Beam reconfiguration of linear array of parallel dipoleantennas through switching with real excitationvoltage distribution

Banani Basu & G. K. Mahanti

Received: 7 April 2011 /Accepted: 3 October 2011# Institut Télécom and Springer-Verlag 2011

Abstract In this paper, authors propose a method based on themodified particle swarm optimization (PSO) for beam recon-figuration of linear array of mutually coupled parallel half-wavelength dipole antennas with real excitation voltageamplitude distribution. Two different beam pairs are generated,one pencil/pencil beam pair and another pencil/flat-top beampair in the horizontal plane. One beam is changed to anotherthrough switching while sharing a common amplitude distri-bution. Two examples are presented, one without ground planeand another in presence of ground plane. Dipoles are connectedto its feed network through a switch, so that it can be turned onor off, depending on the switch position. Beam reconfigurationis achieved by suitably turning the array elements on or offusing same voltage excitation distribution. Modified PSO isused to compute the excitation voltages as well as the switchingconfiguration for each pattern having a prefixed side lobe level.The current in the driven and parasitic elements is determinedvia induced EMF method considering the current distributionon each dipole to be sinusoidal. Proposed method efficientlysynthesizes dual-beam switching the power pattern from pencilto pencil and pencil to flat-top having same or different sidelobe levels using common excitation voltages. It calculates themaximum variation of the active impedance of driven elementsand the power losses when the radiation patterns switch fromone beam to another. The paper calculates the array directivityas the distances between antenna array and the ground panevaries. Three other state-of-the-art metaheuristics like differen-

tial evolution, gravitational search algorithm, artificial beecolony algorithm are also employed for achieving a compar-ative evaluation.

Keywords Modified particle swarm optimization .

Switching . Beam reconfiguration . Linear array . Dipoleantennas .Mutual coupling

1 Introduction

Antenna pattern reconfigurations have many emerging appli-cation in the area of wireless and satellite communication.Several methods of synthesizing reconfigurable dual-beamantenna array by varying the excitation distribution of itsradiating elements have been described in articles [1–7]. In [8],interelement spacing’s are suitably optimized to reconfigure apattern. Another recent work achieved pattern reconfigurationby performing a mechanical displacement of a parasitic arraylocated in front of an active one [9]. The method approximatesthe currents in the driven and parasitic elements via their selfand mutual impedances. However, it has been found that theparasitic array must be very near to the driven array to obtaingood results, which may complicate the implementation of themechanical system that is required to move the parasiticelements. In [10], parasitic elements were used in the designof a wide scanning phase array antenna. Use of parasitic arrayelements reduces the complexity and fitness of the feednetworks by allowing patterns to be synthesized withoutmodification of the active array feed. The switched offelements are illuminated by the active elements because ofmutual coupling. However, switching an array will reconfig-ure the power pattern at a cost of reduced directivity. Toincrease the directivity, a ground plane has been suitablyplaced in front of the array [10]. Due to the complexity in

B. Basu :G. K. Mahanti (*)Department of Electronics and Communication Engineering,National Institute of Technology,Durgapur, Indiae-mail: gautammahanti@yahoo.com

B. Basue-mail: basu_banani@yahoo.in

Ann. Telecommun.DOI 10.1007/s12243-011-0273-8

synthesis problem, analytical methods are not generally usedto design switched array. Therefore, evolutionary optimiza-tion tools such as ant colony optimization [11], geneticalgorithms [12, 13], particle swarm optimization [14–17],pattern search algorithm [18], etc. are used to synthesize anarray for different applications. Deterministic approach [19]has also been applied for thinning a planar array.

Research article [20] deals with the synthesis ofreconfigurable dual-beam array using parasitic elements.Wang et.al. [21] designed arrays by the combination ofgenetic algorithm (GA) and Fast Fourier transform (FFT).

Article [22] described a method based on IFFT andmodified particle swarm optimization for synthesis of thinnedmutually coupled parallel array. When a ground plane wasplaced behind the array an image principle [23, 24] wasapplied to evaluate the self and mutual impedances of theelements so as to obtain the modified mutual impedancematrix of the array.

In this article, we have proposed a method based onmodified particle swarm optimization for synthesis ofreconfigurable array pattern using mutually coupledcenter-fed half-wavelength parallel dipole antennas. Weintroduced two different examples: one without groundplane and another with ground plane for attaining increaseddirectivity. Both the method reconfigured the beam switch-ing the power pattern from pencil to pencil and pencil toflat-top beam having same or different side lobe levels(SLLs) using common excitation voltage. The maximumvariation of the active impedance of driven elements andpower losses are calculated as the radiation patterns switchfrom one beam to another. The work studied the effect ofdistances between antenna array and the ground pane in thearray directivity. The article applied three more population-based optimization algorithms namely differential evolu-tions (DE) [25], gravitational search algorithm (GSA) [26],artificial bee colony algorithm (ABC) [27] in one of thefour design instances to compare the simulation results.

The key difference of the paper from [20] is: excitationvoltage distribution is real in our case, which greatlysimplifies the design of feed network.

Fig. 1 Array of parallel dipoles with ground plane placed at adistance l/4 behind the array

Table 1 Voltage amplitude for the pencil/pencil beam pair and pencil/flat-top beam pair without ground plane

Category Common voltage amplitude distribution for 30 elements

Pencil/pencil pair 0.997 0.3279 0.5467 0.2554 0.4977 0.2342 0.4418 0.5427 0.5902 0.7395

0.7293 0.7421 0.8032 0.6717 0.9897 0.6898 0.9831 0.5894 0.9237 0.5487

0.8216 0.4594 0.5341 0.2826 0.3443 0.2409 0.2743 0.141 0.1128 0.2065

Pencil/flat top pair 0.1206 −0.0208 0.0354 −0.0314 0.0114 0.1634 0.133 0.2826 0.0322 0.3838

0.4758 0.0988 0.7902 0.2532 0.304 0.2098 0.7828 0.4726 0.7426 0.1142

0.7098 0.8724 0.9776 0.9996 0.6036 0.2274 0.4334 −0.6446 −0.2636 −0.3164

Fig. 2 Normalized power pattern for pencil/pencil pair withoutground plane

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2 Methodology

Switching of an array means appropriately turning off someelements in a uniformly spaced or periodic array to generatedifferent patterns with specified radiation characteristics. Inour proposed method, the positions of the elements arefixed and all the elements have two states either “on” or“off,” depending on whether the element is connected to thefeed network or not. The free space far-field pattern F(ϕ)for a linear array (Fig. 1) of half-wavelength dipoleantennas in horizontal plane (x–y plane) [22, 23] in theabsence of any ground plane is given by Eq. (1).

F fð Þ ¼ AF fð Þ � EP fð Þ ¼XNn¼1

Inej n�1ð Þkd cosϕ

" #� EP fð Þ ð1Þ

Element pattern has been assumed omni-directional inthe horizontal plane in the absence of ground plane, i.e.,EP(ϕ)=1.

Here, n=element number, j=imaginary quantity, d=interelement spacing =0.5l, k=2π/l, being the wavenumber, l=wavelength, ϕ being the azimuth angle of thefar-field point measured from x-axis, In=excitation currentamplitude of the n-th element, obtained from [I]N×1=[Z]−1N×N [V]N×1, being [Z] the mutual impedance matrix

of size N X N and [V] the voltage matrix of size N×1. Inour case, excitation voltage Vn is suitably optimized if then-th element is turned “on” and 0 if it is “off.” Theexpressions related to self-impedances Znn and mutualimpedances Zmn in the mutual impedance matrix are takenfrom [23, 24].

When a ground plane is placed at l/4 behind the array(Fig. 1) parallel to x-z plane, to concentrate the radiation inonly one hemisphere of the space, then the image principles[23] are to be applied to evaluate the self and mutualimpedances of the elements so as to obtain the modifiedmutual impedance matrix of the array. The modifiedexpression for far-field pattern in the horizontal plane inpresence of a ground plane [23] is obtained from Eq. (2).

F fð Þ ¼XNn¼1

1� e�jk2h sin f� �

Inej n�1ð Þkd cos f ð2Þ

where h = l/4=distance between ground plane and array.Computation of the radiation diagram requires evalua-

tion of the current distribution on the turn on and turn offelements. Current distribution of each element is modifieddue to the mutual coupling. The vector representing thecurrent distribution on the antenna is given by

I ¼ Z�1V ð3Þwhere V is the voltages applied to driven elements. Optimalconfiguration of the switches and the voltage excitation ofthe driven elements are appropriately computed.

Self-impedances Znn and mutual impedances Znm of Zmatrix is calculated by induced EMF method [23], whichassumes the current distribution on the dipoles to besinusoidal.

When ground plane is placed behind the array imageprinciple is applied for evaluation of the self and mutualimpedances. The ground plane generates an image of eachdipole behind it. Thus, dipoles and their images arepositioned at (xn, 0, 0) and (xn, −yn, 0) respectively withxn=(n-1)d and yn=l/2 for all n∈(1,2,….N).

To approximate this case, self impedance Znn is replacedby (Znn−Znni), where Znn

i is the mutual impedance betweenthe n-th dipole and its image, and mutual impedance Znm isreplaced by (Znm−Znmi), where Znmi is the mutual impedancebetween the n-th dipole and the image of the m-th dipole.

Fig. 3 Normalized power pattern for pencil/flat-top pair withoutground plane

Table 2 Switched off element numbers for pencil/pencil beam pair and pencil/flat top beam pair without ground plane

Category Type of beam Distribution of switching elements

Pencil/pencil pair Pencil beam 1 with -30 dB SLL 0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0

Pencil beam 2 with -25 dB SLL 0,0,0,0,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1

Pencil/flat-top pair Pencil beam with -20 dB SLL 1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0

Flat top beam with -20 dB SLL 0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,1,1,1

Ann. Telecommun.

For both the cases, modified PSO is used to compute theappropriate voltage excitation applied to the individualarray element. Switch locations are also modified accord-ingly in each case to reconfigure the beam having specifiedradiation characteristics.

Thus, the fitness function to be minimized using MPSO togenerate the reconfigurable beam array problem is as follows.

Fitness ¼ c1X pH Xp

� �þ c2Y ftH Yft� �þ c3Y

0ftH Y

0ft

� �ð4Þ

where

Xp ¼ ðSLLop � SLLd

pÞ2Yft ¼ ðSLLo

ft � SLLdftÞ2

Y0ft ¼ ðRippleoft � RippledftÞ2

where H is the Heaviside step function whose value is unitywhen calculated value of maximum side lobe level andripple level is greater than or equal to the desired value andzero elsewhere. The subscripts p and ft indicate the pencilbeam and the flat-top beam, respectively. The coefficients c1,c2, c3 determine the relative weight given to each term.

H(Xp), H(Yft), and H(Y’ ft) are Heaviside step functionsdefined as follows:

H Xp

� �;H Yft

� �;H Y

0ft

� �h i¼ 1; 1; 1½ � if Xp � 0; Yft � 0; Y

0ft � 0

0; 0; 0½ � if Xp < 0; Yft < 0; Y0ft < 0

(

ð5ÞThe lower the fitness, the more fit the array to the

desired specifications. The desired maximum ripple level offlat-top beam is not allowed to exceed 0.5 dB from the peakvalue of 0 dB.

3 Modified particle swarm optimization

Particle swarm optimization [14–17] emulates the swarmbehavior of insects, animals herding, birds flocking, andfish schooling where these swarms search for food in acollaborative manner. Each member in the swarm adapts itssearch patterns by learning from its own experience andother member’s experiences. These phenomena are studiedand mathematical models are constructed. In PSO, amember in the swarm, called a particle, represents apotential solution, which is a point in the search space.The global optimum is regarded as the location of food.Each particle has a fitness value and a velocity to adjustits flying direction according to the best experiences ofthe swarm to search for the global optimum in the D-dimensional solution space. The PSO algorithm is easy toimplement and has been empirically shown to performwell on many optimization problems. The PSO algorithmis an evolutionary algorithm capable of solving difficultmultidimensional optimization problems in various fields.Since its introduction in 1995 by Kennedy and Eberhart[11], the PSO has gained an increasing popularity as anefficient alternative to GA and SA in solving optimizationdesign problems in antenna arrays. As an evolutionaryalgorithm, the PSO algorithm depends on the socialinteraction between independent agents, here called par-ticles, during their search for the optimum solution usingthe concept of fitness.

PSO emulates the swarm behavior and the individualsrepresent points in the D-dimensional search space. Aparticle represents a potential solution. The particle swarmoptimization used in this paper is a real-coded one.

Table 3 Voltage amplitude for the pencil/pencil pair and pencil/flat top beam pair with ground plane

Category Common voltage amplitude distribution for 30 elements

Pencil/Pencil pair 0.59945 0.08231 0.088191 0.14908 0.089801 0.22064 0.23406 0.2975 0.26034 0.3662

0.41271 0.42942 0.54202 0.47944 0.61308 0.47628 0.58219 0.4485 0.5245 0.40867

0.4169 0.37917 0.35197 0.22817 0.3227 −0.0045672 0.15042 0.039013 0.016935 0.022836

Pencil/Flat top pair 0.5404 0.2446 −0.0056 0.2652 −0.06 0.1868 0.1694 0.0908 0.4306 −0.39720.2354 0.4624 −0.0902 0.7338 −0.3838 0.999 −0.0246 0.8456 0.8974 0.9786

0.2682 0.8376 −0.2846 0.5904 0.2452 0.2414 −0.226 0.3838 −0.183 0.204

Table 4 Switched off element numbers for pencil/pencil pair and pencil/flat top pair with ground plane

Category Type of beam Distribution of the switching element

Pencil/pencil pair Pencil beam 2 with -30 dB SLL 0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

Pencil beam 1 with -25 dB SLL 0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0

Pencil/flat-top pair Pencil beam with -18 dB SLL 0,1,1,1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,0,1,1,0

flat top beam with -18 dB SLL 0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0

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The steps involved in modified PSO (MPSO) are given[22] below:

Step1: Initialize positions and associated velocity of allparticles (potential solutions) in the populationrandomly in the D-dimension space.

Step2: Evaluate the fitness value of all particles.Step3: Compare the personal best (pbest) of every particle

with its current fitness value. If the current fitnessvalue is better, then assign the current fitness valueto pbest and assign the current coordinates to pbestcoordinates.

Step4: Determine the current best fitness value in thewhole population and its coordinates. If thecurrent best fitness value is better than globalbest (gbest), then assign the current best fitnessvalue to gbest and assign the current coordinates togbest coordinates.

Step5: Update velocity (Vid) and position (Xid) of the d-thdimension of the i-th particle using the followingequations:

V tid ¼ sign r1ð Þ»wðtÞ»V t�1

id

þ c1»rand1tid» pbestid � X t�1

id

� �þ c2» 1� rand1tid

� �» gbestd � X t�1

id

� � ð6Þ

where sign r1ð Þ ¼ �1; if r1 � 0:05þ1; if r1 > 0:05

�

V tid ¼ Min Vd

max;max Vdmin;V

tid

� �� � ð7Þ

X tid ¼ X t�1

id þ V tid ð8Þ

If X tid > Xd

max then

X tid ¼ X d

min þ rand2tid» X dmax � X d

min

� � ð9Þ

If X tid < Xd

max then

X tid ¼ X d

min þ rand3tid» X dmax � X d

min

� � ð10Þ

where c1, c2=acceleration constants =1.4945, w(t)=inertiaweight changed linearly from 0.9 at the start of generationto 0.4 at 0.8 times the maximum generation number andthereafter it is fixed to 0.4 for the rest of the generation,rand1,rand2, and rand3 are uniform random numbersbetween 0 and 1, t is the current generation number.

In the proposed modified PSO, velocity-clipping tech-nique is applied with time-varying maximum velocity,which decreases linearly from Vd

max to 0.1 Vdmax over the

full range of search, because as the particles approach theoptimal result it is preferred to have them move with lowervelocities.

Eqs. 7, 9, and 10 have been introduced to clamp thevelocity and position along each dimension withinVdmax;X

tid

� �to Vd

min;Xtid

� �value if they try to cross the

desired domain of interest. These clipping techniques aresometimes necessary to prevent particles from explosion.The maximum velocity is set to half of the upper limit ofthe dynamic range of the search (Vd

max= 0.5Xdmax) and the

minimum velocity is set to −0.5Xdmax.

Table 5 Desired and obtained results without ground plane

Design parameters Pencil/pencil pair without ground plane Pencil/flat-top pair without ground plane

Pencil2 Pencil1 Pencil Flat-top

Desired Obtained Desired Obtained Desired Obtained Desired Obtained

Side lobe level in dB −25.00 −25.00 −30.00 −30.00 −20.00 −20.04 −20.00 −19.10Ripple in dB NA NA NA NA NA NA 0.50 0.64

Table 6 Desired and obtained results with ground plane

Design parameters Pencil/pencil pair with ground plane Pencil/flat top pair with ground plane

Pencil1 Pencil2 Pencil Flat-top

Desired Obtained Desired Obtained Desired Obtained Desired Obtained

Side lobe level in dB −25.00 −25.002 −30.00 −30.00 −18.00 −17.80 −18.00 −17.70Ripple in dB NA NA NA NA NA NA 0.50 0.80

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Step6: Repeat steps 2–5 until a stop criterion is satisfied;in our case, it is stopped when there is no furtherupdate of best fitness value for 150 generation.

4 Results

In the first example, we consider a linear array of 30parallel half-wavelength center-fed thin dipole antennas ofradius 0.005l uniformly spaced l/2 apart along x-axis in theabsence of ground plane.

Two cases have been studied under this example. In thefirst case, the excitation voltage distribution is calculated togenerate pencil/pencil beam pair. Switching configurationsare modified to reconfigure the beam at different SLLs.

In the second case, a different set of values of excitationvoltages are calculated. Switching configurations aremodified to reconfigure the beam from pencil to flat-topat same SLL.

Excitation voltage amplitudes are chosen to lie between−1 and +1 for pencil/flat-top pair and between 0 and 1 forpencil/pencil pair for all the cases as listed in Table 1.Figures 2 and 3 show normalized power pattern for pencil/pencil pair and pencil/flat-top pair without ground plane,respectively.

The details of switching elements (on=1 and off=0) forobtaining dual beam in each case are shown in Table 2. Inthe second example, we consider the same array with aground plane placed at a distance l/4 behind the arrayparallel to x–z plane.

Fig. 4 Normalized power pattern for pencil/pencil pair withground plane

Fig. 5 Normalized power pattern for pencil/flat-top pair withground plane

Fig. 6 Directivity versus distance between the array and groundplane

Table 7 Desired and obtained results with ground plane usingdifferent optimization algorithms

Pencil beam Flat top beam

Algorithms SLL SLL Ripple

Desired Obtained Desired Obtained Desired Obtained

DE −18 −18.85 −18 −17.22 0.5 0.88

GSA −18 −18.61 −18 −17.53 0.5 0.99

ABC −18 −18.51 −18 −18.17 0.5 0.89

Ann. Telecommun.

Two cases have been studied like before. In the firstcase, excitation voltage distributions are calculated togenerate dual pencil beam patterns. Switching configura-tions are modified in each case to reconfigure the beams atdifferent SLLs using the same excitation.

In the second case, we calculate a different set of valuesof excitation voltages. Switching configurations are modi-fied to reconfigure the beams from pencil to flat-top usingthe same excitation voltages (Table 3).

The details of switching elements (on=1 and off=0) forboth the cases are shown in Table 4. Desired and obtainedresults of proposed reconfigurable array without and withground plane are shown in Tables 5 and 6, respectively.Figures 4 and 5 show normalized power pattern for pencil/pencil pair and pencil/flat-top pair with ground plane,respectively.

In the example of pencil-flat beam pair without groundplane the maximum variation of real and imaginary parts ofactive impedances of the antenna, when it switches betweenpatterns [28], is found out to be 3.47 and 63.413 Ω,

respectively. Since the flat-topped beam is generated byswitching off many elements, its power is 1.19 dB less thanthe power of the pencil beam [29].

In the example of pencil flat beam pair with groundplane the maximum variation of real and imaginary parts ofactive impedances of the antenna, when it switches betweenpatterns, is found to be 18.38Ω and 7.55Ω respectively. Thepower of flat-topped beam is 5.35 dB less than that of thepencil beam.

The article draws a tradeoff curve between directivityand the height of the linear array above the ground plane.Figure 6. shows that the peak directivities are separatedapproximately by an interval of l/2. For h=0, the arrayelements become shortened and does not radiate.

In the aforesaid analysis, we consider the diameter ofeach dipole to be 0.01l. Current distribution on each dipoleis assumed to be sinusoidal. To obtain the simulation resultsin the four instances presented in the paper, PSO is run for1,000 generations with a particle size of 60. Modificationintroduced in PSO makes it an outstanding candidate in the

Table 8 Amplitude and switching distributions using DE, GSA and ABC

Algorithms Design of pencil and flat top beam pair with ground plane

DE Excitation voltage amp. 0.00034,0.08906,0.21736,0.07512,0.39476,−0.15436,−0.06896,0.02824,0.14534,−0.2243,−0.47698,0.59568,0.27626,0.99964,0.93394,0.79388,0.62556,0.71,0.6446,0.64224,0.3087,0.23418,0.32478,0.26016,−0.12588,0.08264,0.09582,−0.11578,−0.27476,0.30242

Switch combinations Pencil beam Flat top beam

1,1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0 1,1,1,1,0,1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0

GSA Excitation voltage amp. 0.08796,0.07352,−0.01318,−0.13466,0.02404,−0.16796,0.10964,0.03366,−0.0272,−0.26716,0.03216,0.14744,−0.0026,−0.2688,−0.58776,−0.46072,0.23278,0.6374,0.93434,0.83104,0.34668,0.69452,0.24812,0.66008,0.39688,0.25148,0.25486,0.24118,0.21512,0.09466;

Switch combinations Pencil beam Flat top beam

0,0,1,0,1,0,0,0,1,0,1,1,0,0,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1 1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,1,1,1,1,0,1,0,1,1,0,0,0,1

ABC Excitation voltage amp. 0.10646,0.32266,−0.21652,−0.78302,−0.97557,−0.91308,0.21382,0.84052,0.83382,0.64896,0.41944,0.38372,0.55676,0.39928,0.51986,0.38594,0.18664,0.22594,0.21112,0.24908,0.10764,0.13216,−0.34144,0.23434,0.04208,0.1059,0.05172,0.07348,0.13842,0.02904;

Switch combinations Pencil beam Flat top beam

1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1 1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,1,0,1,0,1,1,1,0,1,0,0

Table 9 Parametric setup of different algorithms

DE GSA ABC

Parameter Value Parameter Value Parameter ValuePopulation size 60 Population size 60 Swarm size 30

F 0.8 G0 50 Limit 25

Cr 0.9 α 20

Max cycle 1,000 Max cycle 1,000 Max cycle 2,000

Total function evaluations 60,000 Total function evaluations 60,000 Total function evaluations 60,000

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evolutionary optimization algorithms family. However, weapplied three other state-of-the-art metaheuristics like DE,GSA, ABC [25–27] in an attempt to make a faircomparison among the algorithms regarding their perform-ances. The algorithms are allowed to run for a similarnumber of function evaluation (as used in MPSO) andapplied on a single instantiation of the design problem ofgeneration of pencil-flat beam pair with ground plane.Comparative results obtained are shown in Table 7. Table 8presents the amplitude and switching distributions in eachcase using DE, GSA, and ABC.

The parameters for DE, PSO, and GA are set followingthe guidelines provided in [25–27]. The parametric setupfor all the algorithms are shown in Table 9. Figures 7, 8,and 9 present the corresponding radiation patterns usingDE, GSA, and ABC.

5 Conclusions

This paper presents a technique based on modified particleswarm optimization for reconfiguring the beam using lineararray of parallel half-wavelength dipole antennas with orwithout ground plane. Both the cases modify the switchingconfiguration to generate multiple beams having differentradiation characteristics using common excitation voltages.Thus, the array switches the pattern between differentpencil beams or from pencil to flat top beam. The methodhas application in real-time reconfiguration problems.

The method used real common excitation voltages forgenerating multiple beams through switching. This greatlysimplifies the design of feed network. Moreover inclusionof induced currents on turned off elements allows imped-

ance matching without introducing any modification inactive array feed.

In the optimization problem, the maximum variation ofthe active impedance of driven elements when the radiationpatterns switch from one beam to another for both the casesis calculated. It is noticed that the power of flat-top beam issignificantly less than that of the pencil beam.

The work also studies the effect of distances betweenantenna array and the ground pane in the array directivity.We use DE, GSA and ABC along with PSO in order topresent a comparative analysis in one of the four designinstances.

Realistic antenna with mutual coupling is used in thesimulation in place of isotropic element considering the

Fig. 7 Normalized power pattern for pencil/flat-top pair with groundplane using DE

Fig. 8 Normalized power pattern for pencil/flat-top pair with groundplane using GSA

Fig. 9 Normalized power pattern for pencil/flat-top pair with groundplane using ABC

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practical scenario. The results show the effectiveness of theproposed method applied in the present study.

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