Research Scholar, Dept. of Electronics and Communication Engineering, Andhra University college of

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1 ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) Sde Lobe Reducton of a Concentrc Crcular Antenna Array usng Genetc Algorthm (GA) and Partcle Swarm Optzaton (PSO) K. Rajesh Kumar, S. Aruna, K. Srnvasa Nak Student, Dept. of Electroncs and Communcaton Engneerng, Andhra Unversty College of Engneerng, Andhra Unversty, Vsakhapatnam, Andhra Pradesh, Inda Sr. Assstant Professor, Dept. of Electroncs and Communcaton Engneerng, Andhra Unversty college of Engneerng, Andhra Unversty, Vsakhapatnam, Andhra Pradesh, Inda Research Scholar, Dept. of Electroncs and Communcaton Engneerng, Andhra Unversty college of Engneerng, Andhra Unversty, Vsakhapatnam, Andhra Pradesh, Inda Abstract Crcular antenna array has ganed mmense popularty n the feld of communcatons. It has proved to be a better alternatve over other types of antenna array confguraton due to ts all-azmuth scan capablty, and a beam pattern whch can be kept nvarant. Ths paper s bascally concerned wth the thnnng of a large multple concentrc crcular rng arrays of unformly excted sotropc antennas based on Genetc Algorthm (GA) and Partcle Swarm Optzaton (PSO) methods. In ths paper a 5, 7, 9, 13, 15, and 20 rnged Concentrc Crcular Antenna Arrays (CCAA) wth central element feedng are consdered. The man am of ths work s to reduce the number of antenna array elements wth optzed Frst Null Beamwdth (FNBW), smultaneous reducton n Sde Lobe Level (SLL) and a fxed half power beam wdth (HPBW). Keywords: Concentrc Crcular arrays, Genetc Algorthm (GA), Partcle Swarm Optzaton (PSO), thnnng. I. INTRODUCTION Concentrc Crcular Antenna Array (CCAA) has several nterestng features that make t ndspensable n moble and communcaton applcatons. CCAA has receved consderable nterest for t s symmetrcty and compactness n structure [1-7]. A concentrc crcular array antenna s an array that conssts of many concentrc rngs of dfferent rad and a number of elements on ts crcumference. 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 provdes great flexblty n array pattern synthess and desgn both n narrow band and broadband applcatons. It s also favored n drecton of arrval (DOA) applcatons snce t provdes almost nvarant azmuth angle coverage. Unform CCA s the CCA where all the elements n the array are unformly excted and the nter-element spacng n ndvdual rng s kept almost half of the wavelength. For larger number of rngs wth unform exctatons, the sde lobe n the UCCA drops to about 17.5 db. Lot of research has gone nto optzng antenna structures such that the radaton pattern has low sde lobe level. Ths very fact has drven 119 researchers to optze the CCAA desgn. Although unformly excted and equally spaced antenna arrays have hgh drectvty at the same tme they suffer from hgh sde lobe level. Reducton n sde-lobe level can be brought about n ether of the followng ways, ether by keepng exctaton ampltudes unform but changng the poston of antenna elements or by usng equally spaced array wth radally tapered ampltude dstrbuton. These processes are referred to as thnnng. Thnnng not only reduces sde lobe level but also brngs down the cost of manufacturng by decreasng the number of antenna elements [9]. There are varous global optzaton tools for thnnng such as Genetc Algorthms (GA) [8], Partcle Swarm Optzaton (PSO) etc. The PSO algorthm has proved to be a better alternatve to other evolutonary algorthms such as Genetc Algorthms (GA), Ant Colony Optzaton (ACO) etc [12]. n handlng certan knds of optzaton problems. In ths work, thnnng of large multple concentrc crcular rng arrays of sotropc antennas s done based on GA and PSO. II. ANTENNA ARRAYS In ths chapter the basc emphass s made on array theory. Here the number of elements and the spacng between the elements (d=0.5λ) s consdered to be same for the entre above mentoned antenna arrangements. In an array of dentcal elements, there are at least fve controls that can be used to shape the overall pattern of the antenna. These are 1. The geometrcal confguraton of the overall array (lnear, crcular, rectangular, sphercal.etc) 2. The relatve dsplacement between the elements. 3. The exctaton ampltude of the ndvdual elements. 4. The exctaton phase of the ndvdual elements. 5. The relatve pattern of the ndvdual elements. A. Concentrc crcular array antenna (CCAA) Below fgure shows the general confguraton of CCAA wth M concentrc crcular rngs, where the m th (m = 1, 2 M) rng has a radus r m and the correspondng number of elements s Nm. If all the elements (n all the rngs) are assumed to be sotopc sources, the radaton

2 ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) pattern of ths array can be wrtten n terms of ts array factor only. Referrng to Fg. 1, the far feld pattern of a thnned CCAA n x-y plane may be wrtten as [10] AF(, I) M N m m 1 1 I exp( j( k. r cos( ) ) m.sn. (1) Where I denotes current exctaton of the th element of the m th rng, k = 2π /λ, λ beng the sgnal wave-length. If the elevaton angle, Φ = constant, then (1) may be wrtten as a perodc functon of θ wth a perod of 2π radan.e. the radaton pattern wll be a broadsde array pattern. The azmuth angle to the th element of the m th rng s Φ.The elements n each rng are assumed to be unformly dstrbuted [11]. chosen that optzaton of SLL remans more donant than optzaton of FNBW computed and THINNED and CF never becomes negatve. In (4) the two beam wdths, FNBW computed and FNBW (I =1) bascally refer to the computed frst null beam wdths n degree for the nonunform exctaton case and for unform exctaton case respectvely. Mnzaton of CF means maxmum reductons of SLL both n lower and upper sdebands and lesser FNBW computed as compared to FNBW (I =1). The evolutonary optzaton technques employed for optzng the current exctaton weghts resultng n the nzaton of CF and hence reductons n SLL, FNBW and THINNED are descrbed n the next secton. In ths case, I s 1 f the m th element s turned on and 0 f t s off. All the elements have same exctaton phase of zero degree. An array taper effcency can be ar Number of elements n the array turned ON Total number of elements n the array III. EVOLUTIONARY TECHNIQUES Fg. 1: Concentrc crcular antenna array (CCAA) Φ and α are also obtaned from as: 2 (( 1) / Nm) (2) Kr sn cos( ) (3) m. 0 θ 0 s the value of θ where peak of the man lobe s obtaned. After defnng the array factor, 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 W1 *(10^ ( SLL1 / 20) 10^ ( SLL2 / 20)) W *( FNBW FNBW( I 1)) (4) 2 computed W3 * THINNED FNBW s an abbrevated form of frst null beam wdth, or, n smple terms, angular wdth between the frst nulls on ether sde of the man beam. The value of FNBW (I =1) for concentrc crcular antenna array wth 9 rngs s 7.2 degrees. W 1 (unt less), W 2 (degree -1 ) and W 3 are the weghtng factors. θ 0 s the angle where the hghest maxmum of central lobe s attaned n θ Є [-π π]. SLL 1 s the sde lobe level n the lower band and SLL 2 s the sde lobe level n the upper band. W 1, W 2 and W 3 are so A. Genetc algorthm (GA) A genetc algorthm s a search technque used n computng to fnd exact or approxmate solutons to optzaton and search problems. Genetc algorthms are a partcular class of evolutonary algorthms (also known as evolutonary computaton) that use technques nspred by evolutonary bology such as nhertance, mutaton, selecton, and crossover (also called recombnaton). A typcal genetc algorthm requres two thngs to be defned: ). a genetc representaton of the soluton doman. ).a ftness functon to evaluate the soluton doman. 1. [Start] Generate random populaton of n ndvduals (.e. sutable soluton for the problem) 2. [Ftness] Evaluate the ftness of each ndvdual n the populaton 3. [New populaton] create new populaton by repeatng followng steps untl the new populaton s created a).[selecton] Select two parent ndvduals from populaton accordng to ther ftness b).[cross over] wth a cross over probablty, cross over the parents to form new off strng (chldren) c).[mutaton] wth a mutaton probablty, mutate new off strng at each locus d). [Acceptng] Place new off strng n the new populaton 120

3 ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) 4. [Replace] Use new generated populaton for a further run of the Algorthm 5. [Test] f the end of the condton s satsfed, stops, and returns the best soluton n current populaton 6. [Loop] Go to step 2 B. 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. The below fgure shows the basc ternology and the process of PSO Where, V k s the velocty of th partcle at k th teraton; W s the weghtng functon; C1 and C2 are the weghtng factors; Rand 1 and Rand 2 are two random numbers between 0 and 1. S k s the current poston of partcle at teraton k;pbest s the personal best of partcle ;gbest s the group best among all pbests for the group. The searchng pont n the soluton space can be modfed by the followng equaton: S S V ( k 1) k ( k 1) (6) v. Loop to step () untl a stoppng crteron s met, usually a maxmum number of teratons (generatons). IV. COMPUTATIONAL RESULTS 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,dє[λ/2,λ] For all the cases,θ 0 =0 s consdered so that the peak of the man lobe starts from the orgn. Best chosen maxmum populaton pool sze= 120, maxmum teraton cycles for optzaton= 50, and C1 = C2 = 1.5. For ths case r m =m λ/2 Fg. 2: Ternology and the process of PSO The procedure for mplementng the global verson of PSO s gven by the followng steps:. Intalze a (populaton) of partcles wth random postons and veloctes n the n-dmensonal problem space usng a unform probablty dstrbuton functon;. For each partcle n swarm, evaluate ts ftness value; Inter-element spacng n each rngs are d m = λ/2 The number of equally spaced elements n rng m s gven by N m =2πr m /d m. The results of 5, 9 and 20 rngs of CCAA are shown n below A. Fully populated array results. v. Compare each partcle s ftness evaluaton wth the current partcle s pbest. If current value s better than pbest, set ts pbest value to the current value and the pbest locaton to the current locaton n n- dmensonal space; Compare the ftness evaluaton wth the populaton s overall prevous best. If current value s better than gbest, then reset gbest to the current partcle s array ndex and value; v. Change the velocty and poston of the partcle accordng to below equatons respectvely Mathematcally, veloctes of the partcles are modfed accordng to the followng equaton V C k1 2 W * V * rand 2 k C * rand 1 *( gbest S k ) 1 *( pbest S k ) (5) 121 Fg. 3 Radaton pattern of fully populated array for M=5 rngs

4 ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) Fg. 4 Radaton pattern of fully populated array for M=9 rngs Fg. 8 Radaton pattern for CCAA wth central element feedng for M=9 rngs by usng GA Fg. 5 Radaton pattern of fully populated array for M=20 rngs B. Results of CCAA usng genetc algorthm (GA) Convergence Profle The nmum CF values are plotted aganst the number of teraton cycles to get the convergence profles as shown n below fgures. Fg. 9 Convergence Profle for CCAA wth central element feedng for M=9 rngs by usng GA Fg. 6 Radaton pattern for CCAA wth central element feedng for M=5 rngs by usng GA Fg. 10 Radaton pattern for CCAA wth central element feedng for M=20 rngs by usng GA Fg. 7 Convergence Profle for CCAA wth central element feedng for M=5 rngs by usng GA Fg. 11 Convergence Profle for CCAA wth central element feedng for M=20rngs by usng GA 122

5 ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) C. Results of CCAA usng partcle swarm optzaton: Fg. 12 Radaton pattern for CCAA wth central element feedng for M=5 rngs by usng PSO Fg. 16 Radaton pattern for CCAA wth central element feedng for M=20 rngs by usng PSO Fg. 13 Convergence Profle for CCAA wth central element feedng for M=5 rngs by usng PSO Fg. 17 Convergence Profle for CCAA wth central element feedng for M=20 rngs by usng PSO Table 1: The below tabular form shows the comparson between Genetc Algorthm and Partcle Swarm Optzaton for 5, 9, and 20 rng concentrc crcular array antenna Fg. 14 Radaton pattern for CCAA wth central element feedng for M=9 rngs by usng PSO Parameters Number of rngs Fully populated array GA based synthesze d thnned array PSO based syntheszed thnned array 5 rngs dB dB dB Fg. 15 Convergence Profle for CCAA wth central element feedng for M=9 rngs by usng PSO Sde Lobe Level (SLL, n db) 9 rngs 20 rngs dB dB dB dB dB dB Beam 5 rngs Wdth between 9 rngs Frst Nulls (FNBW, n 20 rngs degree) Half-power 5 rngs

6 Beam Wdth (HPBW, n degree) Number of elements turned OFF Number of elements turned ON ISSN: ISO 9001:2008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) 9 rngs rngs rngs rngs rngs rngs rngs rngs [8] R. L. Haupt, and D. H. Werner, Genetc Algorthms n Electromagnetcs, IEEE Press Wley-Interscence, [9] R. L. Haupt, Thnned concentrc rng arrays, Antennas and Propagaton Socety Internatonal Symposum, AP-S IEEE, pp.1-4, 5-11 July [10] D.Mandal, S. P. Ghoshal, and Debanjal Sadhu, Thnned concentrc crcular array antennas synthess usng Improved partcle swarm optzaton, ACEEE Int.J.on Communcaton, vol. 02,No.02, July [11] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Swarm Intellgence Based Optmal Desgn of Concentrc Crcular Antenna Array, Journal of Electrcal Engneerng, vol. 10, no. 3, pp , [12] D. Mandal, S. P. Ghoshal, and A. K. Bhattacharjee, Improved Swarm Intellgence Based Optmal Desgn of Concentrc Crcular Antenna Array, In: IEEE Appled Electromagnetcs Conference AEMC 09, pp.1-4, Dec.14-16, 2009, Kolkatta. AUTHORS PROFILE S V. CONCLUSION PSO gves better results n reducng total number of antenna elements and Sde Lobe Level. The Half Power Beam wdth (HPBW) of the syntheszed array pattern wth fxed nter-element spacng s reman same to that of a fully populated array of same shape and sze n case of PSO. Compared to GA, the PSO gves better results n optzaton of FNBW. The PSO technque yeld convergence to the nmum SLL n less than 25 teratons, where as GA technque yeld convergence to the nmum SLL n more than 25 teratons. REFERENCES [1] C. Stearns and A. Stewart, An nvestgaton of concentrc rng antennas wth low sde lobes, IEEE Trans. Antennas Propag., vol. 13(6), pp , Nov [2] R. Das, Concentrc rng array, IEEE Trans. Antennas Propag., vol. 14(3), pp , May [3] N. Goto and D. K. Cheng, On the synthess of concentrcrng arrays, IEEE Proc., vol. 58(5), pp , May [4] L. Bller and G. Fredman, Optzaton of radaton patterns for an array of concentrc rng sources, IEEE Trans. Audo Electroacoust., vol. 21(1), pp , Feb [5] M D. A. Huebner, Desgn and optzaton of small concentrc rng arrays, In Proc. IEEE AP-S Symp., pp , [6] R. L. Haupt, Optzed element spacng for low sde lobe concentrc rng arrays, IEEE Trans. Antennas Propag., vol. 56(1), pp , Jan [7] M. Dessouky, H. Sharshar, and Y. Albagory, Effcent sde lobe reducton technque for small-szed concentrc crcular arrays, Progress In Electromagnetcs Research, vol. PIER 65, pp , K. Rajesh kumar born n Vsakhapatnam, Andhra Pradesh. He completed hs SSC from Board of Secondary Educaton n kotak Salesan school at Vsakhapatnam. He has completed hs B.tech(ECE) from JNTUK Unversty n Chatanya Engneerng College, Vsakhapatnam n Andhra Pradesh. He had successfully completed hs B.Tech Man project ttled wreless mesh network for buldng and automaton. Presently, he s pursung hs Master s degree n Radar & Mcrowave Engneerng from Andhra Unversty, Vsakhapatnam, Andhra Pradesh. S. Aruna, receved the Bachelor of Engneerng n Electroncs and Communcaton Engneerng from Andhra Unversty and the Master of Engneerng n Electronc Instrumentaton Engneerng from JNTU Kaknada. Currently, she s workng as Assstant Professor n the department of Electroncs and Communcaton Engneerng, Andhra Unversty College of Engneerng (A). She has presented many techncal papers n natonal & nternatonal conferences at Canada, Jodhpur and Vsakhapatnam. She has attended many Workshops. She s member of IETE & IST. Her Research nterests nclude Array Antennas, EMI/EMC and Soft Computng. K Srnvasa Nak receved the Bachelor of Engneerng n Electroncs and Communcaton Engneerng n the year of 2005 from Andhra Unversty and the Master of Engneerng n Electronc Instrumentaton Engneerng n 2008 from Andhra Unversty College of Engneerng (A). Currently, he s workng towards hs Ph.D degree n the department of Electroncs and Communcaton Engneerng, Andhra Unversty College of Engneerng (A). Hs Research nterests nclude Array Antennas, EMI/EMC and Soft Computng. He s a lfe member of SEMCE (Inda). 124