  Large intelligent surfaces (LISs) constitute a new and promising wireless
communication paradigm that relies on the integration of a massive number of
antenna elements over the entire surfaces of man-made structures. The LIS
concept provides many advantages, such as the capability to provide reliable
and space-intensive communications by effectively establishing line-of-sight
(LOS) channels. In this paper, the system spectral efficiency (SSE) of an
uplink LIS system is asymptotically analyzed under a practical LIS environment
with a well-defined uplink frame structure. In order to verify the impact on
the SSE of pilot contamination, the SSE of a multi-LIS system is asymptotically
studied and a theoretical bound on its performance is derived. Given this
performance bound, an optimal pilot training length for multi-LIS systems
subjected to pilot contamination is characterized and, subsequently, the
performance-maximizing number of devices that the LIS system must service is
derived. Simulation results show that the derived analyses are in close
agreement with the exact mutual information in presence of a large number of
antennas, and the achievable SSE is limited by the effect of pilot
contamination and intra/inter-LIS interference through the LOS path, even if
the LIS is equipped with an infinite number of antennas. Additionally, the SSE
obtained with the proposed pilot training length and number of scheduled
devices is shown to reach the one obtained via a brute-force search for the
optimal solution.
