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A Parallel Electromagnetic Genetic-Algorithm Optimization (EGO) Application for Patch Antenna Design Frank 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 genetic algorithm (GA) optimization (EGO) application developed for the cluster supercomputing platform. A representative patch antenna design example for commercial wireless applications is detailed, which illustrates the versatility and applicability of the method. We show that EGO allows us to combine the accuracy of full-wave EM analysis with the robustness of GA optimization and the speed of a parallel computing algorithm. A representative patch antenna design case study is presented. We illustrate the use of EGO to design a dual-band antenna element for wireless communication (1.9 and 2.4 GHz) applications. The resulting antenna exhibits acceptable dual-band operation (i.e., better than 10 dB return loss with 5.3 and 7% operating bandwidths at 1.9 and 2.4 GHz) while maintaining a cross-pol maximum field level at least 11 dB below the co-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 emphasis on increasingly stringent system requirements in both the commercial as well as military sectors, in addition to maintaining low costs in manufacturing, operations and maintenance. For the military, the new paradigm shift is toward network-centric warfare, wherein a major emphasis is placed on the complex interaction between the various information subsystems that comprise a complete military system. Hence, the desire is to obtain a system that is capable of reconnaissance, data analysis, ordnance control, communications, etc., all in a real-time setting via an ad hoc virtual network. Antenna designs for both groundand airborne-based subsystems present a unique challenge, in that they should be as simple as possible and low-cost while at the 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 3 G wireless technology, broadband cellular technology that handles 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 Laboratory, Pasadena, CA 91109 USA. Y. Rahmat-Samii and M. Manteghi are with the Antenna Research and Measurement Laboratory, Department of Electrical Engineering, University of 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 remarkable specifications in terms of bandwidth, gain, multiband operation, and physical (e.g., size) constraints. As a result, designers have had to turn to ever-more ingenious methods to achieve these goals. A technique that has become quite popular over the last several years has been the use of evolutionary optimization strategies for electromagnetic design. In particular, the use of genetic algorithms (GA) has exploded onto the research scene with great success, predominantly due to its particular characteristics that make it an ideal tool that marries quite well with existing EM analysis techniques [1]–[5], and typically yields results that satisfy the given requirements in a nonintuitive fashion. A great deal of effort has already been expended in furthering both the computational maturity of GA optimization in electromagnetics [3], [6]–[8], as well as in extending the domain of applications to include quite ingenious designs [9]–[18]. Two distinct focus areas in which GA optimization has yielded quite fruitful results are novel pattern synthesis [19]–[30] and broadband (or multiband) operation [31]–[34]. Another area in which the use of GA designs shows promise is the development of “smart” antennas [35]. In this article, we describe an electromagnetic GA optimization (EGO) application (introduced in [36]) that has been developed for the cluster supercomputing platform, and is thus quite powerful and apropos for today’s tough antenna design problems. A representative patch antenna design example for commercial applications is detailed, which illustrates the versatility and applicability of the method. We show that EGO allows us to combine the accuracy of full-wave EM analysis with the robustness of GA optimization and the speed of a parallel computing algorithm. In Section II, the EGO application software architecture proposed in [36] is presented in greater detail, i.e., the EM analysis procedure and parallel infrastructure is fully developed. In particular, we present a more in-depth development of the parallel application architecture. The single-program multiple data model is in essence a key feature that allows us to use the more accurate full-wave method of moments (MoM) simulations in conjunction with the evolutionary optimization approach. We also provide a more detailed treatment of parameter extraction steps required by the GA’s fitness function after the MoM solution has been computed. Although not explicitly made use of in the present study, Section II-A describes a more general functionality implicit in EGO for the design of N-port guided-wave and radiating structures. Section III then presents a detailed representative patch antenna design case study. We illustrate the
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use of EGO to design a dual-band linearly polarized antenna element for wireless communication (1.9 and 2.4 GHz) applications. The resulting antenna exhibits acceptable dual-band operation (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 rejection between bands) while maintaining a cross-pol maximum field level at least 11 dB below the co-pol maximum. II. EGO APPLICATION SOFTWARE ARCHITECTURE In this section, we present an overview of the main functional components that make up EGO. The EGO application was designed with versatility in mind, i.e., the ability to handle a given class of problems with a reasonable degree of thoroughness. Although this paper concerns itself with a particular patch antenna design, EGO is equipped to handle more generalized patch topologies. To enact this generality, we make provisions for the possibility of multiport antenna structures. As a result, the EM analysis engine is equipped with the ability to extract the relevant parameters, i.e., S-parameters, VSWR, etc. This is described in Section II-A below. In specifying desired characteristics of a radiating structure, one is typically concerned with both terminal characteristics (e.g., input match, input impedance) as well as pattern features (e.g., sidelobe levels, far-field distribution, polarization). To this end, EGO also incorporates the ability to handle such multiobjective goals with the aid of a hybrid fitness function, described in Section II-B along with some salient features of the parallel implementation. A. Method-of-Moments (MoM) Formulation For the MoM simulations we use HEMI, a hybrid EFIE/MFIE iterative MoM solver developed at UCLA [37]. Among its many features, HEMI is able to compute the currents on rather large metallic structures with connected wires by employing a hybrid PO/MoM technique that allows one to use the PO approximation over the large smoothly-varying surfaces, combined with an explicit MoM calculation for the currents on the wires and the surface regions in the vicinity of the junctions. For our particular patch antenna models, we simply invoke HEMI to run in full MoM mode, thus providing us with the most accurate computation of the currents on the entire structure. In this mode, HEMI is simply solving the conventional EFIE on the conducting surfaces using RWG triangular bases over the 2-D body surfaces, and linear interpolating polynomials over the 1-D wire segments. Since this technique has been extensively covered in the literature, we will omit the details of the formulation and focus instead on the particular aspects associated with the GA optimization scheme. In particular, the relevant parameters must be extracted from the EM simulation for subsequent use by the GA via the fitness function. Hence, the proper choice of parameter set is problemspecific and invariably linked to the fitness function definition. For example, in designing patch antennas, one typically desires a good input match ( at the th port) over the frequency band of interest, and possibly some specific radiation pattern characteristics. To obtain the VSWR for a (generally) multiport antenna structure, we proceed as follows. First, we
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make use of generalized network parameters, using an admittance matrix representation
.. .
.. .
.. .
.. .
.. .
(1) The -matrix properly accounts for mutual coupling between the ports, and relates the terminal voltages to currents. Equivalently, we could make use of a -matrix or other representation, but (1) is more convenient since the short-circuit currents at the ports are readily available from the MoM solution. To comelements, we first define canonical right-hand pute the side vectors
.. .
.. .
.. .
.. .
(2)
for the MoM linear systems , . here is the interaction (moment) matrix, and Note that should not be confused with a generalized impedance matrix. Realizing that the right-hand side of (1) is a subset of the MoM allows us to trivially compute the currents elements columnwise, using , and (2). We should note that the decomposition defined by (2) is quite general, in that any arbitrary excitation and resulting current distribution is obtained via a linear superposition over this “source basis” (3) (4) are known complex scalars. Once we have where the -matrix, the -parameter matrix is obtained using the , with denoting the (diagonal) characteristic admittance matrix. Because of the radiation (and possible Ohmic) loss present in the antenna, is not unitary, with denoting the Hermitian conjugate and i.e., the identity matrix. However, it is completely general, and independent of the load termination(s) on the ports. We can then choose to work with the -parameters directly, or perhaps characterize the input match at the th port in terms of an active VSWR (similar to the concept employed in phased array theory [38]–[40]), defined as follows. We begin by defining an active reflection coefficient at the th port as (5) where denotes the forward-wave amplitude into the th port, are the scattering parameters ( similarly and denotes the backward-wave amplitude at the th port). Note that
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(5) above takes into account the th port reflection as well as backward-wave reflections at the th port due to forward waves ports. Note also that (5) reverts originating at the other back to the conventional definition for a single-port device, i.e., . Hence, an N-port active 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 imterms can then be found by applying the plicit in (5). The appropriate boundary conditions at the loaded ports. In general . However, if the ports are terminated then, , , . In this case, we see that in matched loads, , and (6) can be replaced by the more conventional expression (7)
B. Parallel Genetic Algorithm Implementation PGAPack is a parallel GA library written in C by David Levine at Argonne National Laboratory [41]. The library supports integer, real, binary, and character-valued native data types as well as user-defined types. PGAPack also contains various crossover, mutation, and selection operators. The EGO application manager was written in FORTRAN90, and is responsible for overseeing the optimization run, as well as performing any relevant post-processing steps. For instance, a fast frequency sweep algorithm was included in EGO as a post-processing feature, to rapidly compute the VSWR data (typically for visualization purposes) over the extended band of interest. In this mode, the same patch model is identically replicated over the processor pool, with each node computing the MoM solution at a particular frequency. The mixed-language (F90/C) application architecture did not present much of an obstacle because the PGAPack functions are callable from FORTRAN. It is also noteworthy that function bindings in C and FORTRAN are quite similar, thus simplifying the library calling conventions. Additionally, 2-D and 3-D mesh visualization is possible by having EGO generate Tecplot1-specific model files. The Linux clusters are interconnected using both fast 100 Mb/s Ethernet and Myrinet (2.4 Gb/s) crossbar networks. Using the message passing interface (MPI) user-level library in conjunction with the sequential FORTRAN90 code allows us to implement a conventional single-program/multiple-data (SPMD) application model. In essence, MPI provides each compute node with an identical copy of the executable to independently run, using a unique input data set. MPI then orchestrates the gathering of pertinent output data that is transferred to the “master” processor, on which the GA is running. In the context of the parallel GA, this basically means that the individual fitness evaluations (MoM runs) are distributed across the “slave” nodes, 1Amtec
Tecplot9.2, www.amtec.com.
each of which is performing the simulation on a unique chromosome in the population. Since there is literally no communication between the compute nodes and the front-end node during evaluations, and only a few kBytes of information being transferred during the I/O sequences, our application does not have to contend with latency and/or bandwidth issues. In addition, proper load balancing is achieved by choosing the percentage of chromosomes replaced per subsequent generation equal to the number of nodes. In other words, the population size and the replacement percentage are re-computed based on the number of processors using the following rule:
(8) where “ ” denotes the floor function. For example, if we choose processors, and a replacement factor, to use chromosomes then using a population of ensures that at the start of each GA iteration all 26 processors will be busy evaluating 10 percent of the new generation. Thus, load balancing simply means that the cluster as a whole is being used as efficiently as possible during the program’s execution. , where We can define a speedup factor as is the single-processor execution time, and the -processor execution time. In general, a given portion of the code is sequential, and the rest is parallelizable. Amdahl’s Law incorporates this key concept and expresses the resulting speedup as (9) where is the sequential fraction of the code, is the total number of compute nodes. In EGO , and , as a and we have the ideal case of linear speedup result of our SPMD implementation with near-zero latency and proper load balancing. This linear factor implies a remarkable acceleration of the execution time, which is in fact what renders the use of a full-wave MoM simulator feasible. Under any other circumstances, we would be forced to use many of the approximation schemes reported throughout the literature to alleviate the heavy resource burden of the EM simulations, and to a certain degree incurring a reduction in the overall accuracy of the results. In practice, the accuracy and convergence rate of a GA optimization scheme depends primarily on two key factors: the parameter encoding scheme and the choice of fitness function. Both of these are fundamentally responsible for setting the settopological characteristics of the solution space. Although the GA is a very robust technique as a result of its stochastic nature, it is nonetheless prudent to choose a fitness function and an encoding scheme that is consistent with the underlying physics of the problem, since the optimization routine itself has no direct knowledge of what in fact is being optimized. In our particular case, we have chosen to make use of a binary encoding schema, with an -gene chromosome consisting of the OFF/ON subsections of a rectangularly-discretized patch template. The details of the implementation will be given in Section III.
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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 a field symmetry condition along the E-plane.
The fitness function definition proceeds as follows. At each frequency, the mismatch error is the relative deviation of the port active VSWR from a target value over active ports
(10) A (least mean-square) measure is used to represent the overall input match error as
(11)
Note that (11) is a discrete function of frequency. In the GA context, each individual of the population is evaluated over the requisite band, consisting of the same distribution of frequency samples. This ensures that proper load balancing is maintained by the parallel algorithm at run-time, with all MoM evaluations occupying approximately the same amount of time. The total mismatch error over the frequency band is then determined by a second measure
, . Here, accounts for the (rewhere accounts for the (transmission) flection) losses, while losses in an analogous manner. The overall fitness measure over the frequency band and total number of ports is then taken into , where denotes account by the objective function the total error due to wave reflection/transmission at the input ports. Assuming we are only interested in designs exhibiting linearly-polarized fields. we can define a similar objective funcfor the pattern polarization error, with tion . Note that we have defined a simplistic polarization error based on the axial ratio between the peak crossand co-polarized components at a single frequency. In principle, one could use Ludwig’s definition and incorporate more elaborate schemes. However, the simple definition used here is practical enough for proof-of-concept use. The corresponding fitness function(s) are then given by (14) where partition of unity
. The total fitness value is then given by a
(15) (12)
In addition, we could also include the possible port-to-port transmission loss in this error definition by using a hybrid fitness
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 because the solution space is bounded, and for our applications, typically continuous. III. PATCH DESIGN STUDY A. Dual-Band Patch for Wireless Communications
(13)
Fig. 1(a) illustrates the reference E-patch configuration first reported in [42] for broadband wireless communications appli-
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Fig. 2. Input return loss of the E-patch design shown in Fig. 1(a). The return loss of a canonical rectangular patch is shown as well for comparison.
cations. Essentially, the resonant slots serve the purpose of reactively loading the patch, which results in a bandwidth increase as , shown in Fig. 2. The relevant dimensions are: , , , , , , and the coaxial feed probe is loand cated at . The height of the patch is from the ground plane. Note that at 3 GHz. Thus, a dense enough cells at this MoM mesh would ensue if we used upper band edge. The discretization scheme imposed on the surface conductor for the GA binary chromosome description of the patch [2] is shown in Fig. 1(b). The background structure is tessellated in the form of a 2-D rectangular array of 48 binary (0/1) elements. The cells are 6 mm 6 mm square each. Each individual cell (or allele, in GA parlance) is in turn mapped onto a RWG triangular basis, thus subdivided into two adjacent triangles that share a common edge. Since E-plane field symmetry is imposed (to reduce the cross-pol component), only half the actual patch needs to be encoded for the GA algorithm. Note the probe feed location along the symmetry plane, with two patches permanently fixed to the ON (P or 1) state. This ensures that all models have a probe feed that is electrically connected to a 12 mm 12 mm island at minimum. The balance of the elements are in a free (F) state, waiting to be turned either ON (P) or OFF (0) by a particular chromosome description. As a result, possible patch topologies exist within the solua total of , , and the tion space. In Fig. 1(b), coaxial feed probe is located at and . Fig. 3 shows the H-plane [the -plane in Fig. 1(a)] far-field 2.1 and 2.5 GHz. The patterns for the E-patch antenna, at patterns have been normalized to a zero dB co-pol peak in this and all subsequent results shown herein. This should allow the reader to assess the relative cross-pol amplitude levels readily. The cross-pol levels are better than 12 dB down from the co-pol in this antenna, due to the E-plane current (and resulting field) symmetry. Unless otherwise noted, the following GA parameter values are applicable to all the results presented in this section: 200 generations, 260 chromosomes, selection type is tournament,
Fig. 3. Normalized H-plane (calculated) far-field patterns for the E-patch antenna. Both the co-pol and cross-pol components are shown, at the resonant frequencies f = 2:1 and 2:5 GHz. Note cross-pol level is 12 dB lower than co-pol.
Fig. 4. Computed and measured jS j for EGO-optimized patches corresponding to = 0:0 and = 1:0 in (15).
replacement, crossover type is 2-point, crossover probability is , probability of mutation is and convergence criteria = total number of generations. The single-processor execution time for the simulation of an individual chromosome is 13 minutes using our development cluster consisting of 32 Pentium III-450 MHz CPUs. Each node of this machine has 512 MB RAM and an 8 GB hard drive. As an example, with the abovementioned GA parameter set, performing all 200 iterations on a single serial machine would take approximately —a prohibitive length of time. The same calculation using 26 nodes , i.e., takes approximately a 26-fold reduction in the execution time, in accordance with (9). We should note that these figures are approximate in the sense that the th generation requires the initial evaluation of all 260 chromosomes, which we have neglected for the sake of simplifying the comparison.
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Fig. 5.
Computed and measured jS
Fig. 6.
(a) Mean fitness convergence rate and (b) best fitness convergence rate for two typical optimization runs with = 0:6; 0:7.
j
for EGO-optimized patches corresponding to (a) = 0:2; 0:4 and (b) = 0:6; 0:7 in (15).
Fig. 4 shows a comparison between the measured and calculated return loss for two particular EGO-optimized designs. , which according to (15) imOne is optimized with plies a fitness function with . In other words, the GA is essentially searching for a patch that yields the optimal pattern polarization characteristics defined earlier. The other has , i.e., . In this case, the GA is searching for a patch that results in the best input match characteristics at the and GHz. new desired resonant frequencies of cases are Similar comparisons for the depicted in Fig. 5. Note that in these particular cases, (15) reveals that the optimization is searching for solutions that meet the desired input match in addition to far-field polarization charvalues indicate that in these two acteristics. The cases we’re placing a bit more emphasis on the polarization puwe are pririty of the far-field radiation, while for marily searching for solutions minimizing the input return loss of the patch. Fig. 5(a) shows good agreement between the measured and computed data. Fig. 5(b) shows excellent agreement case, and only a slight 5% shift in resonant frefor the case. quency for the cases. It in Some discrepancy is evident in the fact appears to be an issue with the MoM solution for patch
topologies that contain multiply-connected regions, i.e., connected only at one or more vertices to the rest of the patch surface. This peculiarity occurs as a result of the discretization chosen for the patch surface. The RWG basis functions used in the MoM algorithm do not allow current through such regions connected at isolated points. Nevertheless, a current distribution does exist on these particular elements. It occurs as a consequence of current transfer from continuously (simply) connected regions of the patch via the surrounding edge-connected basis functions, as well as induced current from coupling to the surrounding structure. In practice, this should be the identical scenario for the actual antenna, and as such the two are consistent. However, in the actual device, imprecise etching can lead to either small (but finite-width) channels that allow current in the vertex-connected regions or small gaps that separate the single vertex into two. In either case, the resulting current distribution will obviously differ slightly from the computed (ideal) distribution. Hence, it appears that the differences in the results for the aforementioned patches are due to imprecise manufacturing. This however does bring up an important aspect of GA optimization. Although the optimized design may perform quite well (and meet all the requisite electrical specs), it is the responsibility of the designer to ensure that the resulting design is in
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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 with respect to dimensional and material tolerances. For example, in our particular case, EGO could perhaps include an additional constraint that disallows patches with such problematic features, or the patches themselves should be manufactured with tighter etching tolerances. The GA convergence behavior (fitness value versus genera, 0.7 in (15)] is tion) for two typical optimization runs [ shown in Fig. 6. The data is based on the GA parameters mentioned earlier in this section. Note that 200 generations is nominally sufficient for the algorithm to achieve convergence. The evolution of the average fitness is shown in Fig. 6(a), while that of the fittest chromosome is depicted in Fig. 6(b). Note the typical GA behavior, wherein the fittest individual remains dominant over several generations before exhibiting a discrete increase as the overall mean fitness of the population increases monotonically. and Fig. 7 shows the normalized H-plane co-pol far-field patterns for the GA-patch having a cross-pol , at and 2.4 GHz. The fitness parameter of E-plane patterns are omitted here in the interest of brevity. This should not be a hindrance since we are primarily interested in the cross-pol characteristics of the patch designs. The patches reside on a finite ground plane of dimensions referred to in Fig. 1. The calculated cross-pol levels are at least 15 dB down from the zero dB co-pol peak, which is expected since the GA in this case is strictly optimizing the pattern characteristics. The case is depicted in Fig. 8. actual measured patch for the The patch resides on a thin low-permittivity sheet for ease of manufacturing as well as structural support. Note that a continuous current path exists from the feed “island” to the rest of the patch, i.e., the feed is not reactively-coupled to the radiating element. This is interesting because we have not explicitly imposed such a constraint on the physical attributes of the patch topology in the GA. A similar graph is shown in case. Fig. 9 for the The normalized H-plane patterns for the case are in Fig. 11. A similar graph shown in Fig. 10, and for case. Here, the calculated is shown in Fig. 12 for the cross-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-permittivity sheet used for structural support.
to the , this relatively higher cross-pol level is the result of optimizing over a different fitness landscape. In other , thus placing words, (15) implies that a greater emphasis on the antenna’s input match characteristics. This can be correlated to a diminished emphasis on the polarization characteristics [the complimentary quantity in (15)], an inherent feature of using a partition of unity. Fig. 13 shows a comparison of the normalized measured and calculated H-plane co-pol and cross-pol far-field patterns for the GA patch, shown in Fig. 14. This particular configuration turns out to be the optimal choice of for our proposed design criteria, based on our heuristic design approach. Excellent agreement is observed at both operating frequencies. The measured cross-pol levels are 5 dB higher than those calculated. However, we should note that the measurements were a bit troublesome for the available test chamber (an anechoic chamber equipped with an HP 8510B network analyzer and 8363A swept source), which has an operating bandwidth lying slightly above the test frequencies of our antenna. are The patterns corresponding to fitness parameter shown in Fig. 15. In Fig. 16, we have the normalized H-plane case. The patch topology is shown the patterns for the in Fig. 17. The cross-pol levels are less than 10 dB lower than , i.e., the peak co-pol as expected since in this case we are optimizing the input VSWR exclusively.
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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. 10. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 0:4.
Fig. 11. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 0:5.
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Fig. 12. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 0:6.
Fig. 13. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 0:7.
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 of input match and pattern characteristics. IV. CONCLUSION In this article, we have presented an EGO application that has been developed for the cluster supercomputing platform. The
application (based on the Single-Program/Multiple Data architecture model) results in a linear speedup factor, with performance that is basically proportional to the number of processor nodes. As a result, we are able to make use of HEMI, a full-wave MoM solver to fulfill the task of performing the electromagnetic analysis of the antenna structures. The GA portion of the application is handled by PGAPack, a parallel GA library that is quite powerful and customizable. Making use of a hybrid fitness function in the GA, we were able to heuristically explore the parameter/solution space (over ) while concurrently allowing the GA to find the global maximum for . As a result of this particular tool configuration, EGO allows us to combine the accuracy of full-wave EM analysis with the robustness of GA optimization and the speed of the parallel computing environment. To illustrate EGO’s usefulness, a representative patch antenna design example for commercial wireless applications was detailed. We described the design of a dual-band antenna element for wireless communication (1.9 and 2.4 GHz) applications. The , and measureoptimal patch geometry was found at ments of this GA-optimized configuration exhibited good agreement with calculations. The resulting antenna exhibited acceptable dual-band operation (e.g., better than 10 dB input match
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Fig. 15. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 0:8.
Fig. 16. Normalized (a) co-pol and (b) cross-pol far-field components for the GA patch topology corresponding to the fitness parameter = 1:0. [2] [3]
[4]
[5]
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 11 dB below the co-pol maximum.
[6]
[7]
[8]
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[10] Y. Rahmat-Samii and H. Mosallaei, “GA optimized Luneberg lens antennas; characterizations and measurements,” in Proc. Int. Symp. Antennas and Propagation, Aug. 2000, pp. 979–982. [11] H. Mosallaei and Y. Rahmat-Samii, “Non-uniform Luneburg lens antennas: a design approach based on genetic algorithms,” in IEEE Antennas and Propagation Soc. Int. Symp. Dig., July 1999, pp. 434–437. , “RCS reduction of canonical targets using genetic algorithm [12] synthesized RAM,” IEEE Trans. Antennas Propagat., vol. 48, pp. 1594–1606, Oct. 2000. , “Nonuniform Luneberg and two-shell lens antennas: radiation [13] characteristics and design optimization,” IEEE Trans. Antennas Propagat., vol. 49, pp. 60–69, Jan. 2001. [14] A. F. Muscat and C. G. Parini, “Novel compact handset antenna,” in Proc.11th Int. Conf. Antennas and Propagation, Apr. 2001, pp. 336–339. [15] J. Bartolic, Z. Sipus, N. Herscovici, D. Bonefacic, and R. Zentner, “Planar and cylindrical microstrip patch antennas and arrays for wireless communications,” in Proc. 11th Int. Conf. Antennas and Propagation, Apr. 2001, pp. 569–573. [16] J. C. Maloney, M. P. Kesler, L. M. Lust, L. N. Pringle, T. L. Fountain, P. H. Harms, and G. S. Smith, “Switched fragmented aperture antennas,” in IEEE Antennas and Propagation Soc. Int. Symp. Dig., July 2000, pp. 310–313. [17] D. Lee and S. Lee, “Design of a coaxially fed circularly polarized rectangular microstrip antenna using a genetic algorithm,” Microwave and Opt. Technol. Lett., vol. 26, no. 5, pp. 288–291, Sept. 2000. [18] E. E. Altshuler, “Design of a vehicular antenna for GPS/Iridium using a genetic algorithm,” IEEE Trans. Antennas Propagat., vol. 48, pp. 968–972, June 2000. [19] A. Lommi, A. Massa, E. Storti, and A. Trucco, “Sidelobe reduction in sparse linear arrays by genetic algorithms,” Microwave and Opt. Technol. Lett., vol. 32, no. 3, pp. 194–196, Feb. 2002. [20] C. H. Chen and C. C. Chiu, “Novel radiation pattern by genetic algorithms, in wireless communication,” in Proc. IEEE Vehicular Technology Conf., May 2001, pp. 8–12. [21] P. Lopez, J. A. Rodriguez, F. Ares, and E. Moreno, “Low-sidelobe patterns from linear and planar arrays with uniform excitations except for phases of a small number of elements,” Electron. Lett., vol. 37, no. 25, pp. 1495–1497, Dec. 2001. [22] S. Okubo, “A simplification of feed systems of a nonuniformly spaced linear array antenna using genetic algorithm,” Trans. Soc. Instrument and Control Eng., vol. 37, no. 4, pp. 271–280, Apr. 2001. [23] K. L. Virga and D. Beauvarlet, “The effects of the element factor on low sidelobe circular arc array performance,” in Proc. IEEE Antennas and Propagation Soc. Int. Symp. Dig., July 2000, pp. 1206–1209. [24] M. M. Dawoud and M. Nuruzzaman, “Null steering in rectangular planar arrays by amplitude control using genetic algorithms,” Int. J. Electron., vol. 87, no. 12, pp. 1473–1484, Dec. 2000. [25] T. Gunel, “An optimization approach to the synthesis of rectangular microstrip antenna elements with thick substrates for the specified far-field radiation pattern,” Int. J. Elect. Commun., vol. 54, no. 5, pp. 303–306, 2000. [26] B. J. Barbisch, D. H. Werner, and P. L. Werner, “A genetic algorithm optimization procedure for the design of uniformly excited and nonuniformly spaced broadband low sidelobe arrays,” Appl. Comput. Electromagn. Soc. J., vol. 15, no. 2, pp. 34–42, July 2000. [27] K. N. Sherman, “Phased array shaped multi-beam optimization for LEO satellite communications using a genetic algorithm,” in Proc. IEEE Int. Conf. Phased Array Systems and Technology, May 2000, pp. 501–504. [28] Y. C. Chung and R. L. Haupt, “Amplitude and phase adaptive nulling with a genetic algorithm,” J. Electromagn. Waves and Applications, vol. 14, no. 5, pp. 631–649, 2000. [29] H. X. Hang and L. D. Yun, “Sidelobe reduction of plane array using genetic algorithm,” Acta Electronica Sinica, vol. 27, no. 12, pp. 119–120, Dec. 1999. [30] S. Lindenmeier and P. Russer, “Automatic optimization of high gain antenna arrays,” in Proc. Int. Conf. Microtechnologies, Sept. 2000, pp. 121–124. [31] S. D. Rogers, C. M. Butler, and A. Q. Martin, “Realization of a geneticalgorithm-optimized wire antenna with 5:1 bandwidth,” Radio Sci., vol. 36, no. 6, pp. 1315–1325, Nov.–Dec. 2001. [32] A. Kerkhoff, R. Rogers, and H. Ling, “The use of the genetic algorithm approach in the design of ultra-wideband antennas,” in Proc. IEEE Radio and Wireless Conf. , Aug. 2001, pp. 93–96. [33] H. Choo, A. Hutani, L. C. Trintinalia, and H. Ling, “Shape optimization of broadband microstrip antennas using genetic algorithm,” Electron. Lett., vol. 36, no. 25, pp. 2057–2058, Dec. 2000.
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Frank J. Villegas (S’92–M’95) was born in La Habana, Cuba, in 1964. He received the B.S.E.E. and M.S.E.E. degrees from the University of Houston, Houston, TX, in 1993 and 1995, respectively, and the Ph.D. degree in electrical engineering from the University of California at Los Angeles, in 2002. From 1993 to 1995, he was a Research Assistant in the Department of Electrical and Computer Engineering, University of Houston, studying leaky mode characteristics in planar waveguide structures. From 1995 to 1998, he was with TRW ES&TD, Redondo Beach, CA, engaged in the design of passive microwave, millimeter-wave and MMIC components, and MMIC packaging issues. From 1998 to 1999, he was with WaveBand Corporation, Torrance, CA, working on R&D of millimeter-wave scanning antennas for military and commercial applications, such as imaging and collision avoidance radar. From 1999 to 2002, he was with the High Performance Computing Group, Jet Propulsion Laboratory (JPL), Pasadena, CA, where he was mainly involved in various projects dealing with the application of parallel processing solutions to electromagnetic design problems, e.g., parallel genetic algorithm (GA) optimization for novel planar antenna designs, using multinode Beowulf supercomputers. From 2002 to 2003, he was with Raytheon Electronic Systems, El Segundo, CA, working on phased-array antenna subsystems design for airborne radar applications. Currently, he is with The Aerospace Corporation, El Segundo, CA, working on phased-array systems analysis and the development of computational electromagnetics tools for antenna design. He has written various journal and conference publications. His research interests include electromagnetic applications of periodic structures (e.g., phased arrays), traveling (leaky) wave and microstrip antennas, evolutionary (GA) optimization, leakage phenomena in planar waveguide circuits, and numerical techniques in electromagnetics.
VILLEGAS et al.: PARALLEL EGO APPLICATION FOR PATCH ANTENNA DESIGN
Tom Cwik (S’79–M’79–SM’94–F’01) was born in Chicago, IL. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois, Urbana-Champaign, in 1979, 1981, and 1986, respectively. After receiving the M.S. degree, he spent the summer at the Very Large Array, National Radio Astronomy Laboratory, Socorro, NM. Following this Assistantship, he spent the following year at the Joint Institute for Laboratory Astrophysics, National Bureau of Standards (Now NIST), Boulder CO. Upon completion of the Ph.D. degree, he was awarded a Postdoctoral Fellowship at the Electronics Research Laboratory, Norwegian Institute of Technology, Trondheim, Norway. Since 1988, he has been at the Jet Propulsion Laboratory (JPL), Pasadena, CA, where he is currently Manager of the Earth Science Instruments & Technology Office. Prior to this position he was Technical 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 Laboratory at JPL. He has led a team that proposed and was awarded the NASA flight mission Aquarius, a mission to be launched later this decade to measure sea surface salinity from space. His work has included the development and use of integrated electromagnetic design tools for instrument design at proposal and build stages; the invention and analysis of microdevice components for electromagnetic coupling and filtering in remote sensing instruments; and algorithm development for high performance computational electromagnetic applications. He has made contributions to frequency selective surface design and analysis and asymptotic analysis in reflector antenna systems. He has edited one book and one journal special issue, published seven book chapters, over 30 refereed journal papers, and 108 conference papers. He is the coauthor of the patent Efficient Radiation Coupling to Quantum-Well Radiation-Sensing Array via Evanescent Waves Dr. Cwik was a Fellow at the Texas Institute for Computational and Applied Mathematics in 1997, and received the IEEE Gordon Bell Award Finalist award in 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 electrical engineering from the University of Illinois, Urbana-Champaign. He was a Guest Professor with the Technical University of Denmark (TUD) during summer 1986. He was a Senior Research Scientist at NASA’s Jet Propulsion Laboratory, California Institute of Technology, Pasadena, before joining the University 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 Consultant to many aerospace companies. He has been Editor and Guest Editor of many technical journals and book publication entities. He has authored and coauthored more than 500 technical journal articles and conference papers and has written 17 book chapters. He is the coauthor of Impedance Boundary Conditions 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 research contributions in diverse areas of electromagnetics, antennas, measurement and diagnostics techniques, numerical and asymptotic methods, satellite and personal communications, human/antenna interactions, frequency selective surfaces, electromagnetic band-gap structures and the applications of the genetic algorithms, etc., (visit http://www.antlab.ee.ucla.edu). On several occasions, his work has made the cover of many magazines and has been featured on several TV newscasts.
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Dr. Rahmat-Samii is a Member of Sigma Xi, Eta Kappa Nu, Commissions A, B, J, and K of the United States National Committee for the International Union for Radio Science (USNC/URSI), Antennas Measurement Techniques Association (AMTA), and the Electromagnetics Academy. He was elected as a Fellow 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’s Research Council Representatives to the URSI General Assemblies held in various parts of the world. In 2001, he was elected as the Foreign Member of the Royal Academy of Belgium for Science and the Arts. He was also a member of 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 triennially to the Most Outstanding Young Radio Scientist in North America. In 1992 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 Illinois ECE Distinguished Alumni Award. In 2000, he was the recipient of IEEE Third Millennium Medal and AMTA Distinguished Achievement Award. In 2001, he was the recipient of the Honorary Doctorate in physics from the University of Santiago de Compostela, Spain. In 1993, 1994, and 1995, three of his Ph.D. students were named the Most Outstanding Ph.D. Students at UCLA’s School of Engineering and Applied Science. Seven others received various Student Paper Awards at the 1993 to 2002 IEEE AP-S/URSI Symposiums. He was also a Member of the Strategic Planning and Review Committee (SPARC) of the 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 was the elected 1995 President and 1994 Vice-President of the IEEE Antennas and Propagation Society. He was one of the Directors and Vice President of the Antennas Measurement Techniques Association (AMTA) for three years. He was appointed an IEEE Antennas and Propagation Society Distinguished Lecturer and presented lectures internationally. He has been the plenary and millennium session speaker at many national and international symposia. He has also served as 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 and Technology, and Who’s Who in Engineering He is the designer of the IEEE Antennas and Propagation Society logo that is displayed on all IEEE ANTENNAS AND PROPAGATION publications.
Majid Manteghi was born in Aligodarz, Iran, on April 14, 1971. He received the B.S and M.S. degrees in electrical engineering from The University of Tehran, Tehran, Iran, 1993 and 1997, respectively. He is currently working toward the Ph.D. degree in electrical engineering, with emphasis on applied electromagnetics and antennas, at The University of California, Los Angeles (UCLA). From 1994 to 1997, he was a Research Assistant in the Microwave Laboratory, University of Tehran, where he worked on microstrip patch antennas, array designs, traveling wave antennas, handset antennas, base transceiver station (BTS) single and dual polarized antennas, reflector antennas, and UHF transceiver circuits and systems. From 1997 to 2000, he worked in the telecommunication industry in Tehran where he served as the head of an RF group for a GSM BTS project. In fall 2000, he joined to the Antenna Research, Analysis, and Measurement Laboratory (ARAM), UCLA. His research area includes ultrawide-band impulse radiating antennas, miniaturized patch antennas, multiport antennas, and dual frequency dual polarized stacked patch array designs.
