ACEEE Int. J. on Communication, Vol. 02, No. 02, July 2011

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1 ACEEE Int. J. on Councaton, Vol., No., July Thnned Concentrc Crcular Array Antennas Synthess usng Iproved Partcle Swar Optzaton Durbadal Mandal, Debanjal Sadhu and Sat Prasad Ghoshal Departent of Electroncs and Councaton Engneerng, Natonal Insttute of Technology Durgapur, West Bengal, Inda- 739 Eal: Departent of Electrcal Engneerng, Natonal Insttute of Technology Durgapur, West Bengal, Inda- 739 Eal: Abstract Crcular antenna array has ganed ense popularty n the feld of councatons nowadays. It has proved to be a better alternatve over other types of antenna array confguraton due to ts all-azuth scan capablty, and a bea pattern whch can be ept nvarant. Ths paper s bascally concerned wth the thnnng of a large ultple concentrc crcular rng arrays of unforly excted sotropc antennas based on Iproved Partcle Swar Optzaton (IPSO) ethod. In ths paper a 9 rnged Concentrc Crcular Antenna Array (CCAA) wth central eleent feedng s consdered. The coputatonal results show that the nuber of antenna array eleents can be brought down fro 79 to 47 wth sultaneous reducton n Sde Lobe Level of about db wth a fxed half power beawdth. Keywords- Concentrc Crcular Antenna Arrays; Partcle Swar Optzaton; Thnnng; Sdelobe Level I. INTRODUCTION Concentrc Crcular Antenna Array (CCAA) has several nterestng features that ae t ndspensable n oble and councaton applcatons. CCAA [-] has receved consderable nterest for ts syetrcty and copactness n structure. A concentrc crcular array antenna s an array that conssts of any concentrc rngs of dfferent rad and a nuber of eleents on ts crcuference. Snce a concentrc crcular array does not have edge eleents, drectonal patterns syntheszed wth a concentrc crcular array can be electroncally rotated n the plane of the array wthout a sgnfcant change of the bea shape. CCAA provdes great flexblty n array pattern synthess and desgn both n narrow band and broadband applcatons. It s also favoured n drecton of arrval (DOA) applcatons snce t provdes alost nvarant azuth angle coverage. Unfor CCA s the CCA where all the eleents n the array are unforly excted and the nter-eleent spacng n ndvdual rng s ept alost half of the wavelength. For larger nuber of rngs wth unfor exctatons, the sde lobe n the UCCA drops to about 7.5 db. Lot of research has gone nto optzng antenna structures such that the radaton pattern has low sdelobe level. Ths very fact has drven researchers to optze the CCAA desgn. Although unforly excted and equally spaced antenna arrays have hgh drectvty at the sae te they suffer fro hgh sde lobe level. Reducton n sde-lobe level can be brought about n ether of the followng ways, ether by eepng exctaton apltudes unfor but changng the poston of antenna eleents or by usng equally spaced array wth radally tapered apltude dstrbuton. These processes are referred to as thnnng. Thnnng not only reduces sde lobe level but also brngs down the cost of anufacturng by decreasng the nuber of antenna eleents [, 3]. There are varous global optzaton tools for thnnng such as Genetc Algorths (GA) [8], Partcle Swar Optzaton (PSO) [4-7] etc. The PSO algorth has proved to be a better alternatve to other evolutonary algorths such as Genetc Algorths (GA), Ant Colony Optzaton (ACO) etc. n handlng certan nds of optzaton probles.ths paper proposes a ethod for thnnng a large ultple concentrc crcular rng arrays of sotropc antennas based on PSO. The rest of the paper s organzed as follows: In secton II, the general desgn equatons for the CCAA are stated. Then, n secton III, a bref ntroducton for the PSO s presented. Coputatonal results are presented n secton IV. Fnally the paper concludes wth a suary of the wor n secton V. II. DESIGN EQUATION Fg. shows the general confguraton of CCAA wth M concentrc crcular rngs, where the th ( =,,, M) rng has a radus r and the correspondng nuber of eleents s N. If all the eleents (n all the rngs) are assued to be sotopc sources, the radaton pattern of ths array can be wrtten n ters of ts array factor only. Referrng to Fg., the far feld pattern of a thnned CCAA n x-y plane ay be wrtten as [7]: Correspondng author: Durbadal Mandal Eal: durbadal.bttu@gal.co ACEEE DOI:.IJCOM... 63

2 Fgure. Concentrc crcular antenna array (CCAA). where I denotes current exctaton of the th eleent of the th rng, / ; beng the sgnal wave-length. If the elevaton angle, = constant, then () ay be wrtten as a perodc functon of wth a perod of π radan.e. the radaton pattern wll be a broadsde array pattern. The azuth angle to the th eleent of the th rng s. The eleents n each rng are assued to be unforly dstrbuted. and are also obtaned fro [3] as: ACEEE DOI:.IJCOM...63 / N () Kr sn cos (3) s the value of where pea of the an lobe s obtaned. After defnng the array factor, the next step n the desgn process s to forulate the objectve functon whch s to be nzed. The objectve functon Cost Functon CF ay be wrtten as (4): FNBW s an abbrevated for of frst null beawdth, or, n sple ters, angular wdth between the frst nulls on ether sde of the an bea. CF s coputed only f FNBW FNBW I and correspondng soluton coputed of current exctaton weghts s retaned n the actve populaton otherwse not retaned. W ( untless F ) and W F ( radan ) are the weghtng factors. s the angle where the hghest axu of central lobe s attaned n,. sl s the angle where the axu sdelobe AF, sl I s attaned n the lower band and sl s the ACEEE Int. J. on Councaton, Vol., No., July angle where the axu sdelobe AF, s attaned sl I n the upper band. W F andw F are so chosen that optzaton of SLL reans ore donant than optzaton of FNBW coputed and CF never becoes negatve. In (4) the two beawdths, FNBW and coputed FNBW bascally refer to the coputed frst null beawdths n radan for the non-unfor exctaton case and for unfor exctaton case respectvely. Mnzaton of CF eans axu reductons of SLL both n lower and upper sdebands and lesser FNBW as copared to FNBW coputed I I. The evolutonary optzaton technques eployed for optzng the current exctaton weghts resultng n the nzaton of CF and hence reductons n both SLL and FNBW are descrbed n the next secton. In ths case, I s f the -th eleent s turned on and f t s off. All the eleents have sae exctaton phase of zero degree. An array taper effcency can be calculated fro ar nuber of eleents n the array turned on total nuber of eleents n the array III. EVOLUTIONARY TECHNIQUES EMPLOYED A. Partcle Swar Optzaton (PSO) PSO s a flexble, robust populaton-based stochastc search/ optzaton technque wth plct parallels, whch can easly handle wth non-dfferental objectve functons, unle tradtonal optzaton ethods. PSO s less susceptble to gettng trapped on local opta unle GA, Sulated Annealng, etc. Eberhart and Sh [4] developed PSO concept slar to the behavor of a swar of brds. PSO s developed through sulaton of brd flocng n ultdensonal space. Brd flocng optzes a certan objectve functon. Each partcle nows ts best value so far (pbest). Ths nforaton corresponds to personal experences of each partcle. Moreover, each partcle nows the best value so far n the group (gbest) aong pbests. Naely, each partcle tres to odfy ts poston usng the followng nforaton: The dstance between the current poston and pbest. The dstance between the current poston and gbest. Matheatcally, veloctes of the partcles are odfed accordng to the followng equaton [5, 6]: where V s the velocty of th partcle at th teraton; w s the weghtng functon; C j s the weghtng factor; rand s the rando nuber between and ; S s the current poston of partcle at teraton ; pbest s the personal best of partcle ; gbest s the group best aong all pbests for the group. The searchng pont n the soluton space can be odfed by the followng equaton:

3 ACEEE Int. J. on Councaton, Vol., No., July S V S (6) The frst ter of (5) s the prevous velocty of the partcle. The second and thrd ters are used to change the velocty of the partcle. Wthout the second and thrd ters, the partcle wll eep on flyng n the sae drecton untl t hts the boundary. Naely, t corresponds to a nd of nerta and tres to explore new areas. The values of w, C and C are gven n the next secton. B. Iproved Partcle Swar Optzaton (IPSO) The global search ablty of tradtonal PSO s very uch enhanced wth the help of the followng odfcatons. Ths odfed PSO s tered as IPSO [5, 6]. ) The two rando paraeters rand and rand of (5) are ndependent. If both are large, both the personal and socal experences are over used and the partcle s drven too far away fro the local optu. If both are sall, both the personal and socal experences are not used fully and the convergence speed of the technque s reduced. So, nstead of tang ndependent rand and rand, one sngle rando nuber r s chosen so that when s large, s sall and vce versa. Moreover, to control the balance of global and local searches, another rando paraeter s ntroduced. For brds flocng for food, there could be soe rare cases that after the poston of the partcle s changed accordng to (6), a brd ay not, due to nerta, fly toward a regon at whch t thns s the ost prosng for food. Instead, t ay be leadng toward a regon whch s n the opposte drecton of what t should fly n order to reach the expected prosng regons. So, n the step that follows, the drecton of the brd s velocty should be reversed n order for t to fly bac nto the prosng regon. s ntroduced for ths purpose. Both cogntve and socal parts are odfed accordngly. Fnally, the odfed velocty of j th coponent of th partcle s expressed as follows: V r sgn r3 V r C r pbest S r C r gbest S where r, r and r are the rando nubers between and ; 3 S s the current poston of partcle at teraton ; the personal best of th partcle at th teraton; (7) pbest s gbest s the group best aong all pbests for the group at th teraton. The searchng pont n the soluton space can be odfed by the followng equaton (6). sgn r 3 s a functon defned as: sgn r when d.5, 3 = when >.5. (8) IV. COMPUTATIONAL RESULTS Ths secton gves the coputatonal results for the CCAA synthess obtaned by IPSO technque. Each CCAA antans a fxed optal nter-eleent spacng between the eleents n each rng. The lts of the radus of a partcular rng of CCAA are decded by the product of nuber of eleents n the rng and the nequalty constrant for the nter-eleent spacng, d, d,. For all the cases, = s consdered so that the pea of the an lobe starts fro the orgn. Snce PSO technques are soetes qute senstve to certan paraeters, the sulaton paraeters should be carefully chosen. Best chosen axu populaton pool sze=, axu teraton cycles for optzaton= 5, and C = C =.5. Fg. s a dagra of a 79 eleent concentrc rng array. Nne rngs (N, N,., N 9 ) are consdered for synthess havng (6,, 8, 5, 3, 37, 43, 5, 56) eleents wth central eleent feedng. For ths case r and nter-eleent spacng n each rngs are d. The nuber of equally spaced eleents n rng s gven by N r d Snce the nuber of eleents ust be an nteger, the value n (9) ust be rounded up or down. To eep d, the dgts to the rght of the decal pont are dropped. Table I. lsts the rng spacng and nuber of eleents n each rng for a unfor concentrc rng array wth nne rngs as shown n Fgure. The IPSO generates a set of optal unfor current exctaton weghts for each synthess set of CCAA. I s f the -th eleent s turned on and f t s off. The optal results are shown n Tables II- III. A. Analyss of Radaton Patterns of CCAA Fg. 3 depcts the substantal reductons n SLL wth optal current exctaton weghts after thnnng, as copared to the case of unfor current exctaton weghts and of fully populated array (consderng fxed nter-eleent spacng, dh λ/). As seen fro Table III and Fg. 3, the SLL reduces to H db for the gven Set, wth respect to -7.4 db for unfor exctaton and dh λ/. Further, the above proveent s acheved for an array of H 53% eleents turned off. The above results reveal that the thnned 9 rngs CCAA set wth central eleent feedng yeld reductons n SLL as copared to the fully populated sae array. B. Convergence Profle of IPSO The nu CF values are plotted aganst the nuber of teraton cycles to get the convergence profles as shown n Fg. 4. The IPSO technque yeld convergence to the nu SLL n less than 5 teratons. All coputatons were done n MATLAB 7.5 on core (TM) duo processor, 3. GHz wth GB RAM. (9) ACEEE DOI:.IJCOM

4 ACEEE Int. J. on Councaton, Vol., No., July Fgure. Concentrc rng array wth nne rngs spaced l / apart and d H l/. Fgure 3. Array pattern found by IPSO for 9 rngs CCAA set wth central eleent feedng. TABLE I. RING RADIUS AND NUMBER OF ELEMENTS PER RING FOR A 9-RING CONCENTRIC CIRCULAR ANTENNA ARRAY. TABLE II. EXCITATION AMPLITUDE DISTRIBUTION (I MN ) USING IPSO Fgure 4. Convergence profle for IPSO n case thnned CCAA V. CONCLUSIONS TABLE III. THINNED AND FULLY POPULATED ARRAY RESULTS Ths paper llustrates a PSO based technque for thnnng of large Concentrc Crcular Antenna Array of sotropc eleents. The ultate objectve of the technque s to desgn an array wth a reducton of around 53% of the total eleents used n case of a fully populated array wth a sultaneous reducton n sde lobe level to around db. The IPSO algorth can effcently handle the thnnng of a large ultple concentrc crcular rng arrays of unforly excted sotropc antennas. The Half Power Beawdth (HPBW) of the syntheszed array pattern wth fxed nter-eleent spacng s rean sae to that of a fully populated array of sae shape and sze, oreover has a better sde lobe level. ACEEE DOI:.IJCOM

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