  A reconfigurable intelligent surface (RIS) can be used to improve the channel
gain between a base station (BS) and user equipment (UE), but only if its $N$
reflecting elements are configured properly. This requires accurate estimation
of the cascaded channel from the UE to the BS through each RIS element. If the
channel structure is not exploited, pilot sequences of length $N$ must be used,
which is a major practical challenge since $N$ is typically at the order of
hundreds. To address this problem without requiring user-specific channel
statistics, we propose a novel estimator, called reduced-subspace least squares
(RS-LS) estimator, that only uses knowledge of the array geometry. The RIS
phase-shift pattern is optimized to minimize the mean-square error of the
channel estimates. The RS-LS estimator largely outperforms the conventional
least-squares estimator, and can be utilized with a much shorter pilot length
since it exploits the fact that the array geometry confines the possible
channel realizations to a reduced-rank subspace.
