Patterns Antennas Arrays Synthesis Based on Adaptive Particle Swarm Optimization and Genetic Algorithms

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1 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): Patterns Antennas Arrays Synthess Based on Adaptve Partcle Swarm Optmzaton and Genetc Algorthms B. Kadr 1, M. Brahm 1, I.K. Bousserhane 1, M. Bousahla 2, F.T. Bendmerad 2 1 Bechar Unversty, Faculty of Scences and Technologes, Departement of Electronc P.O.Box 417, 8, Bechar, Algera 2 Abou-Bakr Belka Unversty, Engneerng Scences Faculty, Telecommuncatons Laboratory P.O.Box 23, Tlemcen, Algera Abstract In recent years, evolutonary optmzaton (EO) technques have attracted conserable attenton n the desgn of electromagnetc systems of ncreasng complexty. Ths paper presents a comparson between two optmzaton algorthms for the synthess of unform lnear and planar antennas arrays, the frst one s an adaptve partcle swarm optmzaton () where the nerta weght and acceleraton coeffcent are adjusted dynamcally accordng to feedback taken from partcle s best memores to overcome the lmtatons of the standard PSO whch are: premature convergence, low searchng accuracy and teratve neffcency. The second method s the genetc algorthms () nspred from the processes of the evoluton of the speces and the natural genetcs. The results show that the desgn of unform lnear and planar antennas arrays usng method proves a low se lobe level and acheve faster convergence speed to the optmum soluton than those obtaned by a. Keywords: antennas arrays, planar arrays, synthess, optmzaton methods; adaptve partcle swarm algorthm, genetc algorthm. 1. Introducton Planar antenna arrays have been wely studed due to ther mportance n communcatons ndustry such us moble, wreless communcaton, and other domans [1], n order to seek for an optmal planar antenna arrays feed laws so that the array comples wth the requrements of the user and accordng to precse specfcatons, such us lower se lobes of planar antenna array pattern, controllable beamwth, and the pattern symmetry n azmuth angles. The tradtonal optmzaton methods cannot bear the demand of such complex optmzaton problem. Partcles Swarm Optmzaton (PSO) [2] s an evolutonary algorthm based on the swarm ntellgence. Eberhart and Kennedy frst ntroduced such algorthms n The orgnal concepton comes from the research of food huntng by brds. PSO algorthm can be used to solve the complex global optmzaton problems. Currently, the algorthm and ts varatons are appled to solve many practcal problems. For the optmzaton of the antenna array, the parameters affectng antenna pattern are chosen as the desgn varables [3]. A desred pattern s presented accordng to the radate requrement. The smulaton result show that the calculated pattern approaches the desred pattern and the SLL s very low. Ths knd of optmzaton mproves the effcency of antennas array. 2. Standard Partcle Swarm Optmzaton Recently, the PSO technque has been successfully appled to the desgn of antennas and mcrowave components [4-5]. The results proved that ths method s powerful and effectve for optmzaton problems. PSO s smlar n some ways to Genetc Algorthms () and other evolutonary algorthms, but requres less computatonal bookkeepng and generally fewer lnes of code, ncludng the fact that the basc algorthm s very easy to understand and mplement. In the PSO mechansm, each potental soluton of optmzaton problem s a brd n the soluton space, whch called partcle. Each partcle has a value of ftness detered by objectve functons. They also have a drectonal velocty to control ts move tracks. The partcles chase the optmal soluton by searchng the soluton space. All partcles have ntal postons and veloctes [6], where the postons and veloctes are terated. In each teraton, two best poston are chased to update the partcle. The frst s the optmal soluton found by partcle, whch called personal best poston. The other s the optmal soluton n the entre group, whch called global best poston. In PSO, the -th partcle n the soluton space s detered by a ftness functon s value. The ftness functon s the optmal target, the poston of th partcle can be presented by x x 1, x2,..., x, v v v,..., v stand for the velocty of the th 1, 2 partcle, the optmal soluton come nto beng through teratve searchng, the postons and veloctes of partcles update by personal and global best postons n each Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

2 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): teraton. Let p p p,..., p be the poston vector 1, 2 for an ndvual partcle s best ftness, whch s personal best poston, and g g 1, g2,..., g be the global best poston among all the agents. The postons and veloctes of partcles are updated accordng to the followng equatons (1) and (2) [7]: v x p x c r g x v c1 r1 2 2 x v (2) Where. 7 s the nerta weght, c1 and c2 are the acceleraton coeffcents set to 1.7, r1 and r2 are random numbers n the range [,1], The frst part of (1) s the ntal veloctes of partcles, the second part s cognton, whch expresses the cogtaton of partcles; the thrd part s socal, whch expresses the regstraton of message and cooperaton among partcles. The steps nvolved n standard PSO are shown by the flowchart drawn n fgure 1. (1) 3. Adaptve Partcle Swarm Optmzaton In ths paper, the nerta weght and the acceleraton coeffcent are nether set to a constant value nor set as a lnearly decreasng tme varyng functon [8]. Instead they are defned as a functon of local best (pbest) and global best (gbest) values of the ftness functon of a mzaton problem as gven n Eqs. (3) and (4). The average of all the personal best values n that partcular generaton s termed as ((pbest)average). Inerta weght, gbest 1.1 (3) pbest average Acceleraton coeffcent; ac ac ac 2 1 gbest pbest 1 (4) The nerta weght n (3) s termed global-average local best IW (GLbestIW) and the acceleraton coeffcent n (4) s called global-local best AC (GLbestAC). 4. Genetc Algorthm Fg. 1.Flowchart of PSO algorthm By analogy wth natural selecton and evoluton, n classcal the set of parameters to be optmzed (genes) defnes an ndvual or potental soluton X (chromosome) and a set of ndvuals makes up the populaton, whch s evolved by means of the selecton, crossover, and mutaton genetc operators. The optmzaton process used by the follows the next steps [9]. The genetc algorthm generates ndvuals (ampltude exctatons and phase perturbatons of the antenna elements). The ndvuals are encoded n a vector of real numbers, that represents the ampltudes, and a vector of real numbers restraned on the range (, 2π), that represents the phase perturbatons of the antenna elements. Each ndvual generates an array factor of certan characterstcs of the se lobe level and the drectvty. Then, the genetc mechansms of crossover, survval and mutaton are used to obtan better and better solutons. The genetc algorthm evolves the ndvuals to a global soluton that generates an array factor wth mum se lobe level and maxmum drectvty n the steerng drecton [1-11]. The steps nvolved n are shown by the flowchart drawn n fgure 2. Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

3 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): optmzaton (-4dB) are much better than n the case of (-23dB). Fg. 3 Lnear antennas array Fg. 2 Flowchart of algorthm Ampltude Lnear Antenna Arrays Synthess In ths secton, the and algorthms were mplemented for the synthess of unformly spaced lnear array consttuted wth 16 rectangular mcrostrp antennas (fgure 3). Two examples of lnear antenna array synthess have been consered, the frst one by optmzng only exctaton weghts for a desred radaton pattern specfed by a symmetrcal narrow beam pattern wth a beam wth of 8 degrees and maxmum se lobe levels of -2dB. The second example for the same desred radaton pattern but ponted at 1, the synthess was carred out by optmzng both ampltude and phase weghts. In our smulaton, we have used a populaton sze of 4 for. For, t set wth adaptng nertal weght and acceleraton coeffcents whch s proposed by Ratnaweera and Halgamuge [12] and a populaton sze equal to 3 ndvuals. In fgure 4 we present the result of the frst example of lnear antenna array synthess by the optmzaton of ampltude exctaton coeffcents usng both and. It s clearly seen that the radaton pattern obtaned by meet better the desred pattern than the obtaned by the. The se lobe level obtaned by Fg. 4 Result of a lnear array synthess wth 16 elements applyng both and Number of teratons Fg. 5 Ftness evoluton of and algorthms Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

4 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): From fgure 5, the speed approachng the global optmal of s much quckly than that of, and the ftness values of the best ndvuals of are almost hgher than that of n every populaton. In the second example, the synthess result of a lnear array wth 16 unformly spaced antennas for a desred radaton pattern, smlar to the prevous one but ponted at 1 degrees are shown n fgures 6 and 7. Ampltude of d dx dy 2 (fgure 8), and whose outputs are added together to proved a sngle output. Mathematcally, the normalzed array far-feld pattern s gven by: f (, ) Fs (, ) F M s max n1. N n1 I j e j e m1 k sn cosdx j n1 k sn sn dy j Where f (, ) : Represents the radaton pattern of an element. I : Ampltude coeffcent at element (m, n). : Phase coeffcent at element (m, n). k : Wave number. (5) Fg. 6 Result of a lnear array synthess wth 16 elements applyng both and Number of teratons Fg. 7 Ftness evoluton of and algorthms 6. Planar Antenna Arrays Synthess A mcrostrp antenna have lmted radaton dagram however, when we have an aggregate the performance of radaton dagram wll be remarkable [13]. Let us conser a planar antenna array consttuted of MxN equally spaced rectangular antenna arranged n a regular rectangular array n the x-y plane, wth an nter-element spacng Fg. 8 Planar antennas array. We use the algorthm to fnd the approprate exctaton coeffcents (ampltude and phase), whch shall satsfy the desred radaton pattern. We have chosen a sutable ftness functons that can gue the optmzaton toward a soluton that meets the desred radaton pattern. The ftness functon to be mzed s selected from the work of Chuan Ln [14] whch s descrbed by the equaton below A F ( ) f( ) Max S (6) A ( ) F Where S s the space spanned by the angle θ excludng the manlobe and ρ represents the unknown parameter vector, such as element postons and phases. Ths objectve functon mzes all the selobe levels and maxmzes the power n the man lobe located at θ=θ. We mplemented the two algorthms and for the synthess of unformly spaced planar array of 16 Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

5 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): rectangular patch antennas. Fgures 9 and 11 represent respectvely the synthess result of our array consttuted of 16 elements. It s a queston respectvely of the ampltude and phase optmzaton and the ampltude and phases ponted at 1 degree n order to as well as possble approach the radaton pattern resultng from a desred template specfed by a symmetrcal narrow beam pattern wth a beam wth of 8 degrees and maxmum se lobe levels of -2dB. Durng the smulaton we have used a populaton sze of 4 for Fs. Roulette strategy for selecton one pont crossover and mutaton to flp bts, the value of crossover and mutaton probabltes (p c and p m ) are detered accordng to FLC. The fgures represent the results of plane array synthess conssted of 16 aeral elements. It s notced that the radaton pattern are contaned wthn the lmts mposed by the template and the maxmum of se lobes level s lower than -2 db n such way that the s better than and reaches them respectvely - 35dB and -25 db (fgure 7), -3dB and -22dB (fgure 9) Wth each dagram, on assocates the evoluton of the quadratc error durng the generatons (fgure 1 and 12). From ths fgures the best ftness obtaned by the s better than the obtaned by the. Ampltude Number of teratons Fg. 1 Ftness evoluton of and algorthms Fg. 11 Result of a lnear array synthess wth 16 elements applyng both and (ampltude and phase synthess). -4 Ampltude Fg. 9 Result of a lnear array synthess wth 16 elements applyng both and (only ampltude synthess) Number of teratons Fg. 12 Ftness evoluton of and algorthms Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

6 IJCSI Internatonal Journal of Computer Scence Issues, Vol. 1, Issue 1, No 2, January 213 ISSN (Prnt): ISSN (Onlne): Concluson The optmzaton technques seemed and for the goal to obtan the global mum and to avo remanng to trap n a local mum lke n the case of the deterstc methods. However they present a major dsadvantage whch les n ther calculatve cost and whch beleves accordng to the dmenson of the problem consered and ts dffculty. The advantage of PSO on of s marked as much than the optmzaton varables number s mportant. Indeed for a synthess of antennas array, requres an enormous computng tme, because ths one needs a great teraton number to converge towards an optmal soluton. Included examples on lnear and planar antennas array synthess demonstrate that PSO wth adaptve scheme shows better performance than because of ts smplcty n mplementaton and or computng tme. [11] D. Marcano, F. Duran, Synthess of Antenna Arrays Usng Genetc Algorthms. IEEE Antenna and propagaton Magazne. Vol. 42. NO. 3. June 2. [12] A. Ratnaweera, S.K. Halgamuge, Self-organzng herarchcal partcle swarm optmzer wth tme-varyng acceleraton coeffcent, IEEE Trans. Evol. Comput. vol. 8 (June (3)) (24) [13] Boufeldja Kadr, Mloud Boussalla, Fetl Tark Beudmerad, Phase-Only Planar Antenna Array Synthess wth Fuzzy Genetc Algorthms IJCSI Internatonal Journal of Computer Scence Issues, Vol. 7, Issue 1, No. 2, January 21. [14] Chuan Ln, Anyong Qng and Quanyuan Feng1, Synthess of unequally Spaced Antenna Arrays by a new Dfferental Evolutonary Algorthm, Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS), Vol. 1, No. 1. Aprl 29 References [1] W.Y. We, D.M. Gong, and B.S. Chen, Antenna Theory, X an: The publshng house of Xan Unversty, [2] J. Robnson, Y. Rahmat-Sam, Partcle Swarm Optmzaton (PSO) n Electromagnetcs, IEEE Trans. Antennas Propagaton, vol.52, no.2, February 24, pp [3] Cheng D K, Optmzaton technques for antenna arrays, Proceedngs for IEEE, vol.59 (12), 1988, pp [4] Khoder, M. Chrstodoulou,. Lnear array geometry synthess wth mum selobe level and null control usng partcle swarm optmzaton, IEEE Transactons on Antennas and Propagaton 53 No. 8 (August 25), [5] Ababneh, J. Khoder, M. Db, N, Synthess of nter- dgtal capactors based on partcle swarm optmzaton and artfcal neural networks, Internatonal Journal of RF and M- crowave Computer-Aed Engneerng 16 (July 26), 322{33. [6] J. Kennedy, R. Eberhat, Partcle Swarm Optmzaton, IEEE Int. Conf. Neural Networks (Perth, Australa), vol. IV, 1995, pp [7] T.B. Chen, Y.B. Chen, Y.C. Jao, and F.S. Zhang Synthess of Antenna Array Usng Partcle Swarm Optmzaton Natonal Laboratory of Antennas and Mcrowave Technology, Xan Unversty, X an 7171, P. R. Chna [8] R. Eberhart, Y. Sh, Comparson between genetc algorthms and partcle swarm optmzaton, Lect. Notes Comput. Sc , [9] R. L. Haupt,. Al Introducton to Genetc Algorthms for Electromagnetcs, IEEE Antenna and propagaton Magazne. Vol. 37. pp [1] S. A. Mtlneos, C A, Papagann. G.. I. Verkak. C. N. Capsals, Desgn of Swtched Beam Planar Arrays Usng the Method of Genetc Algorthms, Progress In Electromagnetcs Research. PIER Copyrght (c) 213 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.