(ego) application for patch antenna design

2424 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 9, SEPTEMBER 2004

A Parallel Electromagnetic Genetic-AlgorithmOptimization (EGO) Application for

Patch Antenna DesignFrank J. Villegas, Member, IEEE, Tom Cwik, Fellow, IEEE, Yahya Rahmat-Samii, Fellow, IEEE, and

Majid Manteghi, Member, IEEE

Abstract—In this paper, we describe an electromagnetic geneticalgorithm (GA) optimization (EGO) application developed for thecluster supercomputing platform. A representative patch antennadesign example for commercial wireless applications is detailed,which illustrates the versatility and applicability of the method. Weshow that EGO allows us to combine the accuracy of full-wave EManalysis with the robustness of GA optimization and the speed of aparallel computing algorithm. A representative patch antenna de-sign case study is presented. We illustrate the use of EGO to designa dual-band antenna element for wireless communication (1.9 and2.4 GHz) applications. The resulting antenna exhibits acceptabledual-band operation (i.e., better than 10 dB return loss with 5.3and 7% operating bandwidths at 1.9 and 2.4 GHz) while main-taining a cross-pol maximum field level at least 11 dB below theco-pol maximum.

Index Terms—Genetic algorithms, method of moments (MoM),microstrip antenna, optimization, parallel computing.

I. INTRODUCTION

A current trend in electronics technology is the emphasison increasingly stringent system requirements in both the

commercial as well as military sectors, in addition to main-taining low costs in manufacturing, operations and maintenance.For the military, the new paradigm shift is toward network-cen-tric warfare, wherein a major emphasis is placed on the com-plex interaction between the various information subsystemsthat comprise a complete military system. Hence, the desire is toobtain a system that is capable of reconnaissance, data analysis,ordnance control, communications, etc., all in a real-time settingvia an ad hoc virtual network. Antenna designs for both ground-and airborne-based subsystems present a unique challenge, inthat they should be as simple as possible and low-cost while atthe same time satisfying the particular electrical requirements.In the commercial domain, the development of Wireless Fidelity(WiFi) Internet access systems (IEEE 802.11b), 2.5 G and 3G wireless technology, broadband cellular technology that han-dles high-rate voice and data, etc., has also placed a significant

Manuscript received October 19, 2002; revised April 25, 2003.F. J. Villegas was with Raytheon Electronic Systems, El Segundo, CA

90245-0902 USA. He is now with The Aerospace Corporation, El Segundo,CA 90245–4691 USA.

T. Cwik is with the High Performance Computing Group, Jet Propulsion Lab-oratory, Pasadena, CA 91109 USA.

Y. Rahmat-Samii and M. Manteghi are with the Antenna Research andMeasurement Laboratory, Department of Electrical Engineering, Universityof California at Los Angeles, Los Angeles, CA 90095-1594 USA (e-mail:[email protected]; www.ee.ucla.edu).

Digital Object Identifier 10.1109/TAP.2004.834071

burden on the design of low-cost antennas that achieve quite re-markable specifications in terms of bandwidth, gain, multibandoperation, and physical (e.g., size) constraints.

As a result, designers have had to turn to ever-more inge-nious methods to achieve these goals. A technique that has be-come quite popular over the last several years has been the useof evolutionary optimization strategies for electromagnetic de-sign. In particular, the use of genetic algorithms (GA) has ex-ploded onto the research scene with great success, predomi-nantly due to its particular characteristics that make it an idealtool that marries quite well with existing EM analysis tech-niques [1]–[5], and typically yields results that satisfy the givenrequirements in a nonintuitive fashion. A great deal of efforthas already been expended in furthering both the computationalmaturity of GA optimization in electromagnetics [3], [6]–[8], aswell as in extending the domain of applications to include quiteingenious designs [9]–[18]. Two distinct focus areas in whichGA optimization has yielded quite fruitful results are novel pat-tern synthesis [19]–[30] and broadband (or multiband) opera-tion [31]–[34]. Another area in which the use of GA designsshows promise is the development of “smart” antennas [35].

In this article, we describe an electromagnetic GA optimiza-tion (EGO) application (introduced in [36]) that has been devel-oped for the cluster supercomputing platform, and is thus quitepowerful and apropos for today’s tough antenna design prob-lems. A representative patch antenna design example for com-mercial applications is detailed, which illustrates the versatilityand applicability of the method. We show that EGO allows us tocombine the accuracy of full-wave EM analysis with the robust-ness of GA optimization and the speed of a parallel computingalgorithm. In Section II, the EGO application software architec-ture proposed in [36] is presented in greater detail, i.e., the EManalysis procedure and parallel infrastructure is fully developed.In particular, we present a more in-depth development of the par-allel application architecture. The single-program multiple datamodel is in essence a key feature that allows us to use the moreaccurate full-wave method of moments (MoM) simulations inconjunction with the evolutionary optimization approach. Wealso provide a more detailed treatment of parameter extractionsteps required by the GA’s fitness function after the MoM solu-tion has been computed. Although not explicitly made use of inthe present study, Section II-A describes a more general func-tionality implicit in EGO for the design of N-port guided-waveand radiating structures. Section III then presents a detailed rep-resentative patch antenna design case study. We illustrate the

0018-926X/04$20.00 © 2004 IEEE

VILLEGAS et al.: PARALLEL EGO APPLICATION FOR PATCH ANTENNA DESIGN 2425

use of EGO to design a dual-band linearly polarized antenna el-ement for wireless communication (1.9 and 2.4 GHz) applica-tions. The resulting antenna exhibits acceptable dual-band op-eration (i.e., better than 10 dB return loss with 5.3% and 7%operating bandwidths at 1.9 and 2.4 GHz, and 5 dB rejectionbetween bands) while maintaining a cross-pol maximum fieldlevel at least 11 dB below the co-pol maximum.

II. EGO APPLICATION SOFTWARE ARCHITECTURE

In this section, we present an overview of the main func-tional components that make up EGO. The EGO applicationwas designed with versatility in mind, i.e., the ability to handlea given class of problems with a reasonable degree of thorough-ness. Although this paper concerns itself with a particular patchantenna design, EGO is equipped to handle more generalizedpatch topologies. To enact this generality, we make provisionsfor the possibility of multiport antenna structures. As a result,the EM analysis engine is equipped with the ability to extract therelevant parameters, i.e., S-parameters, VSWR, etc. This is de-scribed in Section II-A below. In specifying desired characteris-tics of a radiating structure, one is typically concerned with bothterminal characteristics (e.g., input match, input impedance) aswell as pattern features (e.g., sidelobe levels, far-field distri-bution, polarization). To this end, EGO also incorporates theability to handle such multiobjective goals with the aid of a hy-brid fitness function, described in Section II-B along with somesalient features of the parallel implementation.

A. Method-of-Moments (MoM) Formulation

For the MoM simulations we use HEMI, a hybrid EFIE/MFIEiterative MoM solver developed at UCLA [37]. Among its manyfeatures, HEMI is able to compute the currents on rather largemetallic structures with connected wires by employing a hybridPO/MoM technique that allows one to use the PO approxima-tion over the large smoothly-varying surfaces, combined withan explicit MoM calculation for the currents on the wires andthe surface regions in the vicinity of the junctions. For our par-ticular patch antenna models, we simply invoke HEMI to run infull MoM mode, thus providing us with the most accurate com-putation of the currents on the entire structure. In this mode,HEMI is simply solving the conventional EFIE on the con-ducting surfaces using RWG triangular bases over the 2-D bodysurfaces, and linear interpolating polynomials over the 1-D wiresegments. Since this technique has been extensively covered inthe literature, we will omit the details of the formulation andfocus instead on the particular aspects associated with the GAoptimization scheme.

In particular, the relevant parameters must be extracted fromthe EM simulation for subsequent use by the GA via the fitnessfunction. Hence, the proper choice of parameter set is problem-specific and invariably linked to the fitness function definition.For example, in designing patch antennas, one typically desiresa good input match ( at the th port) over the fre-quency band of interest, and possibly some specific radiationpattern characteristics. To obtain the VSWR for a (generally)multiport antenna structure, we proceed as follows. First, we

make use of generalized network parameters, using an admit-tance matrix representation

......

......

...

(1)The -matrix properly accounts for mutual coupling betweenthe ports, and relates the terminal voltages to currents. Equiv-alently, we could make use of a -matrix or other representa-tion, but (1) is more convenient since the short-circuit currents atthe ports are readily available from the MoM solution. To com-pute the elements, we first define canonical right-handside vectors

...... ...

...(2)

for the MoM linear systems , .Note that here is the interaction (moment) matrix, andshould not be confused with a generalized impedance matrix.Realizing that the right-hand side of (1) is a subset of the MoMcurrents allows us to trivially compute the

elements columnwise, using ,and (2). We should note that the decomposition defined by (2)is quite general, in that any arbitrary excitation and resultingcurrent distribution is obtained via a linear superposition overthis “source basis”

(3)

(4)

where the are known complex scalars. Once we havethe -matrix, the -parameter matrix is obtained using

, with denoting the (diagonal)characteristic admittance matrix. Because of the radiation (andpossible Ohmic) loss present in the antenna, is not unitary,i.e., with denoting the Hermitian conjugate and

the identity matrix. However, it is completely general, andindependent of the load termination(s) on the ports. We canthen choose to work with the -parameters directly, or perhapscharacterize the input match at the th port in terms of an activeVSWR (similar to the concept employed in phased array theory[38]–[40]), defined as follows. We begin by defining an activereflection coefficient at the th port as

(5)

where denotes the forward-wave amplitude into the th port,and are the scattering parameters ( similarlydenotes the backward-wave amplitude at the th port). Note that


(5) above takes into account the th port reflection as well asbackward-wave reflections at the th port due to forward wavesoriginating at the other ports. Note also that (5) revertsback to the conventional definition for a single-port device, i.e.,

. Hence, an N-portactive VSWR is then defined by

(6)

If the remaining ports are load terminated, the th port“sees” a single equivalent load, due to the averaging effect im-plicit in (5). The terms can then be found by applying theappropriate boundary conditions at the loaded ports. In generalthen, . However, if the ports are terminatedin matched loads, , , . In this case, we see that

, and (6) can be replaced by the more conventional ex-pression

(7)

B. Parallel Genetic Algorithm Implementation

PGAPack is a parallel GA library written in C by DavidLevine at Argonne National Laboratory [41]. The librarysupports integer, real, binary, and character-valued native datatypes as well as user-defined types. PGAPack also containsvarious crossover, mutation, and selection operators. TheEGO application manager was written in FORTRAN90, andis responsible for overseeing the optimization run, as well asperforming any relevant post-processing steps. For instance,a fast frequency sweep algorithm was included in EGO as apost-processing feature, to rapidly compute the VSWR data(typically for visualization purposes) over the extended bandof interest. In this mode, the same patch model is identicallyreplicated over the processor pool, with each node computingthe MoM solution at a particular frequency. The mixed-lan-guage (F90/C) application architecture did not present much ofan obstacle because the PGAPack functions are callable fromFORTRAN. It is also noteworthy that function bindings in Cand FORTRAN are quite similar, thus simplifying the librarycalling conventions. Additionally, 2-D and 3-D mesh visual-ization is possible by having EGO generate Tecplot1-specificmodel files.

The Linux clusters are interconnected using both fast 100Mb/s Ethernet and Myrinet (2.4 Gb/s) crossbar networks. Usingthe message passing interface (MPI) user-level library in con-junction with the sequential FORTRAN90 code allows us to im-plement a conventional single-program/multiple-data (SPMD)application model. In essence, MPI provides each compute nodewith an identical copy of the executable to independently run,using a unique input data set. MPI then orchestrates the gath-ering of pertinent output data that is transferred to the “master”processor, on which the GA is running. In the context of the par-allel GA, this basically means that the individual fitness eval-uations (MoM runs) are distributed across the “slave” nodes,

1Amtec Tecplot9.2, www.amtec.com.

each of which is performing the simulation on a unique chromo-some in the population. Since there is literally no communica-tion between the compute nodes and the front-end node duringevaluations, and only a few kBytes of information being trans-ferred during the I/O sequences, our application does not haveto contend with latency and/or bandwidth issues. In addition,proper load balancing is achieved by choosing the percentage ofchromosomes replaced per subsequent generation equal to thenumber of nodes. In other words, the population size and the re-placement percentage are re-computed based on the number ofprocessors using the following rule:

(8)where “ ” denotes the floor function. For example, if we chooseto use processors, and a replacement factor,then using a population of chromosomesensures that at the start of each GA iteration all 26 processorswill be busy evaluating 10 percent of the new generation. Thus,load balancing simply means that the cluster as a whole is beingused as efficiently as possible during the program’s execution.

We can define a speedup factor as , whereis the single-processor execution time, and the -processorexecution time. In general, a given portion of the code is sequen-tial, and the rest is parallelizable. Amdahl’s Law incorporatesthis key concept and expresses the resulting speedup as

(9)

where is the sequential fraction of the code,and is the total number of compute nodes. In EGO ,and we have the ideal case of linear speedup , as aresult of our SPMD implementation with near-zero latency andproper load balancing. This linear factor implies a remarkableacceleration of the execution time, which is in fact what rendersthe use of a full-wave MoM simulator feasible. Under any othercircumstances, we would be forced to use many of the approx-imation schemes reported throughout the literature to alleviatethe heavy resource burden of the EM simulations, and to a cer-tain degree incurring a reduction in the overall accuracy of theresults.

In practice, the accuracy and convergence rate of a GA op-timization scheme depends primarily on two key factors: theparameter encoding scheme and the choice of fitness function.Both of these are fundamentally responsible for setting the set-topological characteristics of the solution space. Although theGA is a very robust technique as a result of its stochastic nature,it is nonetheless prudent to choose a fitness function and an en-coding scheme that is consistent with the underlying physics ofthe problem, since the optimization routine itself has no directknowledge of what in fact is being optimized. In our particularcase, we have chosen to make use of a binary encoding schema,with an -gene chromosome consisting of the OFF/ON subsec-tions of a rectangularly-discretized patch template. The detailsof the implementation will be given in Section III.


Fig. 1. (a) Geometry of the reference “E-patch” design. Note the finite extent of the ground plane, which allows us to quantify back-plane radiation as well. (b)Patch surface discretization into a 2-D rectangular array of 46 binary (ON/OFF) metallic elements. Only half of the physical structure is modeled, thus imposing afield symmetry condition along the E-plane.

The fitness function definition proceeds as follows. At eachfrequency, the mismatch error is the relative deviation of the portactive VSWR from a target value over active ports

(10)

A (least mean-square) measure is used to represent the overallinput match error as

(11)

Note that (11) is a discrete function of frequency. In the GAcontext, each individual of the population is evaluated overthe requisite band, consisting of the same distribution offrequency samples. This ensures that proper load balancingis maintained by the parallel algorithm at run-time, with allMoM evaluations occupying approximately the same amountof time. The total mismatch error over the frequency band isthen determined by a second measure

(12)

In addition, we could also include the possible port-to-porttransmission loss in this error definition by using a hybridfitness

(13)

where , . Here, accounts for the (re-flection) losses, while accounts for the (transmission)losses in an analogous manner. The overall fitness measure overthe frequency band and total number of ports is then taken intoaccount by the objective function , where denotesthe total error due to wave reflection/transmission at the inputports. Assuming we are only interested in designs exhibiting lin-early-polarized fields. we can define a similar objective func-tion for the pattern polarization error, with

. Note that we have defined a simplistic po-larization error based on the axial ratio between the peak cross-and co-polarized components at a single frequency. In principle,one could use Ludwig’s definition and incorporate more elabo-rate schemes. However, the simple definition used here is prac-tical enough for proof-of-concept use. The corresponding fitnessfunction(s) are then given by

(14)

where . The total fitness value is then given by apartition of unity

(15)

Note that the various fitness functions define compact spaces,i.e., coverable by a finite set of open neighborhoods. In essence,it tends to simplify the optimization search significantly becausethe solution space is bounded, and for our applications, typicallycontinuous.

III. PATCH DESIGN STUDY

A. Dual-Band Patch for Wireless Communications

Fig. 1(a) illustrates the reference E-patch configuration firstreported in [42] for broadband wireless communications appli-


Fig. 2. Input return loss of the E-patch design shown in Fig. 1(a). The returnloss of a canonical rectangular patch is shown as well for comparison.

cations. Essentially, the resonant slots serve the purpose of reac-tively loading the patch, which results in a bandwidth increase asshown in Fig. 2. The relevant dimensions are: ,

, , , ,, , and the coaxial feed probe is lo-

cated at and. The height of the patch is from the ground

plane. Note that at 3 GHz. Thus, a dense enoughMoM mesh would ensue if we used cells at thisupper band edge. The discretization scheme imposed on the sur-face conductor for the GA binary chromosome description ofthe patch [2] is shown in Fig. 1(b). The background structure istessellated in the form of a 2-D rectangular array of 48 binary(0/1) elements. The cells are 6 mm 6 mm square each. Eachindividual cell (or allele, in GA parlance) is in turn mapped ontoa RWG triangular basis, thus subdivided into two adjacent trian-gles that share a common edge. Since E-plane field symmetry isimposed (to reduce the cross-pol component), only half the ac-tual patch needs to be encoded for the GA algorithm. Note theprobe feed location along the symmetry plane, with two patchespermanently fixed to the ON (P or 1) state. This ensures thatall models have a probe feed that is electrically connected toa 12 mm 12 mm island at minimum. The balance of the ele-ments are in a free (F) state, waiting to be turned either ON (P)or OFF (0) by a particular chromosome description. As a result,a total of possible patch topologies exist within the solu-tion space. In Fig. 1(b), , , and thecoaxial feed probe is located at and

.Fig. 3 shows the H-plane [the -plane in Fig. 1(a)] far-field

patterns for the E-patch antenna, at 2.1 and 2.5 GHz. Thepatterns have been normalized to a zero dB co-pol peak in thisand all subsequent results shown herein. This should allow thereader to assess the relative cross-pol amplitude levels readily.The cross-pol levels are better than 12 dB down from the co-polin this antenna, due to the E-plane current (and resulting field)symmetry.

Unless otherwise noted, the following GA parameter valuesare applicable to all the results presented in this section: 200generations, 260 chromosomes, selection type is tournament,

Fig. 3. Normalized H-plane (calculated) far-field patterns for the E-patchantenna. Both the co-pol and cross-pol components are shown, at the resonantfrequencies f = 2:1 and 2:5 GHz. Note cross-pol level is 12 dB lower thanco-pol.

Fig. 4. Computed and measured jS j for EGO-optimized patchescorresponding to � = 0:0 and � = 1:0 in (15).

replacement, crossover type is 2-point, crossover proba-bility is , probability of mutation is and con-vergence criteria = total number of generations. The single-pro-cessor execution time for the simulation of an individual chro-mosome is 13 minutes using our development cluster consistingof 32 Pentium III-450 MHz CPUs. Each node of this machinehas 512 MB RAM and an 8 GB hard drive. As an example, withthe abovementioned GA parameter set, performing all 200 it-erations on a single serial machine would take approximately

—a pro-hibitive length of time. The same calculation using 26 nodestakes approximately , i.e.,a 26-fold reduction in the execution time, in accordance with(9). We should note that these figures are approximate in thesense that the th generation requires the initial evaluation ofall 260 chromosomes, which we have neglected for the sake ofsimplifying the comparison.


Fig. 5. Computed and measured jS j for EGO-optimized patches corresponding to (a) � = 0:2; 0:4 and (b) � = 0:6; 0:7 in (15).

Fig. 6. (a) Mean fitness convergence rate and (b) best fitness convergence rate for two typical optimization runs with � = 0:6;0:7.

Fig. 4 shows a comparison between the measured and cal-culated return loss for two particular EGO-optimized designs.One is optimized with , which according to (15) im-plies a fitness function with . In other words, theGA is essentially searching for a patch that yields the optimalpattern polarization characteristics defined earlier. The other has

, i.e., . In this case, the GA is searching fora patch that results in the best input match characteristics at thenew desired resonant frequencies of and GHz.

Similar comparisons for the cases aredepicted in Fig. 5. Note that in these particular cases, (15) re-veals that the optimization is searching for solutions that meetthe desired input match in addition to far-field polarization char-acteristics. The values indicate that in these twocases we’re placing a bit more emphasis on the polarization pu-rity of the far-field radiation, while for we are pri-marily searching for solutions minimizing the input return lossof the patch. Fig. 5(a) shows good agreement between the mea-sured and computed data. Fig. 5(b) shows excellent agreementfor the case, and only a slight 5% shift in resonant fre-quency for the case.

Some discrepancy is evident in the cases. It infact appears to be an issue with the MoM solution for patch

topologies that contain multiply-connected regions, i.e., con-nected only at one or more vertices to the rest of the patchsurface. This peculiarity occurs as a result of the discretizationchosen for the patch surface. The RWG basis functions usedin the MoM algorithm do not allow current through such re-gions connected at isolated points. Nevertheless, a current dis-tribution does exist on these particular elements. It occurs asa consequence of current transfer from continuously (simply)connected regions of the patch via the surrounding edge-con-nected basis functions, as well as induced current from couplingto the surrounding structure. In practice, this should be the iden-tical scenario for the actual antenna, and as such the two areconsistent. However, in the actual device, imprecise etching canlead to either small (but finite-width) channels that allow currentin the vertex-connected regions or small gaps that separate thesingle vertex into two. In either case, the resulting current distri-bution will obviously differ slightly from the computed (ideal)distribution. Hence, it appears that the differences in the resultsfor the aforementioned patches are due to imprecise manufac-turing. This however does bring up an important aspect of GAoptimization. Although the optimized design may perform quitewell (and meet all the requisite electrical specs), it is the respon-sibility of the designer to ensure that the resulting design is in


Fig. 7. (a) Normalized co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter � = 0:0.

fact mechanically feasible, and more importantly, robust withrespect to dimensional and material tolerances. For example, inour particular case, EGO could perhaps include an additionalconstraint that disallows patches with such problematic features,or the patches themselves should be manufactured with tighteretching tolerances.

The GA convergence behavior (fitness value versus genera-tion) for two typical optimization runs [ , 0.7 in (15)] isshown in Fig. 6. The data is based on the GA parameters men-tioned earlier in this section. Note that 200 generations is nom-inally sufficient for the algorithm to achieve convergence. Theevolution of the average fitness is shown in Fig. 6(a), while thatof the fittest chromosome is depicted in Fig. 6(b). Note the typ-ical GA behavior, wherein the fittest individual remains dom-inant over several generations before exhibiting a discrete in-crease as the overall mean fitness of the population increasesmonotonically.

Fig. 7 shows the normalized H-plane co-pol andcross-pol far-field patterns for the GA-patch having afitness parameter of , at and 2.4 GHz. TheE-plane patterns are omitted here in the interest of brevity. Thisshould not be a hindrance since we are primarily interested inthe cross-pol characteristics of the patch designs. The patchesreside on a finite ground plane of dimensions referred to inFig. 1. The calculated cross-pol levels are at least 15 dB downfrom the zero dB co-pol peak, which is expected since the GAin this case is strictly optimizing the pattern characteristics. Theactual measured patch for the case is depicted in Fig. 8.The patch resides on a thin low-permittivity sheetfor ease of manufacturing as well as structural support. Notethat a continuous current path exists from the feed “island” tothe rest of the patch, i.e., the feed is not reactively-coupled tothe radiating element. This is interesting because we have notexplicitly imposed such a constraint on the physical attributesof the patch topology in the GA. A similar graph is shown inFig. 9 for the case.

The normalized H-plane patterns for the case areshown in Fig. 10, and for in Fig. 11. A similar graphis shown in Fig. 12 for the case. Here, the calculatedcross-pol is 10 dB down from the co-pol peak. In comparison

Fig. 8. Actual measured patch for the � = 0:0 case. Note the low-permittivitysheet used for structural support.

to the , this relatively higher cross-pol level is the re-sult of optimizing over a different fitness landscape. In otherwords, (15) implies that , thus placinga greater emphasis on the antenna’s input match characteristics.This can be correlated to a diminished emphasis on the polar-ization characteristics [the complimentary quantity in (15)], aninherent feature of using a partition of unity.

Fig. 13 shows a comparison of the normalized measured andcalculated H-plane co-pol and cross-pol far-field patterns for the

GA patch, shown in Fig. 14. This particular configu-ration turns out to be the optimal choice of for our proposeddesign criteria, based on our heuristic design approach. Excel-lent agreement is observed at both operating frequencies. Themeasured cross-pol levels are 5 dB higher than those calculated.However, we should note that the measurements were a bit trou-blesome for the available test chamber (an anechoic chamberequipped with an HP 8510B network analyzer and 8363A sweptsource), which has an operating bandwidth lying slightly abovethe test frequencies of our antenna.

The patterns corresponding to fitness parameter areshown in Fig. 15. In Fig. 16, we have the normalized H-planethe patterns for the case. The patch topology is shownin Fig. 17. The cross-pol levels are less than 10 dB lower thanthe peak co-pol as expected since in this case , i.e.,we are optimizing the input VSWR exclusively.


Fig. 9. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter � = 0:2.






Fig. 14. Actual measured patch for the � = 0:7 case.

Based on a heuristic design approach and the foregoing data,the case apparently yields a suitable combination ofinput match and pattern characteristics.

IV. CONCLUSION

In this article, we have presented an EGO application that hasbeen developed for the cluster supercomputing platform. The

application (based on the Single-Program/Multiple Data archi-tecture model) results in a linear speedup factor, with perfor-mance that is basically proportional to the number of processornodes. As a result, we are able to make use of HEMI, a full-waveMoM solver to fulfill the task of performing the electromagneticanalysis of the antenna structures. The GA portion of the ap-plication is handled by PGAPack, a parallel GA library that isquite powerful and customizable. Making use of a hybrid fitnessfunction in the GA, we were able to heuristically explore theparameter/solution space (over ) while concurrently allowingthe GA to find the global maximum for . As a result of thisparticular tool configuration, EGO allows us to combine the ac-curacy of full-wave EM analysis with the robustness of GA op-timization and the speed of the parallel computing environment.To illustrate EGO’s usefulness, a representative patch antennadesign example for commercial wireless applications was de-tailed. We described the design of a dual-band antenna elementfor wireless communication (1.9 and 2.4 GHz) applications. Theoptimal patch geometry was found at , and measure-ments of this GA-optimized configuration exhibited good agree-ment with calculations. The resulting antenna exhibited accept-able dual-band operation (e.g., better than 10 dB input match




Fig. 17. Actual measured patch for the � = 1:0 case.

with 5.3% and 7% operating bandwidths at 1.9 and 2.4 GHz)while maintaining a cross-pol maximum field level at least 11dB below the co-pol maximum.

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Frank J. Villegas (S’92–M’95) was born in LaHabana, Cuba, in 1964. He received the B.S.E.E. andM.S.E.E. degrees from the University of Houston,Houston, TX, in 1993 and 1995, respectively, andthe Ph.D. degree in electrical engineering from theUniversity of California at Los Angeles, in 2002.

From 1993 to 1995, he was a Research Assistantin the Department of Electrical and Computer Engi-neering, University of Houston, studying leaky modecharacteristics in planar waveguide structures. From1995 to 1998, he was with TRW ES&TD, Redondo

Beach, CA, engaged in the design of passive microwave, millimeter-waveand MMIC components, and MMIC packaging issues. From 1998 to 1999,he was with WaveBand Corporation, Torrance, CA, working on R&D ofmillimeter-wave scanning antennas for military and commercial applications,such as imaging and collision avoidance radar. From 1999 to 2002, he waswith the High Performance Computing Group, Jet Propulsion Laboratory(JPL), Pasadena, CA, where he was mainly involved in various projects dealingwith the application of parallel processing solutions to electromagnetic designproblems, e.g., parallel genetic algorithm (GA) optimization for novel planarantenna designs, using multinode Beowulf supercomputers. From 2002 to2003, he was with Raytheon Electronic Systems, El Segundo, CA, workingon phased-array antenna subsystems design for airborne radar applications.Currently, he is with The Aerospace Corporation, El Segundo, CA, workingon phased-array systems analysis and the development of computationalelectromagnetics tools for antenna design. He has written various journaland conference publications. His research interests include electromagneticapplications of periodic structures (e.g., phased arrays), traveling (leaky) waveand microstrip antennas, evolutionary (GA) optimization, leakage phenomenain planar waveguide circuits, and numerical techniques in electromagnetics.


Tom Cwik (S’79–M’79–SM’94–F’01) was born inChicago, IL. He received the B.S., M.S., and Ph.D.degrees in electrical engineering from the Universityof Illinois, Urbana-Champaign, in 1979, 1981, and1986, respectively.

After receiving the M.S. degree, he spent thesummer at the Very Large Array, National RadioAstronomy Laboratory, Socorro, NM. Followingthis Assistantship, he spent the following year atthe Joint Institute for Laboratory Astrophysics,National Bureau of Standards (Now NIST), Boulder

CO. Upon completion of the Ph.D. degree, he was awarded a PostdoctoralFellowship at the Electronics Research Laboratory, Norwegian Institute ofTechnology, Trondheim, Norway. Since 1988, he has been at the Jet PropulsionLaboratory (JPL), Pasadena, CA, where he is currently Manager of the EarthScience Instruments & Technology Office. Prior to this position he wasTechnical Group Supervisor of JPL’s High Performance Computing Group.He is an Affiliate Professor in the Department of Electrical Engineering,University of Washington, Seattle and a Principal Member of the Laboratoryat JPL. He has led a team that proposed and was awarded the NASA flightmission Aquarius, a mission to be launched later this decade to measure seasurface salinity from space. His work has included the development and useof integrated electromagnetic design tools for instrument design at proposaland build stages; the invention and analysis of microdevice components forelectromagnetic coupling and filtering in remote sensing instruments; andalgorithm development for high performance computational electromagneticapplications. He has made contributions to frequency selective surface designand analysis and asymptotic analysis in reflector antenna systems. He hasedited one book and one journal special issue, published seven book chapters,over 30 refereed journal papers, and 108 conference papers. He is the coauthorof the patent Efficient Radiation Coupling to Quantum-Well Radiation-SensingArray via Evanescent Waves

Dr. Cwik was a Fellow at the Texas Institute for Computational and AppliedMathematics in 1997, and received the IEEE Gordon Bell Award Finalist awardin 1992 for parallel processing research.

Yahya Rahmat-Samii (S’73–M’75–SM’79–F’85)received the M.S. and Ph.D. degrees in electricalengineering from the University of Illinois, Ur-bana-Champaign.

He was a Guest Professor with the TechnicalUniversity of Denmark (TUD) during summer 1986.He was a Senior Research Scientist at NASA’sJet Propulsion Laboratory, California Institute ofTechnology, Pasadena, before joining the Univer-sity of California, Los Angeles (UCLA) in 1989.Currently, he is a Professor and the Chairman of

the Electrical Engineering Department, UCLA. He has also been a Consul-tant to many aerospace companies. He has been Editor and Guest Editor ofmany technical journals and book publication entities. He has authored andcoauthored more than 500 technical journal articles and conference papersand has written 17 book chapters. He is the coauthor of Impedance BoundaryConditions in Electromagnetics (Washington, DC: Taylor & Francis, 1995)and Electromagnetic Optimization by Genetic Algorithms (New York: Wiley,1999). He is also the holder of several patents. He has had pioneering researchcontributions in diverse areas of electromagnetics, antennas, measurementand diagnostics techniques, numerical and asymptotic methods, satellite andpersonal communications, human/antenna interactions, frequency selectivesurfaces, electromagnetic band-gap structures and the applications of thegenetic algorithms, etc., (visit http://www.antlab.ee.ucla.edu). On severaloccasions, his work has made the cover of many magazines and has beenfeatured on several TV newscasts.

Dr. Rahmat-Samii is a Member of Sigma Xi, Eta Kappa Nu, CommissionsA, B, J, and K of the United States National Committee for the InternationalUnion for Radio Science (USNC/URSI), Antennas Measurement TechniquesAssociation (AMTA), and the Electromagnetics Academy. He was elected as aFellow of the Institute of Advances in Engineering (IAE) in 1986. Since 1987,he has been designated every three years as one of the Academy of Science’sResearch Council Representatives to the URSI General Assemblies held in var-ious parts of the world. In 2001, he was elected as the Foreign Member of theRoyal Academy of Belgium for Science and the Arts. He was also a memberof UCLA’s Graduate council for a period of three years. For his contributions,he has received numerous NASA and JPL Certificates of Recognition. In 1984,he received the coveted Henry Booker Award of the URSI which is given tri-ennially to the Most Outstanding Young Radio Scientist in North America. In1992 and 1995, he was the recipient of the Best Application Paper Prize Award(Wheeler Award) for papers published in the 1991 and 1993 IEEE ANTENNAS

AND PROPAGATION. In 1999, he was the recipient of the University of IllinoisECE Distinguished Alumni Award. In 2000, he was the recipient of IEEE ThirdMillennium Medal and AMTA Distinguished Achievement Award. In 2001,he was the recipient of the Honorary Doctorate in physics from the Univer-sity of Santiago de Compostela, Spain. In 1993, 1994, and 1995, three of hisPh.D. students were named the Most Outstanding Ph.D. Students at UCLA’sSchool of Engineering and Applied Science. Seven others received various Stu-dent Paper Awards at the 1993 to 2002 IEEE AP-S/URSI Symposiums. He wasalso a Member of the Strategic Planning and Review Committee (SPARC) ofthe IEEE. He was the IEEE AP-S Los Angeles Chapter Chairman (1987–1989)and his chapter won the Best Chapter Awards in two consecutive years. He wasthe elected 1995 President and 1994 Vice-President of the IEEE Antennas andPropagation Society. He was one of the Directors and Vice President of the An-tennas Measurement Techniques Association (AMTA) for three years. He wasappointed an IEEE Antennas and Propagation Society Distinguished Lecturerand presented lectures internationally. He has been the plenary and millenniumsession speaker at many national and international symposia. He has also servedas Chairman and Co-Chairman of several national and international symposia.He is listed in Who’s Who in America, Who’s Who in Frontiers of Science andTechnology, and Who’s Who in Engineering He is the designer of the IEEE An-tennas and Propagation Society logo that is displayed on all IEEE ANTENNAS

AND PROPAGATION publications.

Majid Manteghi was born in Aligodarz, Iran, onApril 14, 1971. He received the B.S and M.S. degreesin electrical engineering from The University ofTehran, Tehran, Iran, 1993 and 1997, respectively.He is currently working toward the Ph.D. degreein electrical engineering, with emphasis on appliedelectromagnetics and antennas, at The University ofCalifornia, Los Angeles (UCLA).

From 1994 to 1997, he was a Research Assistantin the Microwave Laboratory, University of Tehran,where he worked on microstrip patch antennas,

array designs, traveling wave antennas, handset antennas, base transceiverstation (BTS) single and dual polarized antennas, reflector antennas, andUHF transceiver circuits and systems. From 1997 to 2000, he worked in thetelecommunication industry in Tehran where he served as the head of an RFgroup for a GSM BTS project. In fall 2000, he joined to the Antenna Research,Analysis, and Measurement Laboratory (ARAM), UCLA. His research areaincludes ultrawide-band impulse radiating antennas, miniaturized patch an-tennas, multiport antennas, and dual frequency dual polarized stacked patcharray designs.

(ego) application for patch antenna design

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