Antenna Array Synthesis with Chebyshev-Genetic
Algorithm Method
A.Hammami
R.Ghayoula
and A.Gharsallah
Unit´e de recherche:
Circuits et systmes´e lectroniques HF
三年级英语上册Facult´e des Sciences de Tunis,
Campus Universitaire Tunis EL-manar,
2092,
Tunisie
Email:***********************
Abstract—This paper prents the application of a Multiobjec-tive Optimisation Genetic Algorithm for the synthesis of linear antenna arrays.This method for antenna pattern synthesis can suppress multiple interferences by placing nulls at the directions of the interfering sources and placing the main beam in the direction of the desired signal by controlling the pha and the amplitude.To verify the performances of the method,veral illustrative examples are provided to justify the propod pha-amplitude perturbations approach bad on genetic algorithms.
Index Terms—Synthesis method,Genetic-algorithm,Chebyshev ,antenna array.
I.I NTRODUCTION
The antenna array pattern synthesis consist in steering nulls to the direction of interference and placing the main beam directed to the desired signal.In this last decade,veral an-tenna pattern synthesis methods have been developed bad on variety of popular methods[1]-[9].However,antenna pattern synthesis,generally,can be classified into three categories.The first category requires that the antenna posss nulls in the desired directions,which is known as Schelkunoff method. The cond category,the patterns are required to exhibit a desired distribution i
n the entire visible region.This is also known as beam as beam shaping,and can be achieved by using either Fourier Transform or Woodward-Lawson Methods [12].The last category requires that the patterns produced posss narrow beams and low side lobes.This can be achieved through the Taylor line-source,binomial method,SQP method [1][2],Dolph-Chebyshev method[13]and Genetic algorithm method[14]-[18].
In this paper,the technique propod is bad on genetic algorithm method to synthesis steered beams with nulls in desired direction by controlling both the amplitude and pha. The paper is organized as follows;the radiation pattern formulation is prented in ction II.The genetic algorithm method is prented in ction III.Section IV shows the Antenna array synthesis by genetic algorithm method with the simulation results.Section V,andfinally,ction VI makes conclusions.
II.R ADIATION P ATTERN F ORMULATION
2013年广东高考An antenna array is a multiple radiating elements arranged in space and interconnected to produce a directional radiation pattern.The radiation pattern of an antenna array is determined by the number of antenna elements,the type of single elements ud,their positions in space,and the amplitude and pha of the currents feed them[11].We consider a linear array (figure1)of N equispaced isotropic ant
enna elements with interelemnet spacingλ/2,(whereλis the signal wavelength). The elements are excited with current a i and with a gradient of phaφi(i=1,2,...,N)
.
Fig.1.Diagram of an amplitude and pha adaptive linear array. The array factor can be written as
F(θ)=
i=N
∑
i=1预约报名
a i e j(kx i sinθ+φi)(1)
Whereφi∈[φ1,φ1,...,φN]reprents the pha excita-tion of the i tℎelement(the antenna in the beginning is taken as reference of pha:φ1=0),x i reprents the position of the i tℎelement,k=2π/λis the wave number,θis the angle of incidence of desired signal,andλis the signal wavelength.
The problem of interference suppression in antenna array is tofinding the amplitude and the pha for excitations in order to obtain a radiation pattern with the desired t of characteristics(minimum of radiation in direction of the interfering signals and the maximum of radiation indirection of the uful signal).The mathematical model of multi-objective problem is formulated as minimizing an objective function subject to t of constraints.This problem can be written as
minimi−fθ
i (φ)
subject to fθ
i (φ)≤δj with j=m e+1,...,m
−2π≤φn≤2πwitℎn=1,...,N
(2) Where
fθ(φ)=∣n=N
inquiry是什么意思
∑
n=1
a n e j(kx n sinθ+φn)∣2(3)
fθ
i =[fθ
1
长沙环球雅思
,θ2,...,θm
e
)]T is the vector of objective func-
tions,m e is the numbers of the desired signal,θi,θj andδj are the i tℎdirections of the desired signals,the j tℎdirections of interfering signals,and the levels in the regions of the suppresd ctors respectively,and m is the number of the sampled angular direction.a i,with i=1,2,...,N,is a amplitude of each array element which isfind by-40dB Chebyshev.
III.G ENETIC A LGORITHM
The genetic algorithms(AG)are algorithms of optimization. They are techniques inspired of the evolution of the natural species.This theory is bad on the principle of evolution introduced by Charles Darwin,who principle is to create by chance a”population”of solutions.The characteristics of each solution reprent genes[10].viking
Then,one evaluates each solution.The individuals best adapted will be subjected to a succession of operators.The others will be eliminated.Rising generation obtained overall will be adapted to the problem than the preceding one.This process is repeated until the birth of a better solution.The creation of a new population is established starting from the preceding one asfigure2shows it.
1)Pha of lection:This operation makes it possible to adapt the individuals most adapted to the problem.
2)Pha of crossing:This pha relates to the pairs of individuals resulting from the pha of lection and consists of the exchange of parts of chromosomes.This exchange allows the birth of the children obtained starting from the chromosomes of the parents.
3)Pha of change:this third operator is introduced to mitigate the disappearance of information(bits)of the popu-lation.Its role consists in modifying by chance,with a certain probability,the value of a bit[3].
IV.N UMERICAL R ESULTS
To demonstrate the validity of the propod method for steering single,multiple and broad nulls with t
he impod directions by controlling the element excitations,veral com-puter simulation examples using a linear array with one
half
Fig.2.Flow chart of Genetic algorithm.
wave interelement spaced twenty isotropic elements were prented.A40−dB Chebysheff pattern for a20equispaced linear elements is ud as the initial pattern,as shown in figure3.The shape of the amplitude distribution,determined
Fig.3.The initial−40dB Tschebyscheff pattern.
by Chebyshev method at−40dB,can be ud to reduce the sidelobes of the radiation pattern.For a focud beam the amplitude distribution is always symmetric about the center of the array.The optimized excitation magnitudes elements 2
Fig.4.The element excitation required to achieve the desired pattern(20 isotropic elements spaced)given with the Tschebyscheff method. algorithm is applied in order to determine the phas of radiating elements.The phas reprent the”chromosome”that is in turn compod by”genes”.
Figure5shows the chromosome construction.The genetic algorithm parameters which are ud to determine the results are:population size 20,number of generations500,crossover probability0.8.
gene
compriφ1φ2φ3...φN−2φN−1φN
GA cℎromosome
Fig.5.Chromosome construction.
Figure6shows the radiation pattern obtained by controlling both the amplitude and pha with one impod null at −40∘.The maximum SLL and the null depth are−30dB and75dB,respectively.The radiation pattern plot infigure3-4 obtained by using genetic algorithm method demonstrates the aptitude of this technique to prescribe a wide band interference signal.Figure4shows the radiation pattern obtained by controlling both the amplitude and pha with a broad null Δθ=5centered at35.The desired nulls are deeper than 60dB.Thefigure5shows the ability of genetic algorithm method of creating null in the direction of interference at 60and a wide band interference signal centered at-45.The maximum side lobe level SLL and the null depth of thefigure 5are−28.5and−60d
B,respectively.The computed element (amplitude and pha)current excitations offigures6,7and 8are given in TABLE I.
V.C ONCLUSION
In conclusion,we have propod a method for antenna pattern synthesis bad on the genetic algorithms(AG)to form
TABLE I
C OMPUTE
D
E LEMENT C OMPLEX ARRAY WEIGHT
F OR F IGURES6,7AND
8
Synthesized excitations
Fig567
n Amplitude at-40dB pha excitation(degrees)
10.118216.43169.977692.5854
20.1660-14.6007-22.1914121.2293
30.2641-44.6794-51.9815153.0485
40.3817-77.821-84.3627179.9955
50.5121-108.840-115.6460-141.9535
60.6461-139.582-145.6933-113.9599
70.7727180.000180.0000-81.8186
80.8803157.972151.1695-45.6759
90.9587126.735120.0326-17.6211
10 1.000094.70387.629311.7420
11 1.000064.47857.954643.7583
120.958733.38725.582180.3406
130.8803 1.7712-5.7812105.9068
140.7727-29.950-35.7790136.4725
150.6461-60.375-68.5887169.0420
160.5121-92.081-98.9445180.0000
170.3817-124.24-129.9865-128.8854
180.2641-154.850-162.3380-98.3040
190.1660173.879167.9294-66.0978
200.1182142.841135.6758-31.0885 nulls at the directions of interfering signals by controlling the pha
and the amplitude of each array element.The computer simulation results show that the amplitude-pha control,using the genetic algorithms(AG)and-40dB Chebyshev amplitude, is efficient for forming single and broad nulls impod at the directions of interference and maximum main beam in the direction of the desired signal.
3
Fig.7.Pattern synthesis with a wide ctors impod around−35.
Fig.8.Pattern synthesis with null impod at60and a wide ctors impod around−45.
A CKNOWLEDGMENT
The authors would like
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