  Channel estimation (CE) plays a key role in reconfigurable intelligent
surface (RIS)-aided multiple-input multiple-output (MIMO) communication
systems, while it poses a challenging task due to the passive nature of RIS and
the cascaded channel structures. In this paper, a partially decoupled atomic
norm minimization (PDANM) framework is proposed for CE of RIS-aided MIMO
systems, which exploits the three-dimensional angular sparsity of the channel.
In particular, PDANM partially decouples the differential angles at the RIS
from other angles at the base station and user equipment, reducing the
computational complexity compared with existing methods. A reweighted PDANM
(RPDANM) algorithm is proposed to further improve CE accuracy, which
iteratively refines CE through a specifically designed reweighing strategy.
Building upon RPDANM, we propose an iterative approach named RPDANM with
adaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phases
based on previously estimated channel parameters to facilitate CE, achieving
superior CE accuracy while reducing training overhead. Numerical simulations
demonstrate the superiority of our proposed approaches in terms of running
time, CE accuracy, and training overhead. In particular, the RPDANM-APC
approach can achieve higher CE accuracy than existing methods within less than
30 percent training overhead while reducing the running time by tens of times.
