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Neural Network Approach for Synthesis of Uniform

Linear Antenna Arrays

V. V. Vidyadhara Raju1, .!admana"ha Raju#, !.Akhendra kumar$1,# %epartment of &lectronics and 'ommunication &n(ineerin(

Shri Vishnu &n(ineerin( 'olle(e )or *omen+ hima-aram, ndia1-idyadhar1/0(mail.com, #mudunuri$0(mail.com, $akhendra.p0(mail.com

Abstract In this paper, the application of back-propagation and weighted LMS algorithms

are used for the synthesis of antenna arrays. The neural networks help in the modelling of

antenna arrays by acting on the geometric and radio-electric parameters. The main

synthesis problem is to find the weights of the niform Linear !ntenna array elements that

are optimum to pro"ide the radiation pattern with ma#imum reduction in the side lobe

le"el. This techni$ue is used to pro"e its effecti"eness in impro"ing the performance of the

antenna array. The neural network not only allows in establishing important analytical

e$uations for the synthesis of antenna array, but also pro"ides a great fle#ibility between the

system parameters in input and output which makes the synthesis possible due to the

e#plicit relation gi"en by them. . Thus !%% is able to generate effecti"e results of synthesis

compared to that of other classical approaches such as &ourier series, 'olph-chebyche" ()*etc.

Index Terms !%%, ML+,&%, SLL, +/

1. N2R3%U'23N

n modern communication systems there is a need to desi(n an antenna array which meets the desiredradiation characteristics. Antenna arrays are comple4 radiatin( structures whose radiation pattern can "e

considered as the interference "etween electro5ma(netic fields of each radiatin( element. 2he radiationschemes of the Antenna arrays are desi(ned either "y selectin( the appropriate inter element spacin(, or "ythe modification of the amplitudes and phase of the e4citations applied to the respecti-e elements in the array.2o achie-e the desired side5lo"e le-el6SLL7 or half5power "eamwidth 68!*7 or "oth, there is need to sol-ethe synthesis pro"lem which consists of findin( thee4citation distri"ution of the antenna elements or inter5elementspacin( "etween different elements. 2he consideration of analysis pro"lem lies in the determination

of theradiation pattern from a (i-en e4citation or (eometrically usin( numerical tools and the synthesispro"lem can "esol-ed as the in-erse pro"lem of the analysis.Neural network has the a"ility to pro-ide successful solutions tomany comple4 pro"lems which acts as amassi-ely parallel distri"utedstructure. Application of neural networksin the field of antenna arrays helps toreduce the comple4ity of the model "y offerin( an efficient way toincorporate with the real radiatin(properties and the couplin(effects "etween the antenna elements in the synthesisprocess whereas other &

models arecomputati-ely intensi-e and time5consumin(.

Elsevier, 2014

2he de-eloped neural models (i-e instantaneous responses due to performin( only "asicmathematicaloperations and calculatin( elementarymathematic functions.2he most importantcharacteristic of neuralmodels is their (enerali9ationcapa"ility. 2o estimate the separation of antenna array elements, ANNs are "e

Proc. of Int. Conf. on Control, Communication and Power Engineering, CCPE

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trained in order to o"tain desired radiation pattern, 8alf5power "eam width and side lo"e le-els resultin(from-arious space distri"utions of antenna elements.

A neural network model is de-eloped"y definin( the input and output -aria"les of the structure. 2he(enerated data are separated into two (roups :trainin( data and test data. Neural network is trained

usin(trainin( data. 3nce the model has reached re;uiredconditions for accuracy of predictin( outputs, it can"e used for simulation. n this paper, the model inputs are(eometrical parameters, relati-e positions ofantennaelements in a linear array, and model outputs are electricalparameters, such as side lo"e le-el.2his paper considers the application of R)N and L! for re(ular antenna array synthesis. )or (i-en -alues

of the radiation pattern we estimate the phase difference of the e4citations "etween the nei(h"ourin( antennaelements.

. LN&ARARRA an7 with e;ual inter5element spacin( d "etween the elements in

may take a simpler form. *ith the help of the au4iliary -aria"le # defined "y,# > kdBcos6C72he array factor for e-en num"er of elements can "e (i-en "y,

|AF|=2n=1

N

2

(ancos((N12 )))(2)2he array factor for odd num"er of elements can "e (i-en "y,

|AF|=a0+2n=1

N/2

(an cos((N12 )))(3)

#

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*hereaDdenotes the current of the centre element.

2he two desi(n parameters ananddoare tailored in order to o"tain the desired radiation pattern with anaccepta"le tolerance.

. AR2)'ALN&URALN&2*3RES

A (roup of processin( elements 6neurons7 constitute to form an artificial neural network FANNG.2he neurons

are (rouped and ordered in -arious layers which ha-e a network of interconnection wei(hts *j6j,1,....,L7called as synaptic wei(htsF1G. 2he input data Hj is processed with the help of acti-ation function f647.2he"asic model of a sin(le neuron is shown inF#G )i(ure #.

j=1

L

(w jxj+b )(4 )

y=f

*here" is the "ias parameter of the acti-ation function f640

)i(.# asic model of a neuron

V. UL2!L&LA

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V. RA%ALASS)UN'23NN&2*3RE6R)N7

2he R)N is a $5layer network in which the input layer hasan fan5out layer and does not in-ol-e anyprocessin( in it. 2he role of the hidden 6second7 layer is to perform the non5linear mappin( from input space

)i(.$7 "ack propa(ation learnin( rule )i(.M7 multiple layer network

to a hi(her dimensional space which yields the linear separa"le pattern.2he function of the final layer is to

perform a simple wei(hted sum to (i-e a linear outputFG and the architecture for R)N network is shown infi(ure..2he function appro4imation or matchin( the real num"er is done "y R)N network then the output o"tainedmatches the desired output. *hene-er a pattern classificationFG is re;uired a hard5limiter or si(moidfunction can "e placed on the output neurons to (i-e DO1 output -alues. 2he area which is symmetrical aroundthe radial cluster centre then the non5linear function is known as the radial5"asis function.2he most

commonly used radial5"asis function is a Paussian function

x1

x2

x3

input layer

(fan-out)

hidden layer

(weights correspond to cluster centre,

output function usually Gaussian)

output layer

(linear weighted sum)

y1

y2

)i(.7 radial "asis function network

2he &uclidean distance is the distance measured from the centre of the cluster. f, ris the distance from thecluster centre.)or each neuron in the hidden layer, the wei(hts represent the co5ordinates of the centre of the

cluster.

rj=i=1

n

(xiw ij)2

(5)

i=1

n

((x iwij)2/22)(hiddenunit) j=exp

*here 4 is the input, w is the wei(hted -ector,2he -aria"le si(ma, ,defines the width or radius of the "ell5

shape and is somethin( that has to "e determined empirically. *hen the distance from the centre of the

Paussian reaches, the output drops from 1 to D..

M

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Training:

2he wei(hts in the hidden layer in a R) network ha-e units which correspond to the -ector representation

of the centre of a cluster.2he traditional clusterin( al(orithm such as the k5means al(orithm is used to find the

wei(htsFMG. As the trainin( is unsuper-ised the num"er of clusters k, are set in ad-ance. 2he "est fit to the

clusters are founded out "y the al(orithm implemented on them. 2he initial classification is done "y choosin(the closest centre for each item of data, so all the items of data are assi(ned a class from 1 to k.

2he reclassification of data and measurement of the distance "etween the centres are repeated until the sumsof the distances aremonitored and trainin( is halted when the total distance is calculated. 2he hidden layer istrained with unsuper-ised learnin(FG and trainin( of the output layer is done "y standard (radient descenttechni;ueFQG 6Least ean S;uares al(orithm7.

V. SULA23NR&SUL2S

L! output radiation pattern+ean s;uare error performance

0 20 40 60 80 100 120 140 160 180-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

thetha(in degrees)

Arrayfactorgain(indb)

)i(.6a7 the arrayused in the simulations is an 15elements )i(.6"72he ean s;uare error performance of an L! network.

Linear array with inter5element spacin( d >@O#

2he trainin(5set e4amples included sector5width inter-als of #D,SLL inter-als of 5#D d.2he performance of the mean s;uare error for L! Network is shown in the a"o-e fi(ure. and the

e4citation coefficients at the last epoch are noted down for N>1 array elements are shown in ta"le 1.

2AL&. U!%A2&%&H'2A23N'3&))'&N2VALU&S)3RL!

S.N3 Amplitude e4citation usin(L!

1 D.DQ1$

# D.#

$ D.MD

M D.DQ D.1D1#

D.1QD

Q D.D1/

D.DM

/ D./Q

1D D.MM/M

11 D.MQ#1

1# D.MD

1$ D.#1

1M D.M11

1 D.M1

R)N output pattern+

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2he array used in the simulations is an 15elements linear array with inter5element spacin( d > @O#. 2hetrainin(5set e4amples included sector5width inter-als of #D, SLL inter-als of 5#D d are (i-en in fi( Q,

0 20 40 60 80 100 120 140 160 180-40

-35

-30

-25

-20

-15

-10

-5

0

5

theta (in radians)

gainindb

)i(.Q7 radiation pattern of linear array usin( R)N.)i(.7 performance of R) networkean s;uare error performance

2he performance of the mean s;uare error for R) Network is shown in the a"o-e fi(ure. and the e4citationcoefficients at the last epoch are shown in ta"le#.

2AL&. U!%A2&%&H'2A23N'3&))'&N2VALU&S)3RR)N

s.no Amplitude e4citation usin( R)N

1 D./$1# D.MQ$1

$ D.##$/

M D.1D#

D.//

D.

Q D.DM1#

D.#

/ D./M

1D D.Q

11 D.$D$$

1# D.$//D

1$ D./DMD

1M D./1/

1 D.MMD

'omparison of classical approach 6)ourier method7 with neural networks+2he fi(ure./ shows the comparison of the neural approach with fourier method approachF$G for an lineararray with 15elements and with inter5element spacin( d > @O#. 2he trainin(5set e4amples included sector5width inter-als of #D, SLL inter-als of5#Dd.)rom the fi(ure it can "e clearly seen that the neural network approach matches with the desired output ratherthan the classical approach.

V. '3N'LUS3N

Two dierent neural-networ architectures ha!e "een tested and their eecti!eness forarray-pattern synthesis has "een compared# The results show that the two networsexhi"it good performances matching the desired output #Thesetechni$ues can "e used

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in a !ast range of applicationsin which the networs can "e trained o%ine with suita"ledata to carry out real-time processing in order to o"tain the arrayelements& excitations#

)i(./7 comparison of neural network approach with the "asic classical approach

R&)&R&N'&S

F1G R. Sha-ed And . 2ai(, 'omparison Study 3f !attern Synthesis 2echni;ues Usin( Neural Networks,icrowa-e And

3ptical 2echnolo(y Letters O Vol. M#, No. #, Tuly #D #DDM.F#G S.8aykin, Neural Networks+ A 'omprehensi-e )oundation, !rentice 8all, New Tersey, 1///.

F$G alanis, asics of antenna and their desi(n, c(raw 8ill edition,#DD.

FMG E. 8ornik, . Stinchcom"e, And 8. *hite, ultilayer )eed forward Networks Are Uni-ersal Appro4imators,Neural Networks # 61//7, $/:$.

FG R. 8aupt, IAn ntroduction 2o Penetic Al(orithms )or &lectroma(netics,Jeeeantennas And propa(ation, 1)-#,April

1//, !p. Q51.FG L. erad, ). 2. endimerad, S. . eriah And S. A.%jennas, INeural Networks )or Synthesis And 3ptimi9ationof

Antenna Arrays,J Radioen(ineerin(, Vol. 1, No. 1,April #DDQ.

FQG R. P. Ayestarn, ). Las58erasAnd T. A. artne9, INon Uniform5Antenna Array Synthesis Usin( Neural Networks,

JTournal 3f &lectroma(netic *a-es And Applications, Vol. #1, No. , 1DD151D11,#DDQ.

Q