[ieee 2011 mediterranean microwave symposium (mms) - yasmine hammamet, tunisia...

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Phased Uniform Linear Antenna Array Synthesis using Genetic Algorithm

M.A.El Cafsi, R.Ghayoula, H.Trabelsi and A.Gharsallah Unit of Research in High Frequency Electronic Circuits and Systems,

Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis El Manar University Campus Universitaire Tunis – EL Manar 2092 Tunis, Tunisia

aymenelcafsi@gmail.com

Abstract—This paper describes a new method for adaptive beamforming for a phased antenna arrays using genetic algorithm. The algorithm can determinate the values of phase excitation for each antenna to steer the main beam in specific direction. Various results are presented with -10 dB side lobes level. To improve these results, a Chebyshev model was proposed in order to decrease the level of side lobes which consists in amplitude synthesis.

Keywords-component: Adaptive beamforming, Phased antenna arrays, Genetic Algorithm, Chebyshev model, Side lobes, Amplitude synthesis.

I. INTRODUCTION

Smart antenna and specifically adaptive antenna [1] has a great interest in many scientific fields such as telecommunication, medicine, military and astronomy thank to their precision.

In telecommunication field, the principle of adaptive antenna consists to detect the position of the user and send to this location the service [2].

Adaptive antenna uses an antenna array which are a group of elementary antenna s in space that can be on any form (linear, circular and planar). This grouping of radiating elements can combine their capacity to increase the gain in a particular direction and to control the phase gradient applied to the array.

In general, the synthesis of antenna array consists to determine the law of excitation using numerical methods [3] [4] [5] in order to optimize the radiation pattern [6]. Genetic algorithm [7-10] is one of these methods which are based on the principle of evolution of species in their environments.

Electromagnetic problems are often non linear problems with many local minima and genetic algorithm can solve this type of problem by exploiting the solution space to provide an infinity of global solutions randomly.

We start by giving the problem formulation where a mathematical model of uniform linear array was presented.

In section3, some results were showed in two and three dimension and the section 4 will be the conclusion.

II. PROBLEM FORMULATION

The mathematical model of the factor array for an uniform linear array of point sources element patterns lying along the x axis is given by:

0 n

Nj( knd sin( ) )

n 0AF( ) e θ ϕθ +

=

=∑ (1)

Where: N: Number of elements.

2k πλ

= : Number of wave.

d : Spacing between two successive elements.

0θ : Pointing angle of the main beam.

ϕ : Phase excitation.

The first antenna is chosen to be the origin of phase (φ0 = 0°) and amplitude excitation is fixed and equals to 1 for all antennas.

So, the factor array will be:

0 n

N 1j( kdn sin( ) )

n 1AF( ) 1 e θ ϕθ

−+

=

= +∑ (2)

We can see the expression of the factor array as a geometric suite with a reason 0jkd sin( )q e θ= and 0 1q = .

According to the criteria of Cauchy, we can write the expression of geometric suite as a sum:

N 11 qS

1 q

+−=−

(3)

We had idea to use this sum as an objective function for genetic algorithm to find the phase weights to steer the main beam in the desired direction as follows:

2

N 1

nj

n 1

SfunIm( e )ϕ

−

==∑ (4)

Where

0jknd sin( )nn 0q cos( ) e θθ= .

The optimization process of a genetic algorithm is as follows:

Fig.1. Genetic Algorithm.

The algorithm begins with a randomly initial population by evaluate individuals computing their fitness function.

The choice of population diversity is one of important factors which determinate the performance of the algorithm.

Increasing the population size permits to search more point in solution space, reduces the risk of falling into a local minimum and obtain a better global solution but the time of search increases.

(a)

(b)

Fig.2 Performance of algorithm

(a) Evaluation of fitness function

(b) Average distance between Individuals

If the stop condition is satisfied, we have the result otherwise the loop generation is triggered according to Fig. 1.

The loop generation consists of three steps:

- Selection:

In this step, the selection is inspired by the natural selection of individuals.

The most suitable resist and less adapted are eliminated.

Selection tournament is the function used to choose the best parent depending on their size for the next generation.

- Crossover

The second step involves the formation of a new generation of individuals selected from the previous steps.

Crossover operation is based on the principal of exchange made between two chromosomes.

- Mutation:

The last step allows having new genes not yet exploited and it permits to find a new population using Gaussian distribution.

Mutation’s operation helps algorithm to generate individuals with a best fitness function and to increase the space of the search.

The main disadvantage of algorithm consists to provide a random solution: a radiation pattern on any form without the desired steering of the main lobe and some times with a high side lobes levels.

So, we should simulate the algorithm many times at the end to find an acceptable radiation pattern with a lower side lobes levels (-10 dB) and a steered main lobe.

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III. RESULTS We simulated an uniform linear antenna arrays consisting of 10 radiating elements using optimization toolbox of Matlab software [11] and the following table presents some pointing of the main beam:

θ0=20° θ0=30° θ0=40° φ1 0° 0° 0° φ 2 12° 188° -96° φ 3 -86° 75° 73° φ 4 -106° -302° -27° φ 5 -174° -53° 235° φ 6 109° 224° 147° φ 7 46° 54° 355° φ 8 -36° 18° 247° φ 9 -87° -148° 223° φ 10 209° 180° 1°

TABLE I – Phase weights founded for different steering using Genetic Algorithm.

Figs 3, 4 and 5 show a main beam steered respectably at 20, 30 and 40 degree with a -10 dB side lobes level.

Fig.3 Main lobe steered at 20 degree.

Fig.4 Main lobe steered at 30 degree.

Fig.5 Main lobe steered at 40 degree.

We note that side lobes or ambiguity lobes have an important level which can decrease the quality of the signal and must be the minimum as possible.

To improve these results, we added amplitude weights of the Chebyshev’s model [12] for different side lobe level respectively -20, -30 and -40 dB according to Figures below.

Fig.6 Main lobe steered at 20 degree with lower side lobes.

Fig.7 Main lobe steered at 40 degree with lower side lobes.

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Chebyshev’s weights for -40 dB side lobes level have improved most the quality of the pattern radiation according to Figs 6 and 7.

For example, the level of side lobes for a steered main beam at 20 degree has decreased from about -13 dB to slightly above -20 dB.

On the other side, for a beam forming at 40 degree, the level had not improved very well but we have an improvement in the steering by widening the main beam.

To validate the results founded with the software Matlab, a uniform linear antenna array [13] was simulated which the elementary antenna is a simple patch with a λ/4’s transmission line transformer using CST MICROWAVE STUDIO (CST MWS) [14] and showed in Fig 8.

The Length (L) and width (W) of patch is about 41.08 mm designed on substrate with rε = 2.2 permittivity and the thikness of substrate h is equal to1.57 mm.

The λ/4’s transmission has a length of 24.05mm and a width of 0.72 mm.

About the 50 Ω transmission, it has a 15mm of length and a 4.84 mm of width.

Fig8. Uniform linear antenna array.

The resonant frequency of the structure is 2.45 GHz working in the ISM Band (Industrial Scientist Medical band) according with Fig 9.

Fig.9 Return-Loss (S11) dB.

(a)

(b)

Fig.10 Far field of the uniform antenna array

(a) Without amplitude weights

(b) With amplitude weights.

Fig 10 presents the Far Field of the array without and within amplitude weights.

We introduce the amplitude and phase weights founded respectively using Chebychev’s model for -40 dB side lobes levels and Genetic algorithm in CST MW studio software and figs 11 and 12 show some steering.

(a)

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(b)

Fig.11 Beam forming at 20 degree

(a) Without amplitude weights.

(b) With amplitude weights.

(a)

(b)

Fig.12 Beam forming at 40 degree

(a) Without amplitude weights

(b) With amplitude weights

We find a good a concordance between the results found by the two software Matlab (2D) and CST Studio MW (3D).

IV. CONCLUSION

A Uniform phased antenna array synthesis has been proposed and simulated using the Genetic algorithm.

We find a different steered main beam ranging from 20 degree to 40 degree (if you add excitement to each phase a minus sign, we can find a beam forming in reverse way).

The addition of amplitude weights of Chebyshev’s model (for a side lobes level equals to -40 dB) has reduced the level of the lobes of ambiguities in a remarkable way and showed in 2 and 3 Dimension.

REFERENCES

[1] R. Monzingo, T.Miller, “Introduction to Adaptive Arrays”, Wiley & Sons, New York, 1980.

[2] H. Lebret and S.Boyd, “Antenna Array Pattern Synthesis via Convex Optimization”, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 3, MARCH 1997.

[3] W. Wei-Chung, F. Yan and E. Atef.Z, “Linear Antenna Array Synthesis Using Taguchi’s Method: A Novel Optimization Technique in Electromagnetics“, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 3, MARCH 2007.

[4] K. Guney and M. Onay, “Amplitude-Only Pattern Nulling Of Linear Antenna Arrays With The Use Of Bees Algorithm”, Progress In Electromagnetics Research, PIER 70, 21-36, 2007;

[5] K. Guney and M. Onayv, “Synthesis of thinned linear antenna arrays using bees algorithm”, Microwave and Optical Technology Letters, VOL. 53, 795-799, April 2011.

[6] F.B.Gross, “Smart Antennas for Wireless Communication with Matlab”, McGraw-Hill, 2005.

[7] R.L.Haupt, D.H. Werner, “Genetic algorithms in electromagnetic”, Wiley-Interscience, 2007.

[8] R.L. Haupt, “Phase-Only Adaptive Nulling with a Genetic Algorithm”, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL 45, NO 6, JUNE 1997.

[9] Y.Wang, S.Gao, Hang Yu and Z.Tang “Synthesis of Antenna array by Complex-Valued Genetic Algorithm”, International Journal of Computer Science and Network Security, VOL.11 No.1, January 2011.

[10] G. K. Mahanti and N. Pathak, “Synthesis Of Thinned Linear Antenna Arrays With Fixed Sidelobe Level Using Real-Coded Genetic Algorithm”, Progress In Electromagnetics Research, PIER 75, 319-328, 2007.

[11] “Genetic algorithm and direct search toolbox user’s guide”, www.mathworks.com.

[12] R.Ghayoula, A.Gharsallah, N.Fadlallah and M.Rammal “Synthèse de diagramme de rayonnement d’un réseau d’antennes linéaires par la méthode de Dolph-Tchebycheff”,

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4thInternational Conference: Sciences of Electronic, technologics of Information and Telecommunications, March 25-29, 2007-Tunisia.

[13] www.emtalk.com/mwt_mpa.htm.

[14] www.cst.com/Content/Products/MWS/Overview.aspx.