Beamforming Performances of Holographic Surfaces

We investigate the beamforming performance of holographic surfaces implemented as arrays of antenna elements with less than half-wavelength spacing packed in finite surface apertures. We first develop a general expression to quantity the mutual coupling effect among the antennas in an array with arbitrary spatial distribution and arbitrary radiation power patterns. Based on the developed coupling model, we then discuss the beamforming design for holographic surfaces. Numerical results indicate that, by accounting for the mutual coupling effect in the beamforming design, the array densification by packing more antennas in a given surface aperture can enhance the achievable beamforming gain by several dBs compared to that of the conventional half-wavelength spaced antenna arrays, but the enhancement becomes saturated when the spacing is below a critical value, and the saturated enhancement reduces with the increase of the aperture size of the holographic surface.