 Open Access
 Authors : Deussom Djomadji Eric Michel , Souop Koagne Gloire De Dieu , Feudjio Cyrille , Tonye Emmanuel, Michael Ekonde Sone
 Paper ID : IJERTV11IS010179
 Volume & Issue : Volume 11, Issue 01 (January 2022)
 Published (First Online): 09022022
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Social Spider Algorithmbased Approach for Propagation Model Optimization. Application to Yaounde Town
Deussom Djomadji Eric Michel 1
Department of electrical and electronic engineering COT, university of Buea and NASE of YaoundÃ©
Feudjio Cyrille 3
Department of electrical and electronic engineering COT, university of Buea
Souop Koagne Gloire De Dieu 2 Division of ICT, NASPT and ICT, university of YaoundÃ© I
Tonye Emmanuel 4
Department of electrical and telecommunication engineering
NASE of YaoundÃ©, university of YaoundÃ© 1
Michael Ekonde Sone 5
Department of electrical and electronic engineering COT, university of Buea
Abstract: The propagation models are used to forecast the influences of terrains and artificial environments on path loss. They are the basis of coverage planning. Good models ensure the precision of planning. With the deployment of 4G network worldwide, operators need to plan the coverage of their network efficiently, in order to minimize the cost and improve the quality of service. In this paper, the standard K factors model is taken into account to develop a method for tuning propagation models based on the social spider algorithm. The data is collected on the existing CDMA2000 1XEVDO rev B network in the city of YaoundÃ©. The root mean squared error (RMSE) between actual measurements and radio data obtained from the prediction model developed is used to test and validate the technique. The values of the RMSE obtained by the new model and those obtained by the standard model of OKUMURA HATA in urban areas are also compared. Based on RMSE value from the optimized model and OKUMURA HATA, it can be concluded that the new model developed using the social spider algorithm performs better than the OKUMURA HATA model and is more accurate. The new model proposed on Social spider algorithm is more representative of the local environment. This new evolutionary algorithm prove its performance and can be used anywhere to optimize existing propagation models.
Keywords: Social Spider Algorithm, Radio propagation, mobile network, propagation model optimization.

INTRODUCTION
The Internet network, especially broadband, has become an essential resource in everyday life. The challenge today is to offer a good quality services in nomadic and mobile situations. Wireless transmission techniques offer suitable solutions that need to be mastered in order to be able to provide an irreproachable quality of service. The transmission medium is the wireless propagation channel in radio communication systems. Its characteristics, which strongly depend on the environment, influence its performance. In the deployment phase, more accurate field prediction models are
needed to optimize cellular networks. These models are obtained by running tests on existing models like Okumura Hata or COST231 Hata to produce an optimal propagation model that accurately reflects the characteristics of radio propagation in the given environment.
This work is not the first to focus on the optimization of propagation models. Indeed, several people from various backgrounds have already addressed the issue, each tackling a specific aspect of the problem or part of the network. For example, E. Deussom and E. Tonye [1] worked on New Propagation Model Optimization Approach based on Particles Swarm Optimization Algorithm; R. Mardeni and K. F. Kwan [2] presented Optimization of Hata prediction model in suburban area in Malaysia; Chhaya Dalela, and al [3] who worked on tuning of Cost231 Hata model for radio wave propagation prediction; Medeisis and Kajackas [4] presented On the Use of the Universal OkumuraHata Propagation Prediction Model in Rural Areas; Deussom E. and Tonye E. [5] worked on Propagation model optimization based on Artificial Bee Colony algorithm: Application to YaoundÃ© town, Cameroon.; Allam Mousa, Yousef Dama and Al [6] in Palestine presented "Optimizing Outdoor Propagation Model based on Measurements for Multiple RF Cell;
Mingjing Yang and al [7] in China have presented "A Linear Least Square Method of Propagation Model Tuning for 3G Radio Network Planning"; Chen, Y.H. and Hsieh, K.L [8] in Taiwan presented "A Dual Least – Square Approach of Tuning Optimal Propagation Model for existing 3G Radio Network".
In this paper, we propose an optimization approach based on the Social Spider Algorithm (SSA optimization) which is based on a proposed K factors model with 6 coefficients [10][11]. The SSA optimization is capable of optimizing more than 2 coefficients (up to 6 coefficients) in
the K factors model compared to other methods like linear regression mostly used by authors worldwide which are limited on the optimization of only 2 parameters. In addition, SSA can output not only one solution but a set of possible solutions, among them the best one is selected as the final one. This paper will be articulated as follows: in section II, the background, experimental details, and the methodology will be presented, followed in section III by the result obtained after the implementation. In section IV we will present the discussion of the result and finally, we will have a conclusion in section V.

MATERIAL AND METHODS

Propagation environment
In this study, the data is collected from BTS distributed throughout the city of YaoundÃ© on a CDMA1X EVDO RevB network. To do this, 3 areas have been chosen in the city of YaoundÃ© in particular: The dense urban area, namely the city center, the urban area, namely Biyem Assi district, the suburban area namely the Ngousso district. Which correspond respectively to areas with high, medium, and low population agglomerations. The table below shows the areas chosen with the BTS concerned.
Categories
A
B
C
Urban characteristics
Dense urban
Urban
Suburban
Concerned BTS
Ministere PTT
Biyemassi
Ngousso
Categories
A
B
C
Urban characteristics
Dense urban
Urban
Suburban
Concerned BTS
Ministere PTT
Biyemassi
Ngousso
Table 1 : type of environment

Equipment description
– Simplified description of BTS used
BTS involved in our data collection process is HUAWEI Technologies manufactured. The following table shows the specifications of the BTS.
BTS3606
DBS3900
BTS types
Indoor BTS
Distributed BTS (Outdoor)
Number of sectors
3
3
Frequency Band
800MHz
800MHz
Downlink frequency
870 MHz – 880 MHz
870 MHz – 880 MHz
Uplink frequency
825 MHz – 835 MHz
825 MHz – 835 MHz
Max power (mono carrier)
20 W
20 W
BTS Total power (dBm)
43 dBm
43 dBm
BTS3606
DBS3900
BTS types
Indoor BTS
Distributed BTS (utdoor)
Number of sectors
3
3
Frequency Band
800MHz
800MHz
Downlink frequency
870 MHz – 880 MHz
870 MHz – 880 MHz
Uplink frequency
825 MHz – 835 MHz
825 MHz – 835 MHz
Max power (mono carrier)
20 W
20 W
BTS Total power (dBm)
43 dBm
43 dBm
Table 2: BTS characteristics
The BTS engineering parameters are presented in table 3.
BTS
name
Antenna height(m
)
Mean elevatio n
Antenna effective height
Antenna gain(dB)
7/8 feeder cable( m)
Ministry PT_800
40
741,82
47,18
15,5
45
Ngousso
25
712,05
28,95
17
0
Biyem assi
40
709,54
51,46
15,5
45
BTS
name
Antenna height(m
)
Mean elevatio n
Antenna effective height
Antenna gain(dB)
7/8 feeder cable( m)
Ministry PT_800
40
741,82
47,18
15,5
45
Ngousso
25
712,05
28,95
17
0
Biyem assi
40
709,54
51,46
15,5
45
Table 3: BTS parameters (1)
BTS
type
BTS name
Latitude (degree)
Longitude (degree)
BTS
altitude(m)
3606
Ministry PT_800
3, 86587
11,5125
749
3900
Ngousso
3,90097
11,5613
716
3606
Biyem Assi_800
3,83441
11,4854
721
Table 4: BTS parameters (2)
– Other equipment parameters
In order to perform the radio measurements, a vehicle was used, a laptop, a radio measurement software, namely Pilot Pioneer from Dingli communication V6.0, a CDMAtype LG mobile terminal, a GPS terminal, a DC / AC converter to power the laptop during the measurement.
The drive tests done in the area A, B, and C gave the following results.
Figure 1: Drive test in center town
Figure 2: Drive test in Biyem Assi
Figure 3: Drive test in Ngousso

Methodology
– K factors propagation model [1][12]
There are many propagation models presented in scientific literature, but this modeling is based on K factor propagation model. The General form of the K factors model is given by the following equation:
= + () + Ã— + Ã— ()
+ Ã— ()
Here, we have to minimize the Euclidean distance between the measured values of the propagation loss and those predicted by the propagation model. Let = {}=1: the set of measured values; where N represents the total number of measurement points of L. is a possible solution vector to our optimization problem and the column vector defined by equation (5). The evaluation function of the particles will be:
+
Ã— () () +
+
(1)
= { (
( Ã— ))} ()
Lp = K1 + K2 log(d) + K3 Ã— hm + K4 Ã— log(hm) +
K5 Ã— log(hb) + K6 Ã— log(hb) log(d) + K7diffn + Kclutter(2
constant related to the frequency, constant of
=
attenuation of the distance or propagation exponent, and
are correction factors of mobile phone height; and
are correction factors of BTS height, is the diffraction
=
( ( Ã— ))
=
()
factor, and the correction factor due to clutter type. The parameter values vary according to the type of the landscape and the characteristics of the propagation of the city environment;
Equation (1) could also be written in the following form:
= (1 + 7 + ) + 2 log() + 3 Ã—
+ 4
Ã— log() + 5 Ã— log() + 6 Ã— log() log()
1
1
Now assuming that = 1 + 7 + , equation
– Optimization of Propagation model based on the social spider algorithm
The flowchart below represents the determination of the propagation model using the social spider algorithm.

becomes;
= 1 + 2 () + 3 Ã— + 4 Ã— ()
+5 Ã— () + 6 () () (2)
Equation (2) above can be written as follows:
= [1 2 3 4 5 6]
Ã—
Ã—
1
()
( )
( )
()
[( ) ()]In equation (3) only the vector = [1 2 3 4 5 6] (4) is a variable.
1
Figure 4: SSA algorithm implementation flowchart
In this chart, data filtering is made according to the criteria of
Let =
()
( )
( )
(5)
distance and signal strength received:
Table 5: filtering criteria
Distance (m)
Received power (dB)
Minimum
100
110
Maximum
10 000
40
Distance (m)
Received power (dB)
Minimum
100
110
Maximum
10 000
40
[( ) ()]
Therefore, L can be written in the form:
= Ã— ()
With M a constant vector for a given distance d and depending on if we were under a base station of effective height . If in the contrary the distance d varies for different measurement points, vector M becomes a vector for various measures at different distances points .
– Evaluation function
The idea here is to show that using drive test data, the k factors equation and a suitable social spider algorithm, we can obtain a suitable propagation model for a given frequency. This is illustrated below:
Figure 5: implementation bloc diagram
– SSA Presentation
The algorithm then manipulates s to perform a random walk towards . Here we utilize a dimension mask to guide the movement. Each spider holds a dimension mask m, which is a 01 binary vector of length D and D is the dimension of the optimization problem. Initially all values in the mask are zero.
,
,
After the dimension mask is determined, a new following position is generated based on the mask for s. The value of ith dimension of the following position is
In SSA we formulate the search space of the optimization problem as a hyperdimensional spider web [9].
generated as follows:
fo s,i
fo s,i
Ptar ms,i = 0
P
P
P = {
(11)
Each position on the web represents a feasible solution to the
s,i
r
s,i
ms,i = 1
optimization problem and all feasible solutions to the problem have corresponding positions on this web. The web also serves as he transmission media of the vibrations generated by the spiders. Each spider on the web holds a position and the quality (or tness) of the solution is based on the objective function, and represented by the potential of nding a food source at the position. The spiders can move freely on the web. However, they cannot leave the web as the positions o the web represent infeasible solutions to the optimization problem. When a spider moves to a new position, it generates a vibration that is propagated over the web. Each vibration holds the information of one spider and other spiders can get the information upon receiving the vibration

Vibration
In SSA, we use two properties to dene a vibration, namely, the source position and the source intensity of the vibration. we can thus use I(Ps,Ps,t) to represent the intensity of the vibration generated by spider s at the source position. This vibration intensity at the source position is correlated with the tness of its position f(Ps), and we dene the intensity value as follows:
where r is a random integer value generated in [1, pop], and , stands for the ith dimension of the dimension mask m of spider s. Here the random number r for two different dimensions with ,= 1 is generated independently. With the generated , s performs a random walk to the position. This random walk is conducted using the following equation:
( + ) = + ( ( )) Ã— + ( )
(12)
Where denotes elementwise multiplication and R is a vector of random oatpoint numbers generated from zero to one uniformly. After this random walk, s stores its movement in the current iteration for the next iteration. This ends the random walk substep. The nal substep of the iteration phase is the constraint handling. The spiders may move out of the web during the random walk step, which causes the constraints of the optimization problem to be violated. The iteration phase loops until the stopping criteria is matched. After the iteration phase, the algorithm outputs the best solution with the best tness found. The above three phases constitute the complete algorithm of SSA and its
1
( , , ) = (
+ 1) (9)
pseudocode can be found below. [9]
()
where C is a condently small constant such that all possible tness values are larger than C.
We dene the distance between spider a and b as (, ) and we use 1norm (Manhattan distance) to calculate the distance, i.e.,
(, ) = (10)

Search pattern
There are three phases in SSA: initialization, iteration, and nal. These three phases are executed sequentially. In each run of SSA, we start with the initialization phase, then perform searching in an iterative manner, and nally terminate the algorithm and output the solutions found.
In the initialization phase, the algorithm denes the objective function and its solution space.
In the iteration phase, a number of iterations are performed by the algorithm. In each iteration, all spiders on the web move to a new position and evaluate their tness values.

SSA pseudo code [9]
Assign values to the parameters of SSA. Create the population of spiders pop and assign memory for them.
Initialize for each spider.
while stopping criteria not met do for each spider s in pop do Evaluate the tness value of s.
Generate a vibration at the position of s.
end for
for each spider s in pop do
Calculate the intensity of the vibrations V generated by all spiders.
Select the strongest vibration from V .
if The intensity of is larger than then
Store as .
end if
Start
K1el = 32,4 + 20 Ã— log10(Fc); K1ok = 69,55 + 26,16 Ã— log10(Fc);
for i = 1: populationSize
Update .
Generate a random number r from [0,1).
if r > then
Update the dimension mask .
end if
Generate .
Perform a random walk.
Address any violated constraints.
end for end while
Output the best solution found.

Generating the initial population

The key point for the implementation of SSA is the coding of every spider and the generation of the initial population, for this work a spider will be a vector with the form of equation (6). The search space is between the standard OkumuraHata model and the free space propagation model which characterizes a propagation without obstacle. Now let us see how to generate the initial population.
The starting population that is generated is made up of different spiders randomly generated, meeting certain criteria of integrity on the values of the different for = 1:6. Let F be the population. Then =
K1 = K1el + (K1ok – K1el) Ã— rand (1); K3 = 2,49 + 2,49 Ã— rand (1);
K4 = rand (1);
K5 = 13,82 + 13,82 Ã— rand (1);
K6 = 6,55 Ã— rand (1);
K2 = 20 – (K6 Ã— log10(Hb)) + ((36,8 – 20) Ã— rand (1)); P (i, 🙂 = [K1 K2 K3 K4 K5 K6];
End for
End;
In this code, K1ok represents the parameter K1 in the OkumuraHata model; K1el represents the parameter K1 in the free space model. P is the matrix representing the population generated and the size of the population corresponds to the number of distances measured. This generation of the initial population is based on the initial family generation method made in the work of [11]. The initial population generated is an N Ã— 6 matrix that is N rows and 6 columns. Then value of N corresponds to the number of distances measured and the value 6 represents the 6 parameters of the vector K = [K1 K2 K3 K4 K5 K6]. [5] [11] Once the spider population is generated, the SSA is implemented with the different steps explained previously.


RESULTS
After the implementation of SSA on the radio measurement data obtained in YaoundÃ© through drive tests and by setting the parameters as follows: NS= 100; the maximum number of iterations is set to 50; The model will be seen as accurate if the RMSE between drive test data and the predicted ones is less than 8 dB; (RMSE < 8dB) [5].
We obtained different results represented by curves for each area, the black represents the real propagation, the blue
[ ] [5] [10] [11]represents OkumuraHata propagation, the yellow represents
1 2 3 4 5
6 =1:
the free space propagation and the green represents the SSA.
OkumuraHata model, free space and K factors model propagation model put in the form of equation 16 above will produce the values in the following table:
Propagation model
1
2
3
4
5
6
Okumura Hata
146.56
44.9
0
0
– 13.82
6.55
Free space
91.28
20
0
0
0
0
K factors
149
44.9
2.49
0
13.82
6.55
Propagation model
1
2
3
4
5
6
Okumura Hata
146.56
44.9
0
0
– 13.82
6.55
Free space
91.28
20
0
0
0
0
K factors
149
44.9
2.49
13.82
6.55
Table 6: : propagation models into the K factors form.
The first 3 spiders of our initial population will be those corresponding to the OkumuraHata model, free space and K factors model of the table above respectively. The other spiders need to be generated in order to complete the size of the population to spiders. But before doing that, the criteria that every parameter 1 2 3 4 5 6 should respect needs to be defined in order to have a solution that fits
a real propagation model. The population is generated as follows:

Area A: Center town Yaounde
Figure 1: Center town
The table below shows a comparison of the value of the root mean square error for each of the models considered on the curve for the center town case.
Table 7: results from center town YaoundÃ©
Area
results
K1
K2
K3
K4
K5
K6
RMSE
A
SSA
107.99
22.35
0.0025
0
– 13.82
– 6.55
6.71
Okumura Hata
146.56
44.9
0
0
– 13.82
– 6.55
16.977
Free space
91.28
44.9
2.49
0
– 13.82
– 6.55
16.46
We notice that we have a RMSE <8 dB for the new model which confirms the reliability of the result.
Figure 2: evolution of the Cost function with respect to the number of iterations in the Center town Younde

rea B: Biyem Assi district
Figure 3: Biyem Assi district
The table below shows a comparison of the value of the root mean square error for each of the models considered on the curve for the Biyem Assi area.
Table 8: results from the Biyem Assi district
Area
results
K1
K2
K3
K4
K5
K6
RMSE
B
SSA
98.88
22.19
0
0
– 13.82
6.55
5.38
Okumura Hata
146.56
44.9
0
0
– 13.82
6.55
20.7
Free space
91.28
44.9
2.49
0
– 13.82
6.55
14.85
We notice that we have a RMSE <8 dB for the new model which confirms the reliability of the result.
Figure 4: evolution of the Cost function with respect to the number of iterations in the Biyem Assi district

Area C: Ngousso district
Figure 5: Ngousso district
The table below shows a comparison of the value of the root mean square error for each of the models considered on the curve for the area.
Area
results
K1
K2
K3
K4
K5
K6
RMSE
C
SSA
105.35
30.5
0.036
0
– 13.82
– 6.55
7.89
Okumura Hata
146.56
44.9
0
0
– 13.82
– 6.55
20.7
Free space
91.28
44.9
2.49
0
– 13.82
– 6.55
14.85
Area
results
K1
K2
K3
K4
K5
K6
RMSE
C
SSA
105.35
30.5
0.036
0
– 13.82
– 6.55
7.89
Okumura Hata
146.56
44.9
0
0
– 13.82
– 6.55
20.7
Free space
91.28
44.9
2.49
0
– 13.82
– 6.55
14.85
Table 9: results from the Ngousso district
We notice that we have a RMSE <8 dB for the new model which confirms the reliability of the result.
Figure 6: evolution of the Cost function with respect to the number of iterations in the Ngousso district


DISCUSSION
After the implementation of the SSA using the drive tests data from different areas in YaoundÃ©, we obtain a new propagation model derived from K factors model with 6 coefficients with a RMSE which is less than 8dB. This means that the new model is accurate according to [12].
During this implementation, and at different iterations, some parameter values go out of their specific range and later come back in range after further iterations. furthermore, for all the cases we got a fast convergence of the algorithm after less than 10 iterations while running the algorithm for sometimes 100 iterations. Another detail is that, when running the algorithm several times you can obtain different but accurate results with the same value of RMSE. This is explained by the fact the function rand() outputs values randomly within a specific range, we think it is a drawback of this algorithm. However, we got accurate results when running the Social Spider Algorithm.
The final expression of the propagation model we propose for YaoundÃ© is thus:
= . + . () + .
. () . ()
()

CONCLUSION
This paper presents a new method of optimization of propagation models in a given environment based on a newly
proposed optimization scheme known as Social Spider Algorithm. The setout method is original and could be used to design or calibrate propagation models. As an advantage, we can get a set of solutions after using SSA and amongst them, we select the best one (with minimum RMSE). However, we found a very fast convergence of the algorithm while we were expecting it to happen after a big number of iterations. Practical measurements done in the city of YaoundÃ© gave us very good results with an RMSE less than 8dB for most of the selected areas in the city, compared to Okumura Hata RMSE obtained, the new model gives a better result.
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