RESULTSAs an example, an antenna aperture on ground plane, 1.5 ϫ 1.5 in size, has been considered. The aperture distribution is given by Eq. (7), where E o ϭ 0.5 V/m and a ϭ b ϭ 1.5. The tangential components of the near-field samples taken as reference by the GA were computed at a planar grid S f 10 ϫ 10 in size, located 4 away from the antenna aperture and with a /4 uniform spacing. An equivalent model made up of 98 dipoles with a /4 spacing has been considered for S e . For the binary GA, the 196 unknowns of the chromosome have been coded using 9 bits per parameter, with an initial population of 4500 individuals to ensure diversity.Fitness evolution is shown in Figure 2 and the far-field patterns reconstructed with this approach and with the classical FFT-based method are compared with theoretical results in Figure 3 for the ϭ 0°cut. For the FFT case, a planar grid made up of 126 ϫ 126 near-field samples, /5 spaced on a 25 ϫ 25 plane located 4 away from the source has been considered and a 128 ϫ 128 FFT processing has been performed. A 3D far-field pattern analysis showed a maximum error of up to 1.5 dB (1.8 dB) for ϭ Ϯ45°o r 4.6 dB (11 dB) for ϭ Ϯ60°, for the GA (FFT) case. It should be noted that the level of the electric field is already 26 dB below the maximum for ϭ Ϯ60°. Clearly, GAs provide better results than FFT using a smaller scanning area. However, the elapsed CPU time is far higher.
CONCLUSIONSA useful method for predicting the radiation pattern of an antenna from planar near-field samples has been presented. The method reconstructs the source radiation pattern using an equivalent model optimized by means of a genetic-algorithm-based process. The method is appropriate for small-and medium-size antennas, showing a better performance than the classical FFT-based method. For large antennas, the complexity of the equivalent model drastically slows down the optimization process.
ACKNOWLEDGMENTSThis work was partly supported by CICYT/FEDER projects 1FD97-0594-C03-02/ TIC and 1FD1997-1975 [4]. To compute the far fields, we use a near-to-far-field transformation, adapted to the BOR, for efficient calculation of radiation fields based on line integrals along the line contour of equivalent electric and magnetic currents, as opposed to surface integrals that are more costly to compute [5]. To analyze arbitrary BOR geometries, we have developed a mesh generator in conjunction with the commercial geometrical design tool AutoCAD, to systematically create geometry and material input files for the BOR/FDTD solver. We have validated the technique for a number of BOR horns and reflector antennas and have achieved excellent agreement between the numerical results derived in this work and those available in the literature for all of the cases investigated.
BOR/FDTD ALGORITHMOur objective is to solve the Maxwell's equations for BOR geometries in the cylindrical coordinate system that read as follows:In view of the azimuthal symmetry, we can represent the electromagnetic fields as infinite Fourier series expansions:wh...