0.01 0 ) and they are spaced from each other by distances d x ϭ d y ϭ 0.5 0 in the x and ŷ directions, respectively. The elements are phased to radiate a beam in the (, ) ϭ (30°, 0°). For this example, the size of the strong region is 3 ϫ 3 (four elements in forward and four elements in backward runs), and five DFT terms are used. Again a residual error less than 1.5% error is achieved with three iterations. The elapsed CPU time for DFT-FBM is 0.625 sec for this example. Using a conventional MoM approach requires a CPU time of 595.9 sec. Note that three basis functions per dipole is used for this example.As a third example, a 749-element printed dipole with an elliptical boundary is considered (the size of the corresponding rectangular array after introducing the virtual elements is 41 ϫ 25). The array and the substrate parameters are the same as the previous example. Figures 6(a) and 6(b) show a comparison of the magnitude of induced current ͉A nm ͉ for the 4 th and 11 th rows, respectively, obtained via DFT-FBM and conventional MoM. The size of the strong region, the number of DFT terms, and the residual error are also the same as the previous example.As seen in all examples, very good agreement between the DFT-FBM and conventional MoM results has been achieved, thereby establishing confidence in the present DFT-FBM approach. Finally, the CPU times of the DFT-FBM approach and MoM with LU decomposition is compared in Figure 7 for a printed dipole array whose parameters are the same as the ones used in the aforementioned numerical results. As illustrated in the figure, the required CPU time for the DFT-FBM approach is very small compared to that required in the conventional MoM, especially when N tot is very large.
DISCUSSIONS AND CONCLUSIONSEfficient and accurate analysis of electrically large, planar, periodic, finite (phased), arbitrarily contoured arrays of both freestanding and printed dipoles has been presented by introducing the virtual-element concept. Both the computational complexity and the memory-storage requirements are O (N tot The dual-polarized patch antenna has been a popular research topic during recent years, because it can double the capacity of communication systems by means of the frequency reuse, and reduce the multipath fading of received signals in land-based mobile-communication systems by means of the polarization diversity. Until now, many designs of dual-polarized microstrip antennas have been reported . Dual-polarized patch antennas can be realized by feeding the microstrip patch at two orthogonal edges, through edge feed or probe feed, which excites the TM 01 and TM 10 modes with orthogonal polarizations [1]. Both the element itself and its array often achieve isolation of about Ϫ20 dB [2]. The isolation of this kind of dual-polarized antenna can be increased significantly by using thin wire bonds [3], at the expense of additional complexity in antenna fabrication and matching circuits designs. The patch with dual parallel corner-feeding was studied in [4] with isolation of about ...