  In this paper, we adopt a three-stage based uplink channel estimation
protocol with reduced pilot overhead for an reconfigurable intelligent surface
(RIS)-aided multi-user (MU) millimeter wave (mmWave) communication system, in
which both the base station (BS) and the RIS are equipped with a uniform planar
array (UPA). Specifically, in Stage I, the channel state information (CSI) of a
typical user is estimated. To address the power leakage issue for the common
angles-of-arrival (AoAs) estimation in this stage, we develop a low-complexity
one-dimensional search method. In Stage II, a re-parameterized common BS-RIS
channel is constructed with the estimated information from Stage I to estimate
other users' CSI. In Stage III, only the rapidly varying channel gains need to
re-estimated. Furthermore, the proposed method can be extended to multi-antenna
UPA-type users, by decomposing the estimation of a multi-antenna channel with
$J$ scatterers into estimating $J$ single-scatterer channels for a virtual
single-antenna user. An orthogonal matching pursuit (OMP)-based method is
proposed to estimate the angles-of-departure (AoDs) at the users. Simulation
results demonstrate that the proposed algorithm significantly achieves high
channel estimation accuracy, which approaches the genie-aided upper bound in
the high SNR regime.
