Beamforming Performances of Holographic Surfaces.

In this paper, we investigate the beamforming performance of holographic surfaces implemented as lossless antenna arrays with less than half-wavelength spacing. We first develop a method to quantify the mutual coupling effect among the antennas in an array. The developed coupling model is general and applicable to arrays with arbitrary distribution of any type of antennas with arbitrary structure, physical size and radiation power pattern. In particular, it reduces to a neat analytical expression for arbitrarily deployed isotropic antenna arrays. We then discuss the beamforming design for holographic surfaces, and in particular provide analytical beamforming characterizations for arrays with two arbitrarily spaced isotropic antennas. Numerical results indicate that, by accounting for the mutual coupling effect between antennas, the array densification by packing more antennas in a given surface aperture can significantly enhance both the beamforming gain and spatial resolution of the system. The beamforming gain enhancement and beamwidth reduction can be several dBs higher than, and more than half of, those achieved by the conventional half-wavelength spaced antenna arrays in the same surface aperture. The gains of densification become saturated when the antenna spacing is below a critical value, and the saturated gain reduces as the surface aperture increases.