  We consider channel estimation in systems equipped with a reconfigurable
intelligent surface (RIS). In order to illuminate the additional cascaded
channel as compared to systems without a RIS, commonly an unaffordable amount
of pilot sequences has to be transmitted over different phase allocations at
the RIS. However, for a given base station (BS) cell, there exist immanent
structural characteristics of the environment which can be leveraged to reduce
the necessary number of phase allocations. We verify this observation by a
study on discrete Fourier transform (DFT)-based phase allocations where we
exhaustively search for the best combination of DFT columns. Since this
brute-force search is unaffordable in practice, we propose to learn a neural
network (NN) for joint phase optimization and channel estimation because of the
dependency of the optimal phase allocations on the channel estimator, and vice
versa. We verify the effectiveness of the approach by numerical simulations
where common choices for the phase allocations and the channel estimator are
outperformed. By an ablation study, the learned phase allocations are shown to
be beneficial in combination with a different state-of-the-art channel
estimator as well.
