  Channel acquisition is one of the main challenges for the deployment of
reconfigurable intelligent surface (RIS) aided communication systems. This is
because an RIS has a large number of reflective elements, which are passive
devices with no active transmitting/receiving abilities. In this paper, we
study the channel estimation problem for the RIS aided multi-user
millimeter-wave (mmWave) multi-input multi-output (MIMO) system. Specifically,
we propose a novel channel estimation protocol for the above system to estimate
the cascaded channels, which are the products of the channels from the base
station (BS) to the RIS and from the RIS to the users. Further, since the
cascaded channels are typically sparse, this allows us to formulate the channel
estimation problem as a sparse recovery problem using compressive sensing (CS)
techniques, thereby allowing the channels to be estimated with less training
overhead. Moreover, the sparse channel matrices of the cascaded channels of all
users have a common block sparsity structure due to the common channel between
the BS and the RIS. To take advantage of the common sparsity pattern, we
propose a two-step multi-user joint channel estimation procedure. In the first
step, we make use of the common column-block sparsity and project the received
signals onto the common column subspace. In the second step, we make use of the
row-block sparsity of the projected signals and propose a multi-user joint
sparse matrix recovery algorithm that takes into account the common channel
between the BS and the RIS.
