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1 ACEEE Int. J. on Communcatons, Vol. 3, No., March Partcle Swarm Optzaton wth Constrcton Factor and Inerta Weght Approach Based Synthess of Concentrc Crcular Antenna Array wth Non-sotropc Elements Durbadal Mandal, Bpul Goswa, Rajb Kar and Sakt Prasad Ghoshal Department of Electroncs and Communcaton Engneerng. Department of Electrcal Engneerng. Natonal Insttute of Technology Durgapur West Bengal, Inda- 739 Emal: {durbadal.bttu, goswabpul, rajbkarece, Abstract In ths paper, an evolutonary optzaton technque, Partcle Swarm Optzaton wth Constrcton Factor and Inerta Weght Approach (PSOCFIWA) s adopted for the complex synthess of three-rng Concentrc Crcular Antenna Arrays (CCAA) wth non-sotropc elements and wthout and wth central element feedng. It s shown that by selecton of a ftness functon whch controls more than one parameter of the array pattern, and also by proper settng of weght factors n ftness functon, one can acheve very good results. For each optmal desgn, optmal current exctaton weghts and optmal rad are deterned havng the objectve of maxmum Sdelobe Level (SLL) reducton. The extensve computatonal results show that the CCAA desgns havng central element feedng wth non-sotropc elements yeld much more reducton n SLL as compared to the same not havng central element feedng. Moreover, the partcular CCAA contanng 4, 6 and 8 number of elements n three successve rngs along wth central element feedng yelds grand nmum SLL (-46.4 db). Standard Partcle Swarm Optzaton (PSO) s adopted to compare the results of the PSOCFIWA algorthm. Keywords Concentrc Crcular Antenna Array; Non-sotropc Elements; Partcle swarm optzaton; Non-unform Exctaton; Sdelobe Level; Frst Null Beamwdth ACEEE DOI:.IJCOM I. INTRODUCTION A Concentrc Crcular Antenna Array (CCAA) s an array whch contans many concentrc crcular rngs of dfferent rad and a number of antenna elements located on the crcumference of each rng [, ]. CCAA has receved consderable nterest due to ts symmetrcty and compactness n structure. Snce a concentrc crcular array does not have edge elements, drectonal patterns syntheszed wth a concentrc crcular array can be electroncally rotated n the plane of the array wthout a sgnfcant change of the beam shape. CCAA offers great flexblty n array pattern synthess and desgn both n narrowband and broadband applcatons. These salent features of CCAA have made t ndspensable n moble and communcaton applcatons. These antenna arrays have mproved the performance of moble and wreless communcaton systems through effcent 5 spectrum utlzaton, enhancng channel capacty, extendng coverage area and talorng beam shape etc. However, antenna array desgn can not be done on an arbtrary bass as ths may lead to polluton of the electromagnetc envronment and more mportantly, wastage of precous power. The later may prove fatal for power-lted battery-drven wreless devces. Ths has encouraged a lot of research work [3-] n the feld of optsaton of antenna structures, all havng a common objectve of brdgng the gap between desred radaton patterns wth what s practcally achevable. The goal of ths paper s to optze current exctaton weghts and rad n order to nze the SLL, hence workng towards the mprovement of antenna array pattern. In ths approach the structural geometry of the antenna array s manpulated whle preservng the gan of the man beam. Ths paper presents the desgn of concentrc crcular antenna array wth non-sotropc elements. CCAA desgns havng nonsotropc elements () wth and () wthout central element feedng [-3] have been consdered n ths paper. Many synthess methods are concerned wth suppressng the SLL, as the shape of the desred pattern can vary wdely dependng on the applcaton. In ths paper an optmal CCAA s desgned wth the help of Standard Partcle Swarm Optzaton (PSO) [4] and Partcle Swarm Optzaton wth Constrcton Factor and Inerta Weght Approach (PSOCFIWA) [5-6] technques. The array factors due to optmal rad and nonunform exctatons of non-sotropc elements n varous CCAA desgns are exaned to fnd the best possble desgn set. II. DESIGN EQUATION Fg. s an llustraton of the general confguraton of CCAA havng M concentrc crcular rngs, where the m th (m =,,, M) rng has a radus r m and the correspondng number of elements s N m. If all the elements (n all the rngs) are assumed to be sotropc sources, the radaton pattern of ths array can be wrtten n terms of ts array factor only. But the elements consdered n ths paper are non-sotropc. When the actual elements are non-sotropc, the total feld can be

2 ACEEE Int. J. on Communcatons, Vol. 3, No., March formed by multplyng the array factor of the sotropc sources wth the feld of a sngle element. The far-feld radaton pattern of the array ( FF (, I, r) ) s then gven by [] FF (, I, r ) EP (, I, r ). AF, I, r () where EP (, I, r ) gves the element pattern (n ths work; the elemental pattern s consdered to be cos( ) type) whle AF, I, r s the array factor of the sotropc source. Wth reference to Fg., the array factor, AF, I, r for the CCAA n x-y plane may be wrtten as [-3]: AF where I m, I, r I exp jkrm sn cos () m ACEEE DOI:.IJCOM M N = current exctaton of the th element of the m th rng; k / ; beng the sgnal wave-length; =angular separaton between elements measured from postve x-axs. If the elevaton angle, = 9 then () may be wrtten as a perodc functon of wth a perod of π radan. The angle s the element to element angular separaton measured from the postve x-axs. The elements n each rng are assumed to be unformly dstrbuted. and are also obtaned from [] as: / N (3) m Krm cos (4) s the value of where peak of the man lobe s obtaned. After defnng the far-feld radaton pattern, the next step n the desgn process s to formulate the objectve functon whch s to be nzed. The objectve functon Cost-Functon CF may be wrtten as : CF W F W F FF msl, I,,, rm FF msl I rm FF, I, rm FNBW I FNBW computed FNBW s the Frst Null Beam Wdth. W F andw F are the weghng factors. Mnzaton of CF means maxmum reductons of SLL both n lower and upper bands and lesser FNBW computed as compared to FNBW I. The evolutonary technques descrbed below are employed for the optsaton of the current exctaton weghts as well as the rad of the concentrc rngs. Ths results n the nzaton of and hence reductons n both SLL and FNBW. (5) 6 Fgure. Concentrc crcular antenna array (CCAA) III. EVOLUTIONARY TECHNIQUES EMPLOYED A. Partcle Swarm Optzaton (PSO) PSO s a flexble, robust populaton-based stochastc search/optzaton technque wth mplct parallelsm, whch can easly handle wth non-dfferental objectve functons, unlke tradtonal optzaton methods. PSO s less susceptble to gettng trapped on local optma unlke GA, Smulated Annealng, etc. Eberhart and Sh [4] developed PSO concept slar to the behavor of a swarm of brds. PSO s developed through smulaton of brd flockng n multdmensonal space. Brd flockng optzes a certan objectve functon. Each partcle (brd) knows ts best value so far (pbest). Ths nformaton corresponds to personal experences of each partcle. Moreover, each partcle knows the best value so far n the group (gbest) among pbests. Namely, each partcle tres to modfy ts poston usng the followng nformaton: The dstance between the current poston and the pbest The dstance between the current poston and the gbest Slar to GA, n PSO technques also, real-coded partcle vectors of populaton n p are assumed. Each partcle vector conssts of components or sub-strngs as requred number of current exctaton weghts and three rad, dependng on the number of current exctaton elements n each CCAA desgn. Mathematcally, veloctes of the partcle vectors are modfed accordng to the followng equaton [-3]: V k k k k w V C rand pbest S k k C rand gbest S k where V s the velocty of th partcle at k th teraton; w s the weghtng functon; C and C are the postve weghtng fac- tors; rand and rand are the random numbers between k and ; S s the current poston of th partcle vector at k th teraton; k th teraton; k (6) pbest s the personal best of th partcle vector at k gbest s the group best of the group at k th

3 ACEEE Int. J. on Communcatons, Vol. 3, No., March teraton. The searchng pont n the soluton space may be modfed by the followng equaton: k k k S V S (7) The frst term of (6) s the prevous velocty of the partcle vector. The second and thrd terms are used to change the velocty of the partcle. Wthout the second and thrd terms, the partcle wll keep on flyng n the same drecton untl t hts the boundary. Namely, t corresponds to a knd of nerta represented by the nerta constant, w and tres to explore new areas. B. Partcle Swarm Optzaton wth Constrcton Factor and Inerta Weght Approach (PSOCFIWA) Steps of PSOCFIWA as mplemented for optzaton of current exctaton weghts and locaton of elements are adopted from [5-6]. feedng (Case (a)). It s depcted from Tables II-III, SLL reduces to db for case (a) and -4.8 db for Case (b) usng standard PSO algorthm for the CCAA havng N =4, N =6, N 3 =8 elements (Set No. III). Further for Tables IV-V, SLL reduces to db for Case (a) and db (grand nmum SLL as deterned by PSOCFIWA for Case (b) and non-sotropc elements. Ths optmal desgn set along wth central element feedng yelds grand maxmum SLL reducton among all the sets. The above reductons of SLL are deterned by comparng Table I wth Tables II-V. From comparson between Table II wth Table IV and Table III wth Table V t s clear that PSOCFIWA consstently yelds better optmal results than standard PSO. TABLE I. SLL AND FNBW FOR UNIFORMLY EXCITED ( I =) SETS CCAA IV. SIMULATION RESULTS AND DISCUSSIONS Ths secton gves the computatonal results for varous CCAA desgns obtaned by PSO and PSOCFIWA technques. For each optzaton technque ten three-rng (M=3) CCAA desgns are assumed. Each CCAA mantans a fxed optmal nter-element spacng between the elements n each rng. The lts of the radus of a partcular rng of CCAA are decded by the product of number of elements n the rng and the nequalty constrant for the nter-element spacng, d, d,. For all sets of experments, the number of elements for the nner most rng s N, for outermost rng s N 3, whereas the ddle rng conssts of N number of elements. For all the cases, = s consdered so that the centre of the man lobe n radaton patterns of CCAA starts from the orgn. Snce PSO technques are sometmes qute senstve to certan parameters, the parameters should be carefully chosen. Best chosen maxmum populaton pool sze, n p =, maxmum teraton cycles for optzaton, N m =4. The PSO and PSOCFIWA generate a set of optzed non-unform current exctaton weghts and optmal rad for each desgn set of CCAA. I = corresponds to unform current exctaton. Sets of three-rng CCAA (N, N, N 3 ) desgns consdered for both wthout and wth central element feedng are (,4,6), (3,5,7), (4,6,8), (5,7,9), (6,8,), (7,9,), (8,,), (9,,3), (,,3) and (,3,5). Some of the optmal results are shown n Tables II-V. Table I depcts SLL values and FNBW values for all correspondng unformly excted (=) CCAA desgn sets. Analyss of Radaton Patterns of CCAA Fgs. -3 depct the substantal reductons n SLL wth optmal non-unform current exctaton weghts and rad, as compared to the case of non-optmal unform current exctaton weghts and rad (consderng fxed nter-element spacng, d=λ/) usng PSO and PSOCFIWA optzaton technques respectvely. All CCAA desgn sets havng central element feedng (Case (b)) yeld much more reductons n SLL as compared to the same not havng central element ACEEE 7 DOI:.IJCOM TABLE II. CURRENT EXCITATION WEIGHTS, RADII, SLL AND FNBW FOR NON- UNIFORMLY EXCITED CCAA SETS (CASE (A)) USING STANDARD PSO

4 ACEEE Int. J. on Communcatons, Vol. 3, No., March TABLE III. CURRENT EXCITATION WEIGHTS, RADII, SLL AND FNBW FOR NON-UNIFORMLY EXCITED CCAA SETS (CASE (B)) USING STANDARD PSO TABLE IV. CURRENT EXCITATION WEIGHTS, RADII, SLL AND FNBW FOR NON- UNIFORMLY EXCITED CCAA SETS (CASE (A)) USING PSOCFIWA TABLE V. CURRENT EXCITATION WEIGHTS, RADII, SLL AND FNBW FOR NON- UNIFORMLY EXCITED CCAA SETS (CASE (B)) USING PSOCFIWA Fgure. Radaton patterns for a unformly excted CCAA and correspondng standard PSO and PSOCFIWA based non-unformly excted CCAA Set No. III, Case (a) Fgure 3. Radaton patterns for a unformly excted CCAA and correspondng standard PSO and PSOCFIWA based non-unformly excted CCAA Set No. III, Case (b) ACEEE DOI:.IJCOM Convergence profles of PSO and PSOCFIWA The nmum CF values are plotted aganst the number of teraton cycles to get the convergence profles for the optzaton technques. Fgs. 4-5 show the convergence profles for PSO and PSOCFIWA for Set No. III, Case (b) CCAA respectvely. PSO yelds suboptmal hgher values of CF but PSOCFIWA yelds true optmal (least) CF values consstently n all cases. Wth a vew to the above fact, t may fnally be nferred that the performance of PSOCFIWA technque s better as compared to standard PSO. All optzaton programs are wrtten n MATLAB 7.5 verson

5 ACEEE Int. J. on Communcatons, Vol. 3, No., March on core (TM) duo processor, 3. GHz wth GB RAM. Fgure 4. Convergence curve for standard PSO n case of nonunformly excted CCAA (Set No. III, Case (b)) Fgure 5. Convergence curve for PSOCFIWA n case of nonunformly excted CCAA (Set No. III, Case (b)) V. CONCLUSION Ths paper llustrates how to model the optmal desgn of non-unformly excted CCAAs wth optmal rad and nonsotropc elements for maxmum SLL reducton usng Standard PSO and PSOCFIWA. Computatonal results reveal that the optmal desgn of non-unformly excted CCAA offers a consderable SLL reducton wth respect to the correspondng unformly excted and d=ë/ nter-element spacng CCAA. The man contrbuton of the paper s threefold: () All CCAA desgns havng central element feedng yeld much more reductons n SLL as compared to the same not havng central element feedng, () The PSOCFIWA technque outperforms sgnfcantly as compared to standard PSO n terms of soluton optmalty. ) The CCAA desgn havng N =4, N =6, N 3 =8 elements along wth central element feedng and non-sotropc elements gves the grand nmum SLL (-46.4 db) as compared to all other desgn sets as deterned by PSOCFIWA, whch one s thus the grand optmal desgn set among all the threerng desgns. REFERENCES [] C. A. Ballans, Antenna theory analyss and desgn, nd edton, John Wlley and Son s Inc., New York, 997. [] R. L. Haupt, and D. H. Werner, Genetc Algorthms n Electromagnetcs, IEEE Press Wley-Interscence, 7. [3] C. Stearns and A. Stewart, An nvestgaton of concentrc rng antennas wth low sdelobes, IEEE Trans. Antennas Propag., vol. 3, no. 6, pp , Nov [4] R. Das, Concentrc rng array, IEEE Trans. Antennas Propag., vol. 4, no. 3, pp , May 966. [5] N. Goto and D. K. Cheng, On the synthess of concentrcrng arrays, IEEE Proc., vol. 58, no. 5, pp , May 97. [6] L. Bller and G. Fredman, Optzaton of radaton patterns for an array of concentrc rng sources, IEEE Trans. Audo Electroacoust., vol., no., pp. 57 6, Feb [7] M D. A. Huebner, Desgn and optzaton of small concentrc rng arrays, n Proc. IEEE AP-S Symp., 978, pp [8] M G. Holtrup, A. Margulnaud, and J. Cterns, Synthess of electroncally steerable antenna arrays wth element on concentrc rngs wth reduced sdelobes, n Proc. IEEE AP-S Symp.,, pp [9] R. L. Haupt, Optzed element spacng for low sdelobe concentrc rng arrays, IEEE Trans. Antennas Propag., vol. 56(), pp , Jan. 8. [] M. Dessouky, H. Sharshar, and Y. Albagory, Effcent sdelobe reducton technque for small-szed concentrc crcular arrays, Progress In Electromagnetcs Research, vol. PIER 65, pp. 87, 6. [] K. -K. Yan and Y. Lu, Sdelobe Reducton n Array-Pattern Synthess Usng Genetc Algorthm, IEEE Trans. Antennas Propag., vol. 45(7), pp. 7-, July 997. [] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Applcaton of Evolutonary Optzaton Technques for Fndng the Optmal set of Concentrc Crcular Antenna Array, Expert Systems wth Applcatons, (Elsever), vol. 38, pp ,. [3] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Radaton Pattern Optzaton for Concentrc Crcular Antenna Array Wth Central Element Feedng Usng Crazness Based Partcle Swarm Optzaton, Internatonal Journal of RF and Mcrowave Computer-Aded Engneerng, vol., Issue. 5, pp , Sept.. [4] R. C. Eberhart and Y. Sh, Partcle swarm optzaton: developments, applcatons and resources, evolutonary computaton, Proceedngs of the Congress on Evolutonary Computaton, vol. pp. 8 86,. [5] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Desgn of Concentrc Crcular Antenna Array Wth Central Element Feedng Usng Partcle Swarm Optzaton Wth Constrcton Factor and Inerta Weght Approach and Evolutonary Prograng Technque, Journal of Infrared Mll Terahz Waves, vol. 3 (6), pp ,. [6] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Optzed Rad and Exctatons wth Concentrc Crcular Antenna Array for Maxmum Sdelobe Level Reducton Usng Wavelet Mutaton Based Partcle Swarm Optzaton Technques, Telecommuncatons System, (Sprnger), DOI.7/s ,. ACEEE DOI:.IJCOM