  Employing large intelligent surfaces (LISs) is a promising solution for
improving the coverage and rate of future wireless systems. These surfaces
comprise a massive number of nearly-passive elements that interact with the
incident signals, for example by reflecting them, in a smart way that improves
the wireless system performance. Prior work focused on the design of the LIS
reflection matrices assuming full knowledge of the channels. Estimating these
channels at the LIS, however, is a key challenging problem, and is associated
with large training overhead given the massive number of LIS elements. This
paper proposes efficient solutions for these problems by leveraging tools from
compressive sensing and deep learning. First, a novel LIS architecture based on
sparse channel sensors is proposed. In this architecture, all the LIS elements
are passive except for a few elements that are active (connected to the
baseband of the LIS controller). We then develop two solutions that design the
LIS reflection matrices with negligible training overhead. In the first
approach, we leverage compressive sensing tools to construct the channels at
all the LIS elements from the channels seen only at the active elements. These
full channels can then be used to design the LIS reflection matrices with no
training overhead. In the second approach, we develop a deep learning based
solution where the LIS learns how to optimally interact with the incident
signal given the channels at the active elements, which represent the current
state of the environment and transmitter/receiver locations. We show that the
achievable rates of the proposed compressive sensing and deep learning
solutions approach the upper bound, that assumes perfect channel knowledge,
with negligible training overhead and with less than 1% of the elements being
active.
