Linear Antenna Array Optimization
Using Genetic Algorithm
Pawan Kumar
Student M.Tech (ECE)
Electronics and Communication Department
Punjabi University, Patiala
Punjab, India
Manjeet Singh Patterh
Electronics and Communication Department
Punjabi University, Patiala
Punjab, India
Abstract- This paper presents the optimization of
linear antenna array by varying the element
spacing of the antenna elements as well as by
adjusting the feed current amplitudes. Genetic
Algorithm as optimization technique is used to
optimize the array factor, minimize the side lob
level (SLL) and steer the main beam in specific
direction. The nulls are fixed at 𝟖𝟏° and 𝟗𝟗° .
Different results are analyzed for nulls and
reduction in SLL.
GA to good use. GA is a search procedure that uses
random selection for optimization of a function.GA
is different from the four ways.
1) GA work with a coding of parameter set, not the
parameters themselves.
1. INTRODUCTION
Linear Antenna arrays have so many applications
in the field of radar, sonar and communications [1].
Antenna arrays may be placed in any manner like
linear, planer, circular, cylindrical, spherical, etc
[2]. A most popular type of antenna array is the
linear array, which can produce satisfactory narrow
beam, and most importantly radiation pattern
calculation is relatively easy compared to that of
other configurations [3]. The characteristics of
antenna array can be controlled by geometry of the
element and array excitation like: feed current
amplitudes control, phase control, element spacing
control, both amplitude and element spacing or by
changing the type of radiation elements in the
array. For the better result, these variations can be
used alone or combination of them can be used [4].
Global optimization methods such as (GA), Particle
Swarm optimization (PSO) have been used in array
optimization for minimizing the side lobe level
(SLL), improving the performance of antenna array
[5].
2) GA search from a population of points, not a
single point.
3) GA use objective function information, not any
derivative or auxiliary information.
4) GA use probabilistic transition rules, not
deterministic rules [6].
The GA fined their application in various
engineering problems like electromagnetic field
theory, antenna arrays, VLSI circuit partitioning
and many more. GA acquires importance, because
they use random searching methods, and are
capable of solving complicated and nonlinear
search problems. Also, they are not limited by
restrictive assumptions about the search space [7].
The structure of chromosomes, production of
populations, new generations, and crossovers, etc,
are coded with random routines, resulting in a non
biological presentation. According to the biological
perspective, genetics is divided into two categories:
the population genetics of Mendel and molecular
genetics. Mendelian genetics depends on the wellknown empirical experiments of peas. This theory
still has a valid consideration in genetic inheritance
[8]. Software computing tools such as the GA have
been used in various kinds of antenna optimization
problems for a long time [9]. For the optimization
problems biologically based algorithms have been
found such as the GA [10-14]. As an excellent
search and optimization algorithm, GA has gained
more and more attention and has very wide
applications [3, 14].
GA was invented by John Holland in 1965. His
goal of understanding the processes of natural
adaptation and designing biologically-inspired
artificial systems led to the formulation of the
simple genetic algorithm. Since its conception,
genetic algorithms have enjoyed global use by
many researchers and scientists in many different
areas. Although computer scientists can take much
as business, science, and engineering have put the
2. LINEAR ANTENNA ARRAY
Individual antennas of an antenna array system are
also termed as Elements. When the individual
antennas of the array are equally spaced along a
straight line that antenna array is said to be linear.
A uniform linear array is one in which the element
are fed with current of equal magnitude with
uniform progressive phase shift along the line. The
term phase in an antenna arrays and ordinary circuit
Keywords- Feed Current Amplitudes, Element
Spacing, Null-Steering, Side Lobe Level (SLL),
Genetic Algorithm (GA)
has same meaning that is two currents in two
elements are said to be in phase if they reach their
maximum values, flowing in the same direction at
the same instant. Two types of antenna arrays: Broadside Array
 End Fire Array
 Collinear Array
 Phased Array
Broad side array is one which a number of identical
parallel antennas are set up along a line drawn
perpendicular to their respective axes. In the broad
side array individual antennas are equally spaced
along a line and each element fed with current of
equal magnitude, all in the same phase. By doing
so, this arrangement fires in broad-side directions
where there are maximum radiations and relatively
a little radiations in other directions and hence the
radiation pattern broadside array is bidirectional.
The broadside array is bidirectional which radiates
equally well in either direction of maximum
radiations [19].
End fire array in which numbers of identical
antennas are spaced equally along a line and
individual elements are fed with currents of equal
magnitude but their phases varies progressively
along the line in such a way as to make the entire
arrangement substantially unidirectional [19].
In collinear array, the elements are arranged coaxially. The individual elements are fed with equal
in phase current as is the case in the broad side
arrays. A collinear array is a broad side radiator, in
which the direction of maximum radiation is
perpendicular to the line of antenna. This
arrangement gives radiation pattern which, when
viewed through the major axis, closely resembles
with the radiation pattern of a broadside array. But
the radiation pattern of a collinear array has circular
symmetry with its main lobe everywhere
perpendicular to the principal axis [20].
Fig.1: Symmetrically placed linear array [15]


z is the feed current amplitudes.
I are array elements.
3. GENETIC ALGORITHM
GA is an optimization method that works on the
principle of survival of fitness. It is a search
algorithm which is implemented using Matlab
simulation. To evaluate the fitness function there
are various parameters for selection like crossover,
initial
population,
mutation,
reproduction,
selection, stopping criteria, number of generation.
The combination of GA and other optimized
methods should be presented continuously. The
characters of GA are simple thinking, easyimplement and obvious application effect, so it is
very suitable for the optimization of linear antenna
array
elements.
[16].
Phased array is an array of antennas in which the
relative phases of the respective signals feeding the
antennas are set in such a way that the effective
radiation pattern of the array is reinforced in a
desired direction and suppressed in undesired
directions [20].
The technique is implemented on the linear antenna
array elements to get desired nulls and SLL, two
step approach:1) Optimizing the element spacing.
2) Optimizing the feed current amplitudes.
has been implemented.
In the shown figure:

d is element spacing.
α is phase angle.
Fig.2 GA Flow Chart
The important operators of GA can be summarized
viz.
1.
2.
3.
4.
5.
6.
Number of Generations
Initial Population
Crossover
Mutation
Chromosomes
Next generation [6].
If the amplitude is 1 and phase zero for all
elements, the array factor can be simplify to
𝐴𝐹(𝜃) = 2 ∑𝑁
𝑛=1 cos[kzn cos(θ) ]
1. Number of Generations – The upper limit
of generations that the GA can progress into, before
terminating. The sequence is repeated until a
termination condition has been reached such as:1. A result that satisfies the lowest criteria.
2. Getting the particular number of generations.
3. Attaining the exact Computation time.
4. Arriving suitable value and
5. Manual inspection [4].
2. Initial Population ˗ An initial population of
at least 200 random chromosomes is generated. The
value of lower bond and upper bond is fixed.
Reference positions of array factor are calculated
by Taylor approximation method.
3. Crossover – The individuals chosen by
selection recombine with each other and new
individuals will be created. The aim is to get
offspring individuals that inherit the best possible
combination of the characteristics (genes) of their
parents.
4. Mutation – By means of random change of
some of the genes, it is guaranteed that even if none
of the individuals contain the necessary gene value
for the extremum, it is still possible to reach the
extremum
[1].
5. Chromosome – Most GA’s use binary coding
and binary genetic operations. The proposed
approach, however, applies floating point genetic
operations on complex array weighting vectors.
Hence, each chromosome is a vector of complex
numbers and the dimension of the vector is
equivalent to the number of array elements [17].
6. New Generation – The best individuals
chosen from the selection are combined with those
who passed the crossover and mutation, and form
the next generation [18].
4. PROBLEM FORMULATION
Consider an array of antenna consisting of N
number of elements is symmetric about the centre
of the array. The far field array factor of this array
with number of linear antenna elements (N=16) can
be expressed as:𝑁
𝐴𝐹(𝜃) = 2 ∑ In cos[kzn cos(θ) + ∅n ]
(1)
𝑛=1
[5]
(2)
Our Goal is to find the element spacing and feed
current amplitudes {𝑧1, 𝑧2 , … … . 𝑧𝑛 } of elements
that achieves the design requirement by using GA
optimization.
5. METHODOLOGY
The antenna array element arranged in linear
manner in both experiments. By using GA, antenna
element spacing and feed current amplitudes is
optimized so that we can have reduced the SLL and
nulls in the desired direction and then compare the
both.
In the 1st experiment we try to obtain the desired
radiation pattern by optimizing the element spacing
while keeping feed current amplitudes equal to
unity and feed current phase is kept zero.
In the 2nd experiment we optimizing the feed
current amplitudes while keeping the feed current
phase is equal to zero and element spacing is as for
the results obtained in the 1st experiment for getting
the desired radiation pattern.
The results are shown in figures 1 & 2 and tables 1
& 2.
6. RESULT AND DISCUSSION
Figure: 1 shows the radiation pattern for optimized
element spacing of linear antenna array by using
GA optimization technique while keeping feed
current amplitudes equal to unity and current phase
equal to zero. Optimized values of element spacing
obtained to have desired radiation pattern are
shown in figure 1. After optimizing the element
spacing, figure 2 shows the radiation pattern for
optimized feed current amplitudes by keeping the
feed current phase zero and element spacing as
obtained in the 1st experiment. Comparison of the
results shown that the radiation pattern obtained
using experiment 2 is better than that obtained
using experiment 1. It shows that optimizing two or
more input parameters improves the results.
Nulls Position
In Degrees
81°
99°
Experiment 1
-22.0879 dB
-20.5849 dB
Experiment 2
-29.4179 dB
-26.0169 dB
Figure: 1 Optimized Radiation Pattern for
Element Spacing with Reduced Side Lobe Level
of -14.23 dB for N=16 Elements.
Figure: 2. Optimized Radiation Pattern for Feed
current amplitudes with Reduced Side Lobe
Level of -20.56 dB for N=16 Elements.
𝒅𝒏
Element Spacing
𝒘𝒏
Feed current amplitudes
𝒅𝟏
0.4094
𝒘𝟏
0.7796
𝒅𝟐
1.3137
𝒘𝟐
0.6844
𝒅𝟑
2.3107
𝒘𝟑
0.6007
𝒅𝟒
3.3059
𝒅𝟓
𝒘𝟒
0.7432
4.3010
𝒅𝟔
5.3000
𝒘𝟓
0.6208
𝒅𝟕
6.3000
𝒘𝟔
0.6358
𝒅𝟖
7.3000
𝒘𝟕
0.6224
𝒅𝟗
8.3000
𝒘𝟖
0.6265
𝒅𝟏𝟎
9.3000
𝒘𝟗
0.6114
𝒅𝟏𝟏
10.3000
𝒘𝟏𝟎
0.4971
𝒅𝟏𝟐
11.3000
12.3625
𝒘𝟏𝟏
0.4913
𝒅𝟏𝟑
𝒅𝟏𝟒
13.3107
𝒘𝟏𝟐
0.4863
𝒅𝟏𝟓
14.4494
𝒘𝟏𝟑
0.4498
𝒅𝟏𝟔
15.6789
𝒘𝟏𝟒
0.3742
𝒘𝟏𝟓
0.3083
𝒘𝟏𝟔
0.3585
Table: 1. Optimized Element Spacing
Values for N=16 Elements.
Table: 2. Optimized Feed current amplitudes
Values for N=16 Elements.
7. CONCLUSION
We optimized the antenna array element spacing
and feed current amplitudes using GA to obtain the
desired radiation pattern and nulls in the desired
direction. When the results of experiment 1 and
experiment 2 are compared it has been found that
the reduction in SLL is better in case of experiment
2.
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