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Channel Estimation for Reconfigurable Intelligent Surface Assisted Upper Mid-Band MIMO Systems

Jeongjae Lee, Chanwon Kim, Songnam Hong

TL;DR

A conditioning-aware channel estimation framework that transforms the inherently ill-conditioned high-dimensional problem into multiple well-conditioned subproblems via greedy column grouping and stabilizes piecewise LS reconstruction without relying on sparsity assumptions is proposed.

Abstract

The upper mid-band (UMB) spectrum is a key enabler for 6G systems, yet reconfigurable intelligent surface (RIS)-assisted UMB communications face severe channel estimation challenges due to near-field propagation and transitional scattering, which induce strong spatial correlation and ill-conditioned least-squares (LS) formulations. To overcome this limitation, we propose a conditioning-aware channel estimation framework that transforms the inherently ill-conditioned high-dimensional problem into multiple well-conditioned subproblems via greedy column grouping. By systematically separating highly correlated RIS elements into distinct sub-blocks via piecewise RIS phase design, the proposed method directly improves Gram matrix conditioning and stabilizes piecewise LS reconstruction without relying on sparsity assumptions. Simulation results demonstrate that the proposed method significantly outperforms conventional LS and OMP-based estimators in pilot-limited and transitional UMB regimes, achieving robust performance with low computational complexity.

Channel Estimation for Reconfigurable Intelligent Surface Assisted Upper Mid-Band MIMO Systems

TL;DR

A conditioning-aware channel estimation framework that transforms the inherently ill-conditioned high-dimensional problem into multiple well-conditioned subproblems via greedy column grouping and stabilizes piecewise LS reconstruction without relying on sparsity assumptions is proposed.

Abstract

The upper mid-band (UMB) spectrum is a key enabler for 6G systems, yet reconfigurable intelligent surface (RIS)-assisted UMB communications face severe channel estimation challenges due to near-field propagation and transitional scattering, which induce strong spatial correlation and ill-conditioned least-squares (LS) formulations. To overcome this limitation, we propose a conditioning-aware channel estimation framework that transforms the inherently ill-conditioned high-dimensional problem into multiple well-conditioned subproblems via greedy column grouping. By systematically separating highly correlated RIS elements into distinct sub-blocks via piecewise RIS phase design, the proposed method directly improves Gram matrix conditioning and stabilizes piecewise LS reconstruction without relying on sparsity assumptions. Simulation results demonstrate that the proposed method significantly outperforms conventional LS and OMP-based estimators in pilot-limited and transitional UMB regimes, achieving robust performance with low computational complexity.
Paper Structure (15 sections, 14 equations, 2 figures)

This paper contains 15 sections, 14 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Channel and Signal Model
  4. Two-Timescale Channel Estimation Framework
  5. Problem Formulation
  6. Piecewise RIS Phase Design
  7. RIS Grouping Optimization Problem
  8. Proposed Greedy Column Grouping Algorithm
  9. Surrogate Formulation and Rationale
  10. Greedy Partitioning Strategy and Implemenation
  11. Seed Initialization
  12. Sequential Greedy Assignment
  13. Implementation
  14. Simulation Results
  15. Conclusion

Figures (2)

  • Figure 1: Illustration of the RIS-assisted UMB system and piecewise RIS phase design, e.g., $M=16$ and $Q=4$.
  • Figure 2: NMSE performance of different channel estimation methods in the RIS-assisted UMB system. (a) NMSE versus the total pilot overhead. $L^{\rm RB}=L^{\rm UR}=16$. (b) NMSE versus the number of scatterers with a fixed pilot overhead. $Q=16$ and $B=8$. (c) NMSE versus the total pilot overhead for different numbers of RIS groups $Q$. $L^{\rm RB}=L^{\rm UR}=16$.

Theorems & Definitions (1)

  • Remark 1: Computational Complexity Analysis