
-62.8
4
6
2264.8
1485.5
2.0213
80
-65
5
8
1327.2
1485
1.2863
76.1
-61.1
6
9
2063.4
442.82
1.5644
77.8
-62.8
7
11
2209
2552.1
2.6705
82.4
-67.4
8
12
1184.1
1681.7
1.3654
76.6
-61.6
9
13
2050.2
2788.8
2.7644
82.7
-67.7
10
14
2112.1
2090
2.2643
81
-66
11
15
1326.9
1748.4
1.4974
77.4
-62.4
12
16
58.733
2446.2
1.9956
79.9
-64.9
13
17
992.57
2637
2.193
80.7
-65.7
14
18
1272.9
2966.7
2.585
82.1
-67.1
15
20
591.16
2596.3
2.0983
80.3
-65.3
16
21
2465.2
1837.7
2.3773
81.4
-66.4
17
22
1289.8
2969.9
2.5931
82.2
-67.2
18
23
2663.3
1583
2.4192
81.6
-66.6
19
24
1173.5
1438.6
1.1552
75.1
-60.1
20
25
2307.3
2404
2.6252
82.3
-67.3
21
27
2425.5
1494.3
2.1671
80.6
-65.6
22
28
2265.2
2702.6
2.8227
82.9
-67.9
23
29
1132.2
1724
1.3776
76.7
-61.7
24
30
648.06
2535.5
2.0409
80.1
-65.1
25
31
2371.2
2215.9
2.5388
82
-67
26
32
2847.9
1758
2.6637
82.4
-67.4
27
34
2013.8
1999.2
2.1305
80.5
-65.5
28
36
2500.5
1877.9
2.4291
81.6
-66.6
29
37
2306.6
1982.8
2.3372
81.3
-66.3
30
38
501.76
2189.3
1.6893
78.4
-63.4
31
39
2585.9
2672.3
3.0116
83.5
-68.5
32
40
2969.6
2946.9
3.4765
84.7
-69.7

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33
41
1543.3
2307.1
2.0866
80.3
-65.3
34
42
2652.8
1744.3
2.4865
81.8
-66.8
35
43
1764.1
2784.9
2.6113
82.2
-67.2
36
44
464.26
1740.3
1.2408
75.8
-60.8
37
47
2246.1
2588.1
2.722
82.6
-67.6
38
48
2476.8
1452.9
2.1945
80.7
-65.7
39
49
2369.9
2534.6
2.7634
82.7
-67.7
Figure 4 The results of the devices or nodes selected as candidate cluster heads (red square dots) for the open or rural area
based on the set range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm).
The results of the nodes selected as cluster heads by the K-
means algorithm for the urban area based on the set range
of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm) are shown
in Table 5. Table 5 shows that only 4 nodes are selected as
cluster heads in the urban propagation environment and the
node with a received signal strength of -60.8 dBm had the
highest number of 17 slave nodes clustered around it
whereas, the node with a received signal strength of -91.7
dBm had the lowest number of 10 slave nodes clustered
around it.
Again, the results of the nodes selected as cluster heads by
the K-means algorithm for the suburban area based on the
set range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm)
are shown in Table 6. Table 6 shows that 7 nodes are
selected as cluster heads in the urban propagation
environment and the node with a received signal strength of
-66.9 dBm had the highest number of 13 slave nodes
clustered around it whereas, the node with a received signal
strength of -87.4 dBm had the lowest number of 2 slave
nodes clustered around it.
Furthermore, the results of the nodes selected as cluster
heads by the K-means algorithm for the open or rural area
based on the set range of value for RSS (-60 dBm ≤ RSS ≤
-90 dBm) are shown in Table 7. Table 7 shows that 12
nodes are selected as cluster heads in the open or rural
propagation environment and the node with a received
signal strength of -60.1 dBm had the highest number of 13
slave nodes clustered around it whereas, the several cluster
head nodes with a received signal strength lower than -
60.1dBm had the lowest number of 2 slave nodes clustered
around them. The bar chart showing the comparison of the
number of selected candidate cluster heads based on RSS (-
60 dBm ≤ RSS ≤ -90 dBm) and the number of K-means
selected cluster heads for the three different propagation
environments is shown in Figure 5. The results show that
the urban area had the highest path loss, the lowest RSS
value and the lowest number of cluster heads selected by
the K-means algorithm. On the other hand, the open or rural
area had the lowest path loss, the highest RSS value and the
highest number of cluster heads selected by the K-means
algorithm.
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500
y-coordinate (m) Rural/Open Area
x-coordinate (m)
y-coordinate (m) y-coordinate of CH candidate devices (m)

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Table 5 The results of the nodes selected as cluster heads by the K-means algorithm for the urban area based on the set range
of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm)
Device Number
x-coordinate (m)
y-coordinate (m)
d (km)
Lee Path
Loss For
Urban (dB)
RSSI For
Urban (dB)
Number of
Slave Nodes
to the
cluster head
1
1043.1
1602.2
1.2287
101.7
-91.7
10
2
449.99
269.85
0.2355
70.8
-60.8
17
3
982.7
740.2
0.5392
-76.3
-76.3
12
4
1315.9
250.45
0.8532
-84.9
-84.9
7
Table 6 The results of the nodes selected as cluster heads by the K-means algorithm for the suburban area based on the set
range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm)
S/N
Device
Number
x-coordinate
(m)
y-coordinate
(m)
d (km)
Lee Path Loss
For Suburban
(dB)
RSSI For
Suburban
(dB)
Number of
Slave Nodes
to the cluster
head
1
5
133.36
2036
1.5792
102.5
-87.5
6
2
9
2063.4
442.82
1.5644
102.4
-87.4
2
3
15
1326.9
1748.4
1.4974
101.6
-86.6
4
4
26
1190.4
683.53
0.7144
89.3
-74.3
8
5
38
501.76
2189.3
1.6893
103.6
-88.6
3
6
44
464.26
1740.3
1.2408
98.5
-83.5
7
7
45
599.59
50.949
0.46
81.9
-66.9
13
Table 7 The results of the nodes selected as cluster heads by the K-means algorithm for the open or rural area based on the
set range of value for RSS (-60 dBm ≤ RSS ≤ -90 dBm)
S/N
Device
Number
x-coordinate
(m)
y-coordinate
(m)
d (km)
Lee Path Loss
For Rural/Open
(dB)
RSSI For
Rural/Open
(dB)
Number of
Slave Nodes to
the cluster
head
1
3
1758.3
335.12
1.2691
76
-61
5
2
9
2063.4
442.82
1.5644
77.8
-62.8
3
3
13
2050.2
2788.8
2.7644
82.7
-67.7
2
4
14
2112.1
2090
2.2643
81
-66
3
5
21
2465.2
1837.7
2.3773
81.4
-66.4
2
6
24
1173.5
1438.6
1.1552
75.1
-60.1
6
7
30
648.06
2535.5
2.0409
80.1
-65.1
3
8
37
2306.6
1982.8
2.3372
81.3
-66.3
2
9
38
501.76
2189.3
1.6893
78.4
-63.4
3
10
39
2585.9
2672.3
3.0116
83.5
-68.5
2

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SCITECHP420101 366
11
41
1543.3
2307.1
2.0866
80.3
-65.3
3
12
44
464.26
1740.3
1.2408
75.8
-60.8
4
Figure 5 The bar chart of the number of selected as candidate cluster heads based on RSS (-60 dBm ≤ RSS ≤ -90 dBm) and
the number of K-means selected cluster heads for the three different propagation environments
4. Conclusions
The ability of K-means clustering algorithm to select
cluster heads from a set of wireless sensor network nodes is
studies. The key parameter used for the cluster head
selection is the received signal strength which was
calculated suing Lee propagation loss model and link
budget expression. The computation was conducted for the
three different propagation environments, as specified in
the Lee model, namely, the urban , the suburban and the
rural or open area. The results show that the urban area had
the highest path loss, the lowest RSS value and the lowest
number of cluster heads selected by the K-means algorithm.
On the other hand, the open or rural area had the lowest
path loss, the highest RSS value and the l highest number of
cluster heads selected by the K-means algorithm.
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