  We analyze the influence of a reconfigurable intelligent surface (RIS) on the
Gram channel eigenvalues in a high signal-to-noise ratio (SNR) scenario. This
allows to connect specific channel properties with the rank improvement
capabilities of the RIS. In particular, fundamental limits due to a possible
line of sight (LOS) setup between the base station (BS) and the RIS are
derived. Furthermore, dirty paper coding (DPC) based schemes are compared to
linear precoding in such a scenario and it is shown that under certain channel
conditions, the performance gap between DPC and linear precoding vanishes.
