The Potential of Using Large Antenna Arrays on Intelligent Surfaces

In this paper, we consider capacities of single- antenna terminals communicating to large antenna arrays that are deployed on surfaces. That is, the entire surface is used as an intelligent receiving antenna array. Under the condition that the surface area is sufficiently large, the received signal after matched-filtering (MF) can be well approximated by an intersymbol interference (ISI) channel where channel taps are closely related to a sinc function. Based on such an approximation, we have derived the capacities for both one- dimensional (terminals on a line) and high dimensional (terminals on a plane or in a cube) terminal-deployments. In particular, we analyze the normalized capacity $\bar{\mathcal{C}}$, measured in nats/s/Hz/m$^2$, under the constraint that the transmit power per m$^2$, $\bar{P}$, is fixed. We show that when the user-density increases, the limit of $\bar{\mathcal{C}}$, achieved as the wavelength $\lambda$ approaches 0, is $\bar{P}/(2N_0)$ nats/s/Hz/m$^2$, where $N_0$ is the spatial power spectral density (PSD) of noise. In addition, we also show that the number of signal dimensions is $2/\lambda$ per meter deployed surface for the one-dimensional case, and $\pi/\lambda^2$ per m$^2$ deployed surface for two and three dimensional terminal-deployments.