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Optimizing Multicarrier Multiantenna Systems for LoS Channel Charting

Taha Yassine, Luc Le Magoarou, Matthieu Crussière, Stephane Paquelet

TL;DR

This work develops a theoretical identifiability framework for channel charting (CC) in LoS MIMO-OFDM systems, focusing on a phase-insensitive (PI) channel distance that decomposes into radial and angular components. It shows that PI distance suffers long-range and short-range ambiguities, and remedies these with system-design guidelines and a thresholded distance $\tilde{d}^{\star}$ when using uniform circular arrays (UCAs). The authors derive necessary and sufficient conditions for identifiability under ULA and UCA configurations, demonstrating that UCAs provide consistent angular resolution and warp-free neighborhoods, with a roundness criterion guiding parameter choices. Experimental results on synthetic and realistic data confirm substantial improvements in local neighborhood preservation (trustworthiness and Kruskal stress) when applying thresholding and UCA-based designs, validating the proposed framework for CC-enabled sensing tasks.

Abstract

Channel charting (CC) consists in learning a mapping between the space of raw channel observations, made available from pilot-based channel estimation in multicarrier multiantenna system, and a low-dimensional space where close points correspond to channels of user equipments (UEs) close spatially. Among the different methods of learning this mapping, some rely on a distance measure between channel vectors. Such a distance should reliably reflect the local spatial neighborhoods of the UEs. The recently proposed phase-insensitive (PI) distance exhibits good properties in this regards, but suffers from ambiguities due to both its periodic and oscillatory aspects, making users far away from each other appear closer in some cases. In this paper, a thorough theoretical analysis of the said distance and its limitations is provided, giving insights on how they can be mitigated. Guidelines for designing systems capable of learning quality charts are consequently derived. Experimental validation is then conducted on synthetic and realistic data in different scenarios.

Optimizing Multicarrier Multiantenna Systems for LoS Channel Charting

TL;DR

This work develops a theoretical identifiability framework for channel charting (CC) in LoS MIMO-OFDM systems, focusing on a phase-insensitive (PI) channel distance that decomposes into radial and angular components. It shows that PI distance suffers long-range and short-range ambiguities, and remedies these with system-design guidelines and a thresholded distance when using uniform circular arrays (UCAs). The authors derive necessary and sufficient conditions for identifiability under ULA and UCA configurations, demonstrating that UCAs provide consistent angular resolution and warp-free neighborhoods, with a roundness criterion guiding parameter choices. Experimental results on synthetic and realistic data confirm substantial improvements in local neighborhood preservation (trustworthiness and Kruskal stress) when applying thresholding and UCA-based designs, validating the proposed framework for CC-enabled sensing tasks.

Abstract

Channel charting (CC) consists in learning a mapping between the space of raw channel observations, made available from pilot-based channel estimation in multicarrier multiantenna system, and a low-dimensional space where close points correspond to channels of user equipments (UEs) close spatially. Among the different methods of learning this mapping, some rely on a distance measure between channel vectors. Such a distance should reliably reflect the local spatial neighborhoods of the UEs. The recently proposed phase-insensitive (PI) distance exhibits good properties in this regards, but suffers from ambiguities due to both its periodic and oscillatory aspects, making users far away from each other appear closer in some cases. In this paper, a thorough theoretical analysis of the said distance and its limitations is provided, giving insights on how they can be mitigated. Guidelines for designing systems capable of learning quality charts are consequently derived. Experimental validation is then conducted on synthetic and realistic data in different scenarios.
Paper Structure (19 sections, 10 theorems, 25 equations, 9 figures, 1 table)

This paper contains 19 sections, 10 theorems, 25 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. System and channel model
  4. Channel charting
  5. Identifiability
  6. Limitations of channel charting with a ULA
  7. UCA are better than ULA for channel charting
  8. Discussion
  9. Practical consequences of the theoretical findings
  10. Generalization to multipath scenarios
  11. Importance of identifiability for applications
  12. Experiments
  13. Practical influence of system parameters
  14. ULA vs. UCA
  15. Realistic scenario
  16. ...and 4 more sections

Key Result

Lemma 1

In an OFDM system with evenly spaced subcarriers, the radial term is of the form where $D_{N_s}$ is the Dirichlet kernel Bruckner1997 defined as $D_N(x)=\frac{1}{N}\frac{\sin(\frac{x}{2})}{\sin(\frac{x}{2N})}$. It is periodic of period $D_{\bar{f}}=\frac{c}{\Delta_f}$ provided that the absolute delays of both channel observations (i.e., $\tau_i$ and $\tau_j$) are known. Addition

Figures (9)

  • Figure 1: The left figure shows a plot of the similarity $s^\star(\mathbf{h}_\textrm{ref},\mathbf{h})$ between the reference user (green cross and lines) and the rest of the points on the map. The BS is placed at its center. The top right figure shows a plot of $\bar{f}(r_\textrm{ref},r)$ and the bottom right one shows a plot of $\bar{a}(\theta_\textrm{ref},\theta)$. User A (blue cross and lines) is spatially closer to the reference user than user B (red cross/lines), but the distance measure makes the latter appear closer than the former. The objective of this paper is to study theoretically these ambiguities, and propose a new channel distance and system settings that remove them.
  • Figure 2: The identifiable area's outline. Any region A of any shape included in there (e.g., the red region) verifies the necessary condition for identifiability. The green patch represents the identifiable neighborhood of the channel at its center. The orange segment is its radial axis and the yellow arc is its angular axis. The blue segment represents the ULA at the location of the BS. $r$ is the radial center of the area and $\theta$ is its angular center.
  • Figure 3: The left figure shows a plot of the similarity $\tilde{s}^\star(\mathbf{h}_\textrm{ref},\mathbf{h})$ between the reference user (green cross) and the rest of the points on the map. The BS is placed at its center. The top right figure shows a plot of $\bar{f}(r_\textrm{ref},r)$ and the bottom right one shows a plot of $\tilde{a}(\theta_\textrm{ref},\theta)$.
  • Figure 4: The identifiable area's outline. Any region A of any shape included in there (e.g., the red region) verifies the necessary condition for identifiability. The green patch represents the identifiable neighborhood of the channel at its center. The orange segment is its radial axis and the yellow arc is its angular axis. The blue circle represents the UCA at the location of the BS. $r$ is the radial center of the area.
  • Figure 5: Visualization of the distance measure for identifiable neighborhoods at (a) the inner, (b) center and (c) outer edge of the identifiable area as pictured in Fig. \ref{['fig:identifiable_area_UCA']}. The circle outline helps visualize how their shapes deviate from being perfectly round. UEs A and B are considered at the same distance from the point of view of the PI distance.
  • ...and 4 more figures

Theorems & Definitions (22)

  • Definition 1: Strong Identifiability
  • Definition 2: Weak Identifiability
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Corollary 2.1
  • proof
  • Proposition 1
  • proof
  • ...and 12 more