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Phase-Rotated Symbol Spreading for Scalable Rydberg Atomic-MIMO Detection

Jiuyu Liu, Yi Ma, Rahim Tafazolli

TL;DR

This work tackles scalability in RA-MIMO detection by addressing the intrinsic nonlinearity of Rydberg-readout signals. It introduces phase-rotated symbol spreading (PRSS), a transmitter-receiver co-design that transmits each symbol across two time slots with a phase offset of $\phi^{\star}=\pm\frac{\pi}{2}$ to reconstruct an effective linear model $\hat{\mathbf{s}} \approx \mathbf{H}\mathbf{x} + \mathbf{v}_e$, allowing the use of conventional RF-MIMO detectors. The paper derives the optimal phase and analyzes spectral efficiency, showing PRSS achieves $C_{prss} \approx \tfrac{1}{2} C_{rf}$ and delivers substantial BER gains over existing single-slot approaches (e.g., >$2.5$ dB with ML and >$10$ dB with ZF). Simulation results across small and large MIMO configurations corroborate the gains against EM-GS and single-slot RA-MIMO, highlighting the practical potential of PRSS for scalable RA-MIMO. The work also discusses complexity reductions and outlines future directions, including extended noise models, downlink precoding, and synchronization considerations.

Abstract

Multiple-input multiple-output (MIMO) systems using Rydberg atomic (RA) receivers face significant scalability challenges in signal detection due to their nonlinear signal models. This letter proposes phase-rotated symbol spreading (PRSS), which transmits each symbol across two consecutive time slots with an optimal π/2 phase offset. PRSS enables reconstruction of an effective linear signal model while maintaining spectral efficiency and facilitating the use of conventional RF-MIMO detection algorithms. Simulation results demonstrate that PRSS achieves greater than 2.5 dB and 10 dB bit error rate improvements compared to current single-transmission methods when employing optimal exhaustive search and low-complexity sub-optimal detection methods, respectively.

Phase-Rotated Symbol Spreading for Scalable Rydberg Atomic-MIMO Detection

TL;DR

This work tackles scalability in RA-MIMO detection by addressing the intrinsic nonlinearity of Rydberg-readout signals. It introduces phase-rotated symbol spreading (PRSS), a transmitter-receiver co-design that transmits each symbol across two time slots with a phase offset of to reconstruct an effective linear model , allowing the use of conventional RF-MIMO detectors. The paper derives the optimal phase and analyzes spectral efficiency, showing PRSS achieves and delivers substantial BER gains over existing single-slot approaches (e.g., > dB with ML and > dB with ZF). Simulation results across small and large MIMO configurations corroborate the gains against EM-GS and single-slot RA-MIMO, highlighting the practical potential of PRSS for scalable RA-MIMO. The work also discusses complexity reductions and outlines future directions, including extended noise models, downlink precoding, and synchronization considerations.

Abstract

Multiple-input multiple-output (MIMO) systems using Rydberg atomic (RA) receivers face significant scalability challenges in signal detection due to their nonlinear signal models. This letter proposes phase-rotated symbol spreading (PRSS), which transmits each symbol across two consecutive time slots with an optimal π/2 phase offset. PRSS enables reconstruction of an effective linear signal model while maintaining spectral efficiency and facilitating the use of conventional RF-MIMO detection algorithms. Simulation results demonstrate that PRSS achieves greater than 2.5 dB and 10 dB bit error rate improvements compared to current single-transmission methods when employing optimal exhaustive search and low-complexity sub-optimal detection methods, respectively.
Paper Structure (9 sections, 2 theorems, 18 equations, 4 figures, 1 algorithm)

This paper contains 9 sections, 2 theorems, 18 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. RA-MIMO Signal Model and Problem Statement
  3. RA-MIMO Signal Model
  4. Motivation and Design Objectives
  5. PRSS-Assisted RA-MIMO Detection
  6. Optimization and Implementation of PRSS
  7. Numerical and Simulation Results
  8. Conclusion and Outlook
  9. Proof of Theorem \ref{['thm01']}

Key Result

Theorem 1

Given the effective observations $y_{m}^{(1)}$ and $y_{m}^{(2)}$, the optimal phase offset $\phi \in (-\pi, \pi]$ that minimizes the least-squares estimation error of $s_m$ is as follows For $\phi^{\star} = \frac{\pi}{2}$, the optimal estimate of $s_{m}$ is as follows The case $\phi^{\star} = -\frac{\pi}{2}$ yields equivalent performance and is omitted for brevity.

Figures (4)

  • Figure 1: The relationship between $\sigma_{v_{\text{e}}}^{2}$ and $\phi$ is illustrated for RSR $= 30$ dB. It can be observed that $\sigma_{v_{\text{e}}}^{2}$ achieves its minimum value at $\phi^{\star} = \pm \frac{\pi}{2}$, which is equivalent to the original noise variance $\sigma_{v}^{2}$.
  • Figure 2: Effective noise variance versus RSR. At low RSR levels, the Taylor expansion introduces noise amplification, particularly for smaller $\sigma_{v}^{2}$. At high RSR levels, no observable noise amplification occurs.
  • Figure 3: Comparison between PRSS and four benchmarks in $8 \times 4$ MIMO systems. Benchmarks use $4$-QAM while PRSS uses $16$-QAM. ML (PRSS) achieves approximately $3$ dB gain over ML (single $\mathbf{z}$) at a of $10^{-3}$.
  • Figure 4: Comparison between PRSS and benchmarks in large MIMO systems: $M = 128$, $N = 64$. ZF (PRSS) consistently outperforms EM-GS across all achievable RSR values, with performance improving at higher RSR levels.

Theorems & Definitions (5)

  • Theorem 1
  • Corollary 1
  • Remark 1: Interaction with Channel Estimation
  • Remark 2: Spectral Efficiency Analysis
  • Remark 3: Optimality for Non-Gaussian Noise