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

TL;DR

This work tackles CE in RIS-aided MIMO systems by formulating a one-shot, partly decoupled atomic norm minimization (PDANM) framework that exploits 3D angular sparsity of the effective channel. Building on PDANM, it introduces a reweighted variant (RPDANM) to promote sparsity via iterative rank-minimization surrogates and an adaptive phase-control extension (RPDANM-APC) to reduce training overhead by adapting RIS phases during sounding. Theoretical results (SDP-based bounds and equivalence under mild conditions) and complexity analyses establish PDANM as a computationally efficient alternative to full 3D ANM methods, while simulations demonstrate superior CE accuracy and substantially lower training overhead, especially for RPDANM-APC. Overall, the proposed approach enables high-accuracy CE with reduced computational load and training resources, making RIS-aided MIMO CE more practical for large-scale deployments.

Abstract

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.

Figures (10)

• Figure 1: The considered RIS-aided MIMO communication system.
• Figure 2: The adopted slot-based channel sounding procedure.
• Figure 3: An example of groups of partially decoupled atoms in several cases, where the red pentagrams correspond to the partially decoupled atoms and the black dots denote their projections on the $\{ \theta,\phi \}$ plane and $\psi$ axis. The three partially decoupled atoms in Fig. \ref{['fig3a']} are separable on the $\{ \theta,\phi \}$ plane with $L_\mathrm{R}^{*} = 2$ and $L_\mathrm{BU}^{*} = 3$ and the three partially decoupled atoms in Fig. \ref{['fig3b']} are separable on the $\psi$ axis with $L_\mathrm{R}^{*} = 3$ and $L_\mathrm{BU}^{*} = 2$. The four partially decoupled atoms in Fig. \ref{['fig3c']} overlap on both the $\{ \theta,\phi \}$ plane and the $\psi$ axis with $L_\mathrm{R}^{*} = L_\mathrm{BU}^{*} = 3$.
• Figure 4: NMSE of different methods versus iteration index. Dashed lines denote one-step methods and solid curves denote iterative methods.
• Figure 5: NMSE of different methods versus SNR.

Theorems & Definitions (8)

• Proposition 1
• proof
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof