Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-target DoA estimation with a single Rydberg atomic receiver by spectral analysis of spatially-resolved fluorescence

Liangcheng Han, Haifan Yin, Mérouane Debbah

TL;DR

This work tackles multi-target DoA estimation with a single Rydberg atomic receiver by reframing spatially resolved fluorescence as a spectral problem. By operating in a strong LO regime, the atomic response linearizes into a sum of spatial cosines, each corresponding to a target’s direction of arrival via $\Delta k_i = k(\sin\theta_0-\sin\theta_i)$, enabling Prony’s method to recover multiple directions from a single spatial snapshot. The Imaging-based Spectral Estimation (ISE) framework introduces virtual array processing through shifted spatial windows, derives a CRLB benchmark, and demonstrates through simulations near-CRLB performance and robust multi-target resolution across broadband conditions. It removes the prior cell-length dependency, enabling broadband operation and laying groundwork for multi-channel Rydberg receivers and holographic MIMO concepts. Practical implementation is discussed in terms of imaging hardware, LO delivery, and sampling considerations, with future work directed at wireless-system integration.

Abstract

Rydberg-based Direction-of-Arrival (DoA) estimation has been hampered by the complexity of receiver arrays and the single-target, narrow-band limitations of existing single-receiver methods. This paper introduces a novel approach that addresses these limitations. We demonstrate that by spatially resolving the fluorescence profile along the vapor cell, the multi-target problem can be effectively solved. Our approach hinges on the insight that by superimposing incoming signals with a strong local oscillator (LO), the complex atomic absorption pattern is linearized into a simple superposition of sinusoids. In this new representation, each spatial frequency uniquely and directly maps to the DoA of a target. This reduces the multi-target challenge into a spectral estimation problem, which we address using Prony's method. Our approach, termed Imaging-based Spectral Estimation (ISE), inherently supports multi-target detection and restores the full broadband capability of the sensor by removing the restrictive cell-length dependency. This development also shows potential for realizing multi-channel Rydberg receivers and the continuous-aperture sensing required for holographic multiple-input multiple-output (MIMO). We develop a comprehensive theoretical model, derive the Cramer-Rao Lower Bound (CRLB) as a performance benchmark, and present simulations validating the effectiveness of the approach to resolve multiple targets.

Multi-target DoA estimation with a single Rydberg atomic receiver by spectral analysis of spatially-resolved fluorescence

TL;DR

This work tackles multi-target DoA estimation with a single Rydberg atomic receiver by reframing spatially resolved fluorescence as a spectral problem. By operating in a strong LO regime, the atomic response linearizes into a sum of spatial cosines, each corresponding to a target’s direction of arrival via , enabling Prony’s method to recover multiple directions from a single spatial snapshot. The Imaging-based Spectral Estimation (ISE) framework introduces virtual array processing through shifted spatial windows, derives a CRLB benchmark, and demonstrates through simulations near-CRLB performance and robust multi-target resolution across broadband conditions. It removes the prior cell-length dependency, enabling broadband operation and laying groundwork for multi-channel Rydberg receivers and holographic MIMO concepts. Practical implementation is discussed in terms of imaging hardware, LO delivery, and sampling considerations, with future work directed at wireless-system integration.

Abstract

Rydberg-based Direction-of-Arrival (DoA) estimation has been hampered by the complexity of receiver arrays and the single-target, narrow-band limitations of existing single-receiver methods. This paper introduces a novel approach that addresses these limitations. We demonstrate that by spatially resolving the fluorescence profile along the vapor cell, the multi-target problem can be effectively solved. Our approach hinges on the insight that by superimposing incoming signals with a strong local oscillator (LO), the complex atomic absorption pattern is linearized into a simple superposition of sinusoids. In this new representation, each spatial frequency uniquely and directly maps to the DoA of a target. This reduces the multi-target challenge into a spectral estimation problem, which we address using Prony's method. Our approach, termed Imaging-based Spectral Estimation (ISE), inherently supports multi-target detection and restores the full broadband capability of the sensor by removing the restrictive cell-length dependency. This development also shows potential for realizing multi-channel Rydberg receivers and the continuous-aperture sensing required for holographic multiple-input multiple-output (MIMO). We develop a comprehensive theoretical model, derive the Cramer-Rao Lower Bound (CRLB) as a performance benchmark, and present simulations validating the effectiveness of the approach to resolve multiple targets.
Paper Structure (22 sections, 1 theorem, 65 equations, 7 figures, 1 table)

This paper contains 22 sections, 1 theorem, 65 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Theoretical Principles
  3. Rydberg Atom-Based Receiver Architecture
  4. Field Interference and Optical Response
  5. Proposed Approach
  6. Multi-Signal Linearization under LO-Dominance
  7. Spatially-Resolved Readout and Spectral Formulation
  8. Analysis of the Integrated-Power Method as a Special Case
  9. Spectral Estimation via Prony's Method
  10. Performance Analysis: Cramér-Rao Lower Bound
  11. Statistical Model and Fisher Information Matrix
  12. CRLB for Angle of Arrival
  13. Simulation Results
  14. Simulation Parameters
  15. Validation of the Linearization Assumption
  16. ...and 7 more sections

Key Result

Theorem 1

For unambiguous spectral estimation of spatial frequencies, the spatial sampling interval $\Delta x$ and the width $\ell$ of a rectangular window function $w_0(x)$ must satisfy $\Delta x \le \lambda/4$ and $\ell < \lambda/2$, respectively.

Figures (7)

  • Figure 1: Conceptual diagram of the spatially-resolved Rydberg atomic receiver.
  • Figure 2: Flow diagram of the proposed ISE approach. The process begins with (a) capturing the raw fluorescence profile. (b) A set of spatial windows are applied, and (c) the integrated absorption within each window yields the virtual channel measurements $y_j$. (d) A calibration step removes background effects, producing the calibrated signal $\tilde{y}_j$. (e) Prony's method is applied to the calibrated signal to estimate the spatial frequencies, which are then mapped to the final DoA estimates.
  • Figure 3: Validation of the linearization assumption. The true absorption coefficient is compared to the linearized model under (a) weak LO and (b) strong LO conditions.
  • Figure 4: Demonstration of the spectral estimation approach and the impact of LO strength. (a) Accurate DoA estimation under strong LO. (b) Degraded estimation under weak LO. (c) RMSE of DoA estimation versus LO-to-signal ratio.
  • Figure 5: RMSE of DoA estimation versus SNR for single and multiple targets. The performance of Prony's method is compared against the CRLB for the single-target case.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • proof