In this paper, a novel and computationally efficient algorithm which combines Array Signal Processing (ASP) approach with Fourier Optics (FO) is developed in the realm of gain enhancement achieved by placing Uniplanar Compact-Photonic Band Gap (UC-PBG) structures on top of microstrip antennas. The proposed scheme applies FO to the well-known sampling theorem borrowed from Digital Signal Processing (DSP) analysis in the framework of ASP approach which we refer to as the FDA algorithm. The FDA algorithm is suitable for lossless UC-PBG structures with 1-D, 2-D and 3-D lattice of canonical geometrical apertures, such as circular, octagonal, hexagonal, and square. In order to validate the proposed approach, two different UC-PBG structures of octagonal and circular apertures are considered at 2.6 GHz. The UC-PBG structures under consideration consist of two layers positioned above a microstrip antenna; each layer is an array of 9×9 apertures separated by half of the focal length distance of the lens in the near-field of the microstrip antenna. The performance of the microstrip antenna with and without the UC-PBG is reported using numerical simulations performed using CST Microwave Studio (CST MWS) based on the Finite Integration Technique (FIT). The radiation patterns and directivity of the microstrip antenna based on UC-PBG structures are evaluated using the proposed FDA algorithm and validated against numerical results obtained from CST MWS where an excellent agreement is found between the FDA algorithm and the 3-D full wave simulations. The UC-PBG structure of octagonal apertures provides a remarkable enhancement in the bore-sight gain of about 7.8 dBi at 2.6 GHz with respect to that obtained from the conventional microstrip antenna, while the circular apertures provide gain enhancement in excess of 10 dBi above the gain of the same microstrip antenna.
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