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Time-Domain Channel Estimation for Extremely Large MIMO THz Communication Systems Under Dual-Wideband Fading Conditions

Evangelos Vlachos, Aryan Kaushik, Yonina C. Eldar, George C. Alexandropoulos

TL;DR

This work tackles the challenging problem of channel estimation for extremely large MIMO THz links under dual-wideband fading caused by beam squint at both TX and RX. It introduces a time-domain, single-carrier modeling framework and a novel mixed-integer sparse formulation, solved via ADMM with a beamspace ${\\mathbf{Z}}$ representation to exploit sparsity; initialization leverages UE position to accelerate convergence. The proposed method significantly outperforms conventional SC- and MC-based estimators, approaching ideal lower bounds, and demonstrates robustness to position errors. The approach promises practical, high-rate THz communications with scalable complexity, bridging theory and real-world deployments.

Abstract

In this paper, we study the problem of extremely large (XL) multiple-input multiple-output (MIMO) channel estimation in the terahertz (THz) frequency band, considering the presence of propagation delays across the entire array apertures at both communication ends, which naturally leads to frequency selectivity. This problem is known as beam squint and may be pronounced when communications are subject to multipath fading conditions. Multi-carrier (MC) transmission schemes, which are usually deployed in THz communication systems to address these issues, suffer from high peak-to-average power ratio, which is specifically dominant in this frequency band where low transmit power is mostly feasible. Furthermore, the frequency selectivity caused by severe molecular absorption in the THz band necessitates delicate consideration in MC system design. Motivated by the benefits of single-carrier (SC) waveforms for practical THz communication systems, diverging from the current dominant research trend on MC systems, we devise a novel channel estimation problem formulation in the time domain for SC XL MIMO systems subject to multipath signal propagation, spatial wideband effects, and molecular absorption. An efficient alternating minimization approach is presented to solve the proposed mixed-integer sparse problem formulation. The conducted extensive performance evaluation results validate that the proposed XL MIMO estimation scheme exhibits superior performance than conventional SC- and MC-based techniques, approaching the idealized lower bound.

Time-Domain Channel Estimation for Extremely Large MIMO THz Communication Systems Under Dual-Wideband Fading Conditions

TL;DR

This work tackles the challenging problem of channel estimation for extremely large MIMO THz links under dual-wideband fading caused by beam squint at both TX and RX. It introduces a time-domain, single-carrier modeling framework and a novel mixed-integer sparse formulation, solved via ADMM with a beamspace representation to exploit sparsity; initialization leverages UE position to accelerate convergence. The proposed method significantly outperforms conventional SC- and MC-based estimators, approaching ideal lower bounds, and demonstrates robustness to position errors. The approach promises practical, high-rate THz communications with scalable complexity, bridging theory and real-world deployments.

Abstract

In this paper, we study the problem of extremely large (XL) multiple-input multiple-output (MIMO) channel estimation in the terahertz (THz) frequency band, considering the presence of propagation delays across the entire array apertures at both communication ends, which naturally leads to frequency selectivity. This problem is known as beam squint and may be pronounced when communications are subject to multipath fading conditions. Multi-carrier (MC) transmission schemes, which are usually deployed in THz communication systems to address these issues, suffer from high peak-to-average power ratio, which is specifically dominant in this frequency band where low transmit power is mostly feasible. Furthermore, the frequency selectivity caused by severe molecular absorption in the THz band necessitates delicate consideration in MC system design. Motivated by the benefits of single-carrier (SC) waveforms for practical THz communication systems, diverging from the current dominant research trend on MC systems, we devise a novel channel estimation problem formulation in the time domain for SC XL MIMO systems subject to multipath signal propagation, spatial wideband effects, and molecular absorption. An efficient alternating minimization approach is presented to solve the proposed mixed-integer sparse problem formulation. The conducted extensive performance evaluation results validate that the proposed XL MIMO estimation scheme exhibits superior performance than conventional SC- and MC-based techniques, approaching the idealized lower bound.
Paper Structure (27 sections, 2 theorems, 53 equations, 6 figures, 2 tables, 2 algorithms)

This paper contains 27 sections, 2 theorems, 53 equations, 6 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Motivation and Contributions
  4. Notation and Organization
  5. System and Channel Models
  6. Wideband Channel Model
  7. Received Signal Model
  8. Combined TX-RX Beam-Squint Effect
  9. Proposed THz XL MIMO Channel Estimation
  10. Problem Formulation
  11. Idealized Solution of the Decomposed Problem
  12. Exploitation of the Channel's Sparse Structure
  13. Proposed Solution
  14. Derivation of $\mathbf{E}^{(j+1)}$
  15. Derivation of $\mathbf{Z}^{(j+1)}$
  16. ...and 12 more sections

Key Result

Proposition 1

The input/output relationship for the considered $M \times N$ MIMO system over an ${L_p}$-tap multipath THz and wideband channel subject to the combined effects of maximum delay $K$ and after $T$ training instances can be expressed as: where $\mathbf{Y} \in \mathbb{C}^{M \times T}$ denotes the matrix with all $T$ received training signals from all $M$ RX antennas in baseband and $\mathbf{H}$ repr

Figures (6)

  • Figure 1: The beamspace $\Vert \mathbf{Z} \Vert_F^2$ of a $12 \times 8$ MIMO channel matrix (top) and that of its proposed block sparse representation in \ref{['eq:Z_def']} via Proposition 2 (bottom) for the case of ${L_p}=3$ channel propagation paths.
  • Figure 2: Convergence of the the proposed channel estimation algorithm with $N=M=256$, $T=3N=768$, and ${L_p}=6$.
  • Figure 3: Simplified example of the combined time delay profile between the $n$-th TX and the $m$-th RX antenna elements for a $32 \times 32$ MIMO system resulting from the TX/RX spatial wideband effects, multipath propagation, and molecular absorption.
  • Figure 4: Time delay due to the spatial wideband effects versus the carrier frequency in GHz.
  • Figure 5: Channel estimation performance versus the SNR for a $64 \times 64$ MIMO system with ${L_p}=3$, $T=3N=192$, and $\sigma_p^2=10$ dB.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof