International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 332-336 September 2013 www.ijsret.org ISSN 2278 – 0882

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BROADSIDE LINEAR ANTENNA ARRAY SYNTHESIS USINGGENETIC ALGORITHM

Shraddha ShrivastavaAssistant professor, Electronics and communication department

Abstract- This paper is based on optimization ofbroadside linear antenna array. In this paperoptimum value of weights of each antenna element isdetermined which produces radiation pattern withminimum side lobe level .In this work real codedGenetic algorithm is used. MATLAB is used as aplatform. Adaptive feasible mutation rate is usedwhich enables search in broader space alongrandomly generated directions to produce newgenerations. This improves the performance greatlyto achieve the maximum reduction in side lobe levelwith minimum function calls.

Keywords- Side lobe level, Genetic algorithm, broadsidelinear antenna array, Array factor

I. INTRODUCTION

In many communication systems, point to pointcommunication is used, for this highly directive beam ofradiation is required. By arranging several dipoles in theform of an array or other antenna elements this can beachieved. Consider a linear array of n isotropic elementsof equal amplitude and separated by distance d. The totalfield E at a far field point P in the given direction φ isgiven by,

….1

Where Ψ is the total phase difference of the fields fromadjacent sources. It is given by;

One method to achieve a highly directional beam is touse adaptive beamforming.Adaptive beam forming is an

adaptive signal processing technique in which an arrayof antenna is exploited to achieve maximum reception ina look direction in which the signal of interest is present,while signal of same frequency from other directionswhich are not desired (signal of not interest) are rejected.

The characteristics of the antenna array can be controlledby the geometry of the element and array excitation. Butside lobe reduction in the radiation pattern [28],[31]should be performed to avoid degradation of total powerefficiency and the interference suppression [2],[9] mustbe done to improve the Signal to noise plus interferenceratio (SINR). Side lobe reduction and interferencesuppression can be obtained using the followingtechniques: 1) amplitude only control 2) phase onlycontrol 3) position only control and 4) complex weights(both amplitude and phase control).

The process of choosing the antenna parameters toobtain desired radiation characteristics, such as thespecific position of the nulls, the desired sidelobe level[4] and beam width of antenna pattern is known aspattern synthesis. Analytical studies by Stone whoproposed binominal distribution, Dolph the Dolph-Chebyshev amplitude distribution , Taylor, Elliot,Villeneuve Hansen and Woodyard, Bayliss laid thestrong foundation on antenna array synthesis[20]-[24].Today a lot of research on antenna array [2] – [12], isbeing carried out using various optimization techniquesto solve electromagnetic problems due to theirrobustness and easy adaptivity. One among them isGenetic algorithm [13] . R.L.Haupt has done muchresearch on electromagnetics and antenna arrays usingGenetic Algorithm [13]-[22].

In this paper, it is assumed that the array is uniform,where all the antenna elements are identical and equallyspaced. The design criterion considered here is tominimize the sidelobe level [7] at a fixed main beamwidth. Hence the synthesis problem is, finding the

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 332-336 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

weights that are optimum to provide the radiation patternwith maximum reduction in the sidelobe level.

II.GENETIC ALGORITHM

The genetic algorithm is a method for solving bothconstrained and unconstrained optimization problemsthat is based on natural selection, the process that drivesbiological evolution. The genetic algorithm repeatedlymodifies a population of individual solutions. At eachstep, the genetic algorithm selects individuals at randomfrom the current population to be parents and uses themto produce the children for the next generation. Oversuccessive generations, the population "evolves" towardan optimal solution. GA’s can be used when objectivefunction is discontinuous, non differentiable, stochastic,or highly nonlinear. The flowchart is shown in Figure 1.

In this paper, performance improvement is analyzed inorder to obtain a desired pattern of linear antenna arrayusing GA. Fixed mutation rate approach is used inclassical GA.In this paper, adaptive feasible mutation rate is used,which shows improvement in performance throughoutthe evolution.The genetic algorithm uses three main types of rules ateach step to create the next generation from the currentpopulation:

Selection rules select the individuals, calledparents, that contribute to the population at thenext generation.

Crossover rules combine two parents to formchildren for the next generation.

Mutation rules apply random changes toindividual parents to form children.

Two more parameters are involved in GA i.e. populationand number of generations.They are defined as given below

• SelectionEvaluation of the fitness criterion to choose

which individuals from a population will go on toreproduce. Some general methods used are RouletteWheel Selection andTournament Selection

• CrossoverThis is an exchange of substrings denoting

chromosomes, for an optimization problem. It may be asinglepoint cross over , two point cross over.

• MutationMutation allows the population to change by

introduction of random characteristics. Without mutationthe population would quickly converge to a solution thatmay be or may not be correct. Mutation randomlychooses alleles to alter with a probability Pmut.

• PopulationThe number of chromosomes considered in one

generation

• Number of generationsThe maximum number of generations that the

genetic algorithm can evolve into, before terminating.

NO

YES

Fig.1 Flowchart of Genetic Algorithm

INITIALPOPULATION

EVALUATEFITNESS OF

POPULATION

SELECTION

CROSS OVER(MATING)

MUTATION

EVALUATEFITNESS OF

POPULATION

CONVERGED

END

BEGIN

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 332-336 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

III. UNIFORM LINEAR ANTENNAARRAY

Fig. 2 Linear antenna array

In linear antenna array, all the antenna elements arearranged in a single line with equal spacing betweenthem. In Fig 2 it is shown that the antenna elements arearranged with uniformly spacing, in a straight line alongthe y-axis, and N is the total number of elements in theantenna array with the physical separation distance as d,and the wave number of the carrier signal is k =2π/λ.When kd is equal to π (or d= λ/2)

The phase shift between the elements experienced bythe plane wave is kdcosθ. Weights can be applied to theindividual antenna signals before the array factor (AF) isformed to control the direction of the main beam.Thiscorrespond to a multiple-input-single-output (MISO)system. The total AF is just the sum of the individualsignals, given by the

N NAF = ∑ E n = ∑ e jK

n .................................. (2)

n = 1 n = 1

Where En = e jKn and K= (nkd cosθ + βn) is the phasedifference. βn is the phase angle. Only the magnitude ofthe AF in any direction is important, the absolute phasehas no bearing on the transmitted or received signal.Therefore, only the relative phases of the individualantenna signals are important in calculating the AF.

IV. SIMULATION RESULTS

Consider an array of antenna consisting of N number ofelements. It is assumed that the antenna elements aresymmetric about the center of the linear array as shownin fig 3.

Fig.3 Uniform linear antenna array

The far field array factor of this array with an evennumber of isotropic elements (2N) can be expressed as

NAF (θ) = 2 ∑ a n cos (a п/λ d n sin θ) …………(2)

n-1

Where an is amplitude of amplitude of nth element, θ isthe angle from broadside and d n is the distance betweenposition of nth element and array center .The mainobjective of this work is to find an appropriate set ofrequired element weight that gives maximum side lobelevel reduction and narrow main beam width. To find aset of values which produces the array pattern, thealgorithm is used to minimize fitness function.The fitness function associated with this array is themaximum Side Lobe Level of its associated radiationfield pattern to be minimized. The fitness function usedfor this work is given by

Fitness =F1 = 20*log10 (F / max (F))F = abs (H)

Where H is normalized field strength..The antenna model consists of N elements and equallyspacedwith d =0.5λ along the y-axis. The number of elementsare changed while the array geometry and spacingbetween the elements are constant. A continuous GAwith a population size 20 and an adaptive feasiblemutation rate is run for a total of 100 generations usingMATLAB and the best result was found for eachiteration. The cost function is the minimum side lobelevel for the antenna pattern. Simulation is done for N =24 elements. Table 1 shows the amplitude excitations forN=24 elements.

Using adaptive feasible mutation rate better results areobtained as shown in table 2 as compared to resultsobtained by fixed mutation as in [1]..

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V. CONCLUSION

In this paper Genetic algorithm Solver in Optimizationtoolbox of MATLAB is used to obtain maximumreduction in side lobe level relative to the main beam onboth sides of 0°. This paper compares the results of newdesign used in this paper with the design of antennaarray in [1],and it is found that the changes made in thisdesign gives better values of antenna elements weightsas compared to previous work. Adaptive feasiblemutation with single point crossover showed theperformance improvement by reducing the side lobelevel below -20dB in most of the cases.The best sidelobelevel obtained is -26.1 dB for N = 24 which is -14.97 dBin [1]. As a compromise in directivity is observed thework can be extended to improve the directivity alsowhile reducing side lobe level, same experiment can bedone for array with large number of elements ascompared to this.Fig 4 shows the optimized radiationpattern and fig 5 shows the polar plot for N = 24elements.

Fig. 4 Optimized radiation pattern with reduced sidelobe level of -26.1 Db for N= 24 elements

Fig. 5 Radiation pattern for N= 24 elements

Table 1: Amplitudes excitations for N=24 elements

Wn AmplitudeExcitation

W1 0.0637W2 0.1278W3 0.7122W4 0.2699W5 0.6079W6 0.8534W7 0.5249W8 0.9204W9 0.4460W10 0.8140W11 0.5389W12 0.7493W13 0.4959W14 0.5363W15 0.4957W16 0.3957W17 0.4649W18 0.3561W19 0.2090W20 0.3284W21 0.0800W22 0.3627W23 0.1764W24 0.1583

Fig. 6 Mean and best fitness for N = 24 elements.

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International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 332-336 September 2013 www.ijsret.org ISSN 2278 – 0882

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