  The reconfigurable intelligent surface (RIS) plays an important role in
maintaining the connectivity in millimeter wave (mmWave) MIMO systems when the
direct channel between the transceivers is blocked. However, it is difficult to
acquire the channel state information (CSI), which is essential for the design
of RIS phase control matrix and beamforming vectors at the transceivers. In
this paper, we compare the channel estimation (CE) performance and achieved
spectral efficiency (SE) of the purely passive and hybrid RIS architectures. CE
is done via atomic norm minimization (ANM). For the purely passive RIS, we
follow a two-stage procedure to sequentially estimate the channel parameters,
while for the hybrid RIS we estimate the individual channels at the RIS based
on the observations from active RIS elements assuming alternating uplink and
downlink training. The simulation results show that the purely passive RIS
brings better CE and SE performance compared to the hybrid RIS under the same
training overhead. We further consider different setups for the hybrid RIS and
study the tradeoffs among them.
