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Integrated Channel Estimation and Sensing for Near-Field ELAA Systems

Jionghui Wang, Jun Fang, Hongbin Li, Boyu Ning

TL;DR

This work addresses uplink channel estimation and user localization in near-field ELAA mmWave/THz ISAC systems using a tensor decomposition framework. It develops a CPD-based model for LoS-dominated channels and a BTD-based model for general NLoS scenarios, enabling joint multi-user estimation with non-orthogonal pilots and a guaranteed identifiability for $T\ge 2$. The proposed ALS/NLS algorithms extract delay, angle, distance, and path gains from recovered factor matrices, with localization derived from LoS geometry and robust parameter extraction in NLoS via block terms. Simulation results show substantial gains over CS-based approaches in channel estimation and achieve high localization accuracy with reduced training overhead, highlighting the practical potential for scalable near-field ISAC in ELAA systems.

Abstract

In this paper, we study the problem of uplink channel estimation for near-filed orthogonal frequency division multiplexing (OFDM) systems, where a base station (BS), equipped with an extremely large-scale antenna array (ELAA), serves multiple users over the same time-frequency resource block. A non-orthogonal pilot transmission scheme is considered to accommodate a larger number of users that can be supported by ELAA systems without incurring an excessive amount of training overhead. To facilitate efficient multi-user channel estimation, we express the received signal as a third-order low-rank tensor, which admits a canonical polyadic decomposition (CPD) model for line-of-sight (LoS) scenarios and a block term decomposition (BTD) model for non-line-of-sight (NLoS) scenarios. An alternating least squares (ALS) algorithm and a non-linear least squares (NLS) algorithm are employed to perform CPD and BTD, respectively. Channel parameters are then efficiently extracted from the recovered factor matrices. By exploiting the geometry of the propagation paths in the estimated channel, users' positions can be precisely determined in LoS scenarios. Moreover, our uniqueness analysis shows that the proposed tensor-based joint multi-user channel estimation framework is effective even when the number of pilot symbols is much smaller than the number of users, revealing its potential in training overhead reduction. Simulation results demonstrate that the proposed method achieves markedly higher channel estimation accuracy than compressed sensing (CS)-based approaches.

Integrated Channel Estimation and Sensing for Near-Field ELAA Systems

TL;DR

This work addresses uplink channel estimation and user localization in near-field ELAA mmWave/THz ISAC systems using a tensor decomposition framework. It develops a CPD-based model for LoS-dominated channels and a BTD-based model for general NLoS scenarios, enabling joint multi-user estimation with non-orthogonal pilots and a guaranteed identifiability for . The proposed ALS/NLS algorithms extract delay, angle, distance, and path gains from recovered factor matrices, with localization derived from LoS geometry and robust parameter extraction in NLoS via block terms. Simulation results show substantial gains over CS-based approaches in channel estimation and achieve high localization accuracy with reduced training overhead, highlighting the practical potential for scalable near-field ISAC in ELAA systems.

Abstract

In this paper, we study the problem of uplink channel estimation for near-filed orthogonal frequency division multiplexing (OFDM) systems, where a base station (BS), equipped with an extremely large-scale antenna array (ELAA), serves multiple users over the same time-frequency resource block. A non-orthogonal pilot transmission scheme is considered to accommodate a larger number of users that can be supported by ELAA systems without incurring an excessive amount of training overhead. To facilitate efficient multi-user channel estimation, we express the received signal as a third-order low-rank tensor, which admits a canonical polyadic decomposition (CPD) model for line-of-sight (LoS) scenarios and a block term decomposition (BTD) model for non-line-of-sight (NLoS) scenarios. An alternating least squares (ALS) algorithm and a non-linear least squares (NLS) algorithm are employed to perform CPD and BTD, respectively. Channel parameters are then efficiently extracted from the recovered factor matrices. By exploiting the geometry of the propagation paths in the estimated channel, users' positions can be precisely determined in LoS scenarios. Moreover, our uniqueness analysis shows that the proposed tensor-based joint multi-user channel estimation framework is effective even when the number of pilot symbols is much smaller than the number of users, revealing its potential in training overhead reduction. Simulation results demonstrate that the proposed method achieves markedly higher channel estimation accuracy than compressed sensing (CS)-based approaches.
Paper Structure (28 sections, 2 theorems, 80 equations, 5 figures)

This paper contains 28 sections, 2 theorems, 80 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Related Work
  4. Contributions of This Work
  5. System Model
  6. Channel Model
  7. Problem Formulation
  8. Received Signal Model
  9. Low-Rank Tensor Representation
  10. Channel Estimation for LoS-dominated Scenarios
  11. Uniqueness Condition
  12. CP Decomposition
  13. Channel Estimation
  14. Channel Estimation for NLoS Scenarios
  15. CPD Model and Uniqueness Analysis
  16. ...and 13 more sections

Key Result

Theorem 1

Let $k_A$ denote the k-rank of $\boldsymbol{A}$, which is defined as the maximum number $k_A$ such that any $k_A$ columns of $\boldsymbol{A}$ are linearly independent. Let $(\boldsymbol{A},\boldsymbol{B},\boldsymbol{C})$ be a CP solution which decomposes a third-order tensor $\mathcal{Y} \in \mathbb is satisfied, then the CPD of $\mathcal{Y}$ is unique up to scaling and permutation ambiguities. Sp

Figures (5)

  • Figure 1: An ELAA system with multiple users in the near-field.
  • Figure 2: MSEs/CRBs for channel parameter estimation versus SNR (dB), where $T = 4$ and $M = 32$.
  • Figure 3: (a) MSE/CRB for user localization versus SNR (dB), where $T = 4$ and $M = 32$; (b) MSE/CRB for user localization versus the number of RF chains ($M$), where $T=4$ and SNR = $30$ dB; (c) MSE/CRB for user localization versus the pilot sequences ($T$), where $M = 32$ and SNR $= 30$ dB.
  • Figure 4: (a) NMSE versus SNR (dB), where $T = 4$ and $M = 32$; (b) NMSE versus the number of RF chains ($M$), where $T = 4$ and SNR = $30$ dB; (c) NMSE versus the length of pilot sequences ($T$), where $M = 32$ and SNR = $30$ dB.
  • Figure 5: (a) NMSE versus SNR (dB), where $T = 4$ and $M = 64$; (b) NMSE versus the number of RF chains ($M$), where $T = 4$ and SNR = $10$ dB; (c) NMSE versus the length of pilot sequences ($T$), where $M = 64$ and SNR = $10$ dB.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2