  Channel estimation is challenging for the reconfigurable intelligent surface
(RIS)-aided wireless communications. Since the number of coefficients of the
cascaded channel among the base station (BS), the RIS and the user equipments
(UEs) is the product of the number of BS antennas, the number of RIS elements,
and the number of UEs, the pilot overhead can be prohibitively high. In this
paper, we propose a two-timescale channel estimation framework to exploit the
property that the BS-RIS channel is high-dimensional but quasi-static, while
the RIS-UE channel is mobile but low-dimensional. Specifically, to estimate the
quasi-static BS-RIS channel, we propose a dual-link pilot transmission scheme,
where the BS transmits downlink pilots and receives uplink pilots reflected by
the RIS. Then, we propose a coordinate descent-based algorithm to recover the
BS-RIS channel. Since the quasi-static BS-RIS channel is estimated less
frequently than the mobile channel be, the average pilot overhead can be
reduced from a long-term perspective. Although the mobile RIS-UE channel has to
be frequently estimated in a small timescale, the associated pilot overhead is
low thanks to its low dimension. Simulation results show that the proposed
two-timescale channel estimation framework can achieve accurate channel
estimation with low pilot overhead.
