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Channel estimation (CE) plays a key role in reconfigurable intelligentsurface (RIS)-aided multiple-input multiple-output (MIMO) communicationsystems, while it poses a challenging task due to the passive nature of RIS andthe cascaded channel structures. In this paper, a partially decoupled atomicnorm minimization (PDANM) framework is proposed for CE of RIS-aided MIMOsystems, which exploits the three-dimensional angular sparsity of the channel.In particular, PDANM partially decouples the differential angles at the RISfrom other angles at the base station and user equipment, reducing thecomputational complexity compared with existing methods. A reweighted PDANM(RPDANM) algorithm is proposed to further improve CE accuracy, whichiteratively refines CE through a specifically designed reweighing strategy.Building upon RPDANM, we propose an iterative approach named RPDANM withadaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phasesbased on previously estimated channel parameters to facilitate CE, achievingsuperior CE accuracy while reducing training overhead. Numerical simulationsdemonstrate the superiority of our proposed approaches in terms of runningtime, CE accuracy, and training overhead. In particular, the RPDANM-APCapproach can achieve higher CE accuracy than existing methods within less than40 percent training overhead while reducing the running time by tens of times.

Channel Estimation for RIS-Aided MIMO Systems: A Partially Decoupled Atomic Norm Minimization Approach