  Beamforming design with partial channel estimation and feedback for
frequency-division duplexing (FDD) reconfigurable intelligent surface (RIS)
assisted systems is considered in this paper. We leverage the observation that
path angle information (PAI) varies more slowly than path gain information
(PGI). Then, several dominant paths are selected among all the cascaded paths
according to the known PAI for maximizing the spectral efficiency of downlink
data transmission. To acquire the dominating path gain information (DPGI, also
regarded as the path gains of selected dominant paths) at the base station
(BS), we propose a DPGI estimation and feedback scheme by jointly beamforming
design at BS and RIS. Both the required number of downlink pilot signals and
the length of uplink feedback vector are reduced to the number of dominant
paths, and thus we achieve a great reduction of the pilot overhead and feedback
overhead. Furthermore, we optimize the active BS beamformer and passive RIS
beamformer by exploiting the feedback DPGI to further improve the spectral
efficiency. From numerical results, we demonstrate the superiority of our
proposed algorithms over the conventional schemes.
