A beamforming comparative study of least mean square, genetic algorithm and grey wolf optimization algorithms for multipath smart antenna system

TELKOMNIKA Telecommunication, Computing, Electronics and Control
Vol. 18, No. 6, December 2020, pp. 2911~2920
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v18i6.16970  2911
Journal homepage: http://journal.uad.ac.id/index.php/TELKOMNIKA
A beamforming comparative study of least mean square, genetic
algorithm and grey wolf optimization algorithms for multipath
smart antenna system
Asma Issa Mohsin1
, Asaad. S. Daghal2
, Adheed Hasan Sallomi 3
1,2
Al-Furat Al-Awsat Technical University, Iraq
3
Faculty of Engineering, Al-Mustansiriyah University, Iraq
Article Info ABSTRACT
Article history:
Received Jun 15, 2020
Revised Jun 17, 2020
Accepted Jun 25, 2020
Multipath environment is a limitation fact in optimized usage of
wireless networks. Using smart antenna and beamforming algorithms
contributed to that subscribers get a higher-gain signal and better
directivity as well as reduce the consumed power for users and the
mobile base stations by adjusting the appropriate weights for each
element in the antenna array that leads to reducing interference and
directing the main beam to wanted user. In this paper, the performance
of three of beamforming algorithms in multipath environment in terms
of Directivity and side lobe level reduction has been studied and
compared, which are least mean square (LMS), genetic algorithm (GA)
and grey wolf optimization (GWO) technique. The simulation result
appears that LMS algorithm aids us to get the best directivity followed
by the GWO, and we may get most sidelobe level reduction by using
the GA algorithm, followed by LMS algorithm in second rank.
Keywords:
Beamforming
Genetic algorithm
Grey wolf optimization
Least mean square
Smart Antenna
This is an open access article under the CC BY-SA license.
Corresponding Author:
Asaad. S. Daghal,
Engineering Technical College-Najaf,
Al-Furat Al-Awsat Technical University,
Babylon-najaf street, Najaf 54003, Kufa, Iraq.
Email: ad466kent@atu.edu.iq
1. INTRODUCTION
The fact of limited spectrum capacity makes impossible to dispel it for unwanted signals. From here,
researchers started searching for solutions that lead to the optimized utilization for bandwidth [1-3]. One of
the important characteristics of wireless channels is multipath fading effect, which causes the signal to be weak
and distracted, makes the band width busy with interfaces, multipath is considered one of the determinants factors
of network quality [4-6]. The definition of multipath fading in a simple way is the reflection of
the transmitted signal because it collides with existing obstacles such as buildings and vehicles, and this leads to
the arrival of several copies of the signal to the receiver at various time intervals, Figure 1 illustrates a simplified
scenario for multipath signal formation [7-9]. The beamforming is used to steer multiple beams towards
the desired user while the interferers are canceled at the same time. This can be achieved via adjustment of
the beamformers weight vectors, where the quality of the communication channel can maximize through
the process of varying the complex weight [10-12]. A narrow beam with high gain can be achieved through a
large number of antenna elements that combine to construct the array [13]. The antenna array can steer
the beam pattern electronically in particular directions, minimal side lobe level (SLL), and suppress interference

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TELKOMNIKA Telecommun Comput El Control, Vol. 18, No. 6, December 2020: 2911 - 2920
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[14, 15]. However, different techniques have been studied to enhance the system performance in terms of several
objectives, for example, to increase the directivity or reduce the interference. In this article, we used three different
techniques, least mean square (LMS), genetic algorithm (GA) and grey wolf optimization (GWO) to study
the directivity and SSL in a smart antenna system.
Figure 1. Multipath propagation scenario
The main contributions of this paper are:
- The average of directivity has been increased significantly in multipath environment when a LMS is used
for beamforming compared to GA and GWO, which gives a sharper and more precise beam patterns.
- The most average SLL reduction in multipath environment is achieved when using GA for beamforming
followed by LMS in the second level.
- The results show that convergence of a GWO is achieved faster than GA based method. LMS method is
most slow down convergence between these three methods.
The remaining of this paper is organized as follows: in section 2, a geometry configuration of a linear
antenna array and the array factor equations are discussed. A description of the LMS, Genetic and GWO
algorithms and its implementation steps are discussed in same section. A simple explanation about simulation
enforcement is included in section 3, as well as the results of simulation for all three algorithms are presented
and discussed in section 4. While the conclusion presents in section 5.
2. ANTENNA ARRAY CONFIGURATION
The 𝑁-element array is considered a common general linear array. For simplicity, all elements in this
study are assumed that have equal amplitudes and equally spaced. Figure 2 depicts a linear array of an
N-element, which collected isotropic radiation of antenna elements. In this paper, a uniform linear array along
the x-axis consisting of 2N isotropic elements is studied. The array factor (AF) is calculated using the following
equations;
𝐴𝐹 = 1 + 𝑒 𝑗(𝑘𝑑𝑠𝑖𝑛∅+𝜕)
+ 𝑒 𝑗2(𝑘𝑑𝑠𝑖𝑛∅+𝜕)
+ 𝑒 𝑗3(𝑘𝑑𝑠𝑖𝑛∅+𝜕)
+ ⋯ + 𝑒 𝑗(𝑁−1)(𝑘𝑑𝑠𝑖𝑛∅+𝜕)
(1)
where 𝑟 >> 𝑑 represents the far-field condition, a far-field distance is given as
𝑑 = 2𝐷2
/𝜆 (2)
where 𝐷 is the maximum antenna dimension, 𝑟 is the distance from element 𝑛 to far-field point, and 𝜕 is
the phase shift between successive elements as shown in (1) can more precisely express as
𝐴𝐹 = ∑ 𝑒 𝑗(𝑁−1)(𝜓)𝑁
𝑛=1 (3)
where 𝜓 = 𝑘𝑑 sin ∅ + 𝜕. It is noted that if the array is lined up along the 𝑧 − 𝑎𝑥𝑖𝑠 then 𝜓 = 𝑘𝑑 cos ∅ + 𝜕.

TELKOMNIKA Telecommun Comput El Control 
A beamforming comparative study of least mean square (LMS), genetic algorithm... (Assad S. Daghal)
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Figure 2. Uniform linear array geometry
3. LEAST MEAN SQUARE ALGORITHM
In 1959 Widrow and Hoff introduced the LMS algorithm to the world. It is one of the earliest adaptive
algorithms that depends on gradient based method of abrupt. LMS is a search algorithm that use the modifying
of objective function to simplify the gradient vector computation. Figure 3 articulate the flow chart of LMS
algorithm [16-18]. The LMS algorithms can defined mathematically by following equations:
𝑦(𝑛) = 𝑤(𝑛). 𝑋(𝑛) (4)
𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛) (5)
𝑤(𝑛 + 1) = 𝑤(𝑛) + 𝜂 𝑋(𝑛). 𝑒(𝑛) (6)
𝜂 = gain constant and monitor the adaptation rate.
𝑥(𝑛) = input signal.
𝑒(𝑛) = error between desired and output signal
𝑑(𝑛) = desired signal.
where 𝑅 is the correlation matrix
𝜂 = 1/𝑡𝑟𝑎𝑐𝑒 (𝑅)
Figure 3. Flowchart of LMS algorithm

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4. GENETIC ALGORITHM
Genetic algorithm is considered one of the first’s meta-heuristic algorithms. It is classified as global
numerical optimization methods, which got popular by John Holland in 1970s. The GA uses five basic steps
to solve problems and it can be summarized as follow [19-22]:
- Creating initial population of chromosomes randomly. Each chromosome is a possible solution.
- Determine the fitness value and fitness function to solve the problem, and is it need to minimized or
maximized.
- Initially, all the created chromosomes are passed on the Fitness function for evaluation, and then the best
chromosomes that gave us the best solutions are identified. The chromosomes that gave us the worst results
are discarded and in case, we have a new generation of chromosomes.
- Cross over process takes place between the best chromosomes to create new chromosomes. May mutation
process applies on some chromosomes with a certain percentage to give us new chromosomes and new solutions
- This process of step 3 and 4 is repeated within certain iterations to obtain the results required to solve
the problem.
5. GREY WOLF OPTIMIZATION ALGORITHM
The GWO algorithm is considered one of the meta-heuristic algorithms that emulate the social hunting
manner and hierarchical of the grey wolves group. The hunting manner of the grey wolves can be summarized
as follows [23-25]: The first grade, which represents the chi (𝜒) that they are the leaders and can be males or
females. The second grade in the hierarchical is consists of the rho (𝜌) wolves, which followed by the wolves
called gamma (𝛾), while the down sorting of the grey wolves is named mu (𝜇). The hierarchical of the grey
wolves are constituted mathematically throughout counting 𝜒 as the best solution that followed by the 2nd
and
the 3rd
finest solutions 𝜌 and 𝛾, respectively. The remaining of the nominated solutions are supposed to be 𝜇.
The major steps sequence of the grey wolf hunting can be summarized as follows:
- Pursuit, chasing after and draw near the prey.
- Keep tracking, surrounding, and beset the prey until it stops moving.
- Raid towards the prey.
During a hunting process, grey wolves hedge the prey that is mathematically modelled as [9]:
𝐷⃗⃗ = |𝐶. 𝑌𝑝(𝑡)⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ − 𝑌(𝑡)⃗⃗⃗⃗⃗⃗⃗⃗ | (7)
𝑦(𝑡 + 1)⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ = 𝑌𝑝(𝑡)⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ − 𝐴. (𝐷)⃗⃗⃗⃗⃗⃗⃗ (8)
where 𝐶 and 𝐴 are the coefficient vectors, 𝑡 is referred to the current iteration, 𝑌𝑝⃗⃗⃗⃗⃗ represents the location
vector of the prey, and 𝑌⃗ refers to the location vector of the grey wolf. The vectors 𝐶 and 𝐴 are evaluated as;
𝐶 = 2. 𝑟2⃗⃗⃗ (9)
𝐴 = 2𝜒. 𝑟1⃗⃗⃗ − 𝜒 (10)
where components of 𝜒 are decreased linearly from 2 to 0 during the iterations and 𝑟1⃗⃗⃗ , 𝑟2⃗⃗⃗ are random vectors
that lie in the range [0,1]. In the GWO algorithm process, the hunting approach has led by χ, ρ, and γ, where
the other wolves follow those three types of wolves. Further, in the pack of the wolves, it is supposed that
the wolves’ χ, ρ, and γ have the best familiarity about the potential position of the prey. Consequently, the ﬁrst
three best solutions will be save, and the other searching operators will update their locations according to
the position of the best search operator. For this purpose, we use the following equations:
𝐷𝜒⃗⃗⃗⃗⃗ = |𝐶1⃗⃗⃗⃗ . 𝑌𝜒⃗⃗⃗⃗⃗ − 𝑌⃗ |
𝐷𝜌⃗⃗⃗⃗⃗ = |𝐶2⃗⃗⃗⃗ . 𝑌𝜌⃗⃗⃗⃗⃗ − 𝑌⃗ |
𝐷𝛾⃗⃗⃗⃗⃗ = |𝐶3⃗⃗⃗⃗ . 𝑌𝛾⃗⃗⃗⃗ − 𝑌⃗ |
𝑌1⃗⃗⃗⃗⃗ = 𝑌𝜒⃗⃗⃗⃗⃗ − 𝐴1⃗⃗⃗⃗⃗ . (𝐷𝜒)⃗⃗⃗⃗⃗⃗⃗⃗⃗
𝑌2⃗⃗⃗⃗⃗ = 𝑌𝜌⃗⃗⃗⃗⃗ − 𝐴2⃗⃗⃗⃗⃗ . (𝐷𝜌)⃗⃗⃗⃗⃗⃗⃗⃗⃗
𝑌3⃗⃗⃗⃗⃗ = 𝑌𝛾⃗⃗⃗⃗ − 𝐴3⃗⃗⃗⃗⃗ . (𝐷𝛾)⃗⃗⃗⃗⃗⃗⃗⃗⃗
𝑌⃗ (𝑡 + 1) =
𝑌1⃗⃗⃗⃗⃗ +𝑌2⃗⃗⃗⃗⃗ +𝑌3⃗⃗⃗⃗⃗
3 }
(11)
By using (11), and according to the parameters χ, ρ, and γ in the nth-dimensional searching domain, where a
search operator will be updating its location. Also, the ﬁnal location of the search domain would be in a random

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place within a circle that is clariﬁed by the locations of χ, ρ, and γ. So that, χ, ρ, and γ evaluate
the location of the prey, while the rest of the wolves update their locations randomly throughout the prey [26].
6. MATERIALS AND METHODE
In this paper, the performance of the three explained algorithms in section 3 to 4 in beamforming was
compared in multipath environment. To embody multipath environment, two users with three transmitted
signals with different direction of arrival angel for each user were taken. The case of study considered
the distance between the array elements is 0.25λ and the number of elements is 32 in antenna design.
A simulation tool of MATLAB software has been used to analyze the performance of the systems in
beamforming, where a curve between the SLL and main beam pattern has taken into consideration. The main
simulation parameters of this paper are shown in Table 1.
Table 1. Simulation parameters
Parameter Description
Direction of arrival (DOA) angle (1st
user) DOA11 = 50, DOA12 = -30, DOA13 = 70
Direction of arrival (DOA) angle (2nd
user) DOA21 =-50, DOA22 = 0, DOA23 = 30
Frequency 900MHZ
Element spacing 900MHZ
Fitness function for GA and GWO 𝑚𝑖𝑛(𝑚𝑎𝑥(20𝑙𝑜𝑔|𝐴𝐹(Ө)|))
No of iteration for each technique GWO = 10, GA = 200, LMS = 600
7. RESULTS AND DESCUSSIONS
In Table 2 it is noticed that the average value of directivity equal to 14.95 which is higher than
the directivity in the other two algorithms. The higher directivity related to DOA12, DOA21 and DOA23 with
value equal to 15. In Table 3, it is clear that the directivity in the genetic algorithm ranges from 13.76 for DOA22
to 14.26 for DOA13. In Table 4, it is recorded that the average of directivity is about 14.28 and
the highest one is for DOA23 with value equal to 14.5. Directivity average in GA method is the lowest among
the three algorithms with a value equal to 14.03. Average of SLL value for LMS algorithm method is recorded
about 0.207 in Table 2, as it is seen in Figure 4 the highest level of side lobe is for DOA23 with value count to
0.23 and the lowest level of side lobe is o.15 for DOA13 as it is clear in Figure 5. It is chained in Tables 3 and 4
that average of SLL is 0.18 in GA algorithm and 0.21 in GWO algorithm, and it is represented in Figures 6 and 7
that the highest sidelobe level is for DOA22 with value equal to 0.23 and most sidelobe level reduction is for
DOA13. The GWO algorithm has the less SLL reduction in multipath environment. Figure 8 shows that highest
side lobe level is 0.28 for DOA12. In Figure 9, it is obvious that lowest level of side lobe is obtained for DOA21.
Despite the simple differences, the outcomes of all three algorithms are generally close; the GWO algorithm needs
the least number of samples and repetition, means that needs less computation time than the rest of the algorithms,
while the LMS algorithm needs the largest number of samples compared to two other algorithms. The results
elaborated in the following Figures 4-9.
Table 2. Antenna parameters results for array with 32 elements and 0.25 λ inter spacing, by LMS algorithm
DOA Directivity SLL SLL in dB main pattern in dB
DOA11 14.88 0.190476 -4.39 8.18
DOA12 15 0.210526 -9.66 4.15
DOA13 14.98 0.152672 -11.95 1.13
DOA21 15 0.241135 -11.76 1.068
DOA22 15 0.219231 -10.25 3
DOA23 14.86 0.230769 -4.78 8.21
average 14.953 0.207468 -8.79833 4.2896
Table 3. Antenna parameters results for array with 32 elements and 0.25 λ inter spacing, by GA algorithm
DOA11 14.21 0.1643192 9.4 24.63
DOA12 13.94 0.2140673 9.54 24.24
DOA13 14.26 0.14 8.84 25.84
DOA21 13.86 0.207 9.97 25.08
DOA22 13.76 0.233882 10 23.8
DOA23 14.15 0.1582609 8.96 24.7
average 14.03 0.1821059 9.451667 24.715

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Table 4. Antenna parameters result for array with 32 elements and 0.25 λ inter spacing, by GWO algorithm
DOA11 14.35 0.21 47.33 59.37
DOA12 14.02 0.28 48.56 58.37
DOA13 14.31 0.2 47.24 59.14
DOA21 14.13 0.15 42.32 58.26
DOA22 14.38 0.27 49.6 60.16
DOA23 14.5 0.2 46.53 60
average 14.28167 0.218333 46.93 59.21666667
Figure 4. SLL, main lobe of first user and its 3DOAs for N = 32, λ = 0.25 optimized with LMS
Figure 5. SLL, main lobe of second user and its 3DOAs for N = 32, λ = 0.25 optimized with LMS

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Figure 6. SLL, main lobe of first user and its 3DOAs for N = 32, λ = 0.25 optimized with GA
Figure 7. SLL, main lobe of second user and its 3DOAs for N = 32, λ = 0.25 optimized with GA

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Figure 8. SLL, main lobe of first user and its 3DOAs for N = 32, λ = 0.25 optimized with GWO
Figure 9. SLL, main lobe of second user and its 3DOAs for N = 32, λ = 0.25 optimized with GWO
8. CONCLUSION
In this paper, the performance of three types of adaptive algorithms for the beam forming in smart
antenna systems, in terms of preference in directivity and the extent of sidelobe level reduction for multipath
environment has been studied. Despite the simple differences, the outcomes of all three algorithms are

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generally close; the GWO algorithm needs the least number of samples and repetition, means that needs less
computation time than the rest of the algorithms, while the LMS algorithm needs the largest number of samples
compared to two other algorithms. The study shows us that the most sidelobe level reduction occurs when
using the genetic algorithm, followed by the LMS algorithm. The findings demonstrates that LMS algorithm
achieves better results in terms of directivity in multipath environment, followed by GWO algorithm in the
second rank.
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BIOGRAPHIES OF AUTHORS
Asma Issa Mohsin received the B.S. and M. Sc degree in Technical communication engineering
from Engineering Technical College-Najaf, Al-Furat Al-Awsat Technical University, Iraq, in
2007 and 2020, respectively. She is currently work with the Ministry of Oil, Baghdad, Iraq. Her
research interests are in the area of wireless communications, covering smart antenna system,
and optimization techniques.
Asaad S. Daghal received the B.Sc. and M.Sc. degrees in electrical engineering and
communication engineering from the University of Technology, Baghdad, Iraq, in 1998 and
2005, respectively, and the Ph.D. degree in communication engineering from the University of
Kent, Canterbury, U.K., in 2017. He is currently a Lecturer with the Engineering Technical
College of Najaf, Al-Furat Al-Awsat Technical University, Iraq. My research interests include
wireless communications, covering topics such as device-to-device communications, massive
MIMO, cooperative communications, heterogeneous networks, Energy harvesting, smart
antenna, signal processing, coding and information theory.
Adheed Hasan Sallomi is currently a Professor of antenna sysytem at the School of
Engineering, Al-Mustansiriyah University, Baghdad, Iraq. He has authored over 50 papers in
international journals and conferences in the area of wireless communications and two books.
His research interests include antenna systems design and optimaization techniques.

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