A Communication Model for Large Intelligent Surfaces

The purpose of this paper is to introduce a communication model for Large Intelligent Surfaces (LIS). A LIS is modeled as a collection of tiny closely spaced antenna elements. Due to the proximity of the elements, mutual coupling arises. An optimal transmitter design depends on the mutual coupling matrix. For single user communication, the optimal transmitter uses the inverse of the mutual coupling matrix in a filter matched to the channel vector. We give the expression of the mutual coupling for two types of planar arrays. The conditioning number of the mutual coupling matrix is unbounded as the antenna element density increases, so only the dominant values can be inverted within reasonable computation. The directivity is partial but still significant compared to the conventional gain. When the spacing between elements becomes small (smaller than half a wavelength), the directivity surpasses the conventional directivity equal to the number of antennas, as well as the gain obtained when modeling the surface as continuous. The gain is theoretically unbounded as the element density increases for a constant aperture.