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Low-Complexity OTFS-Based Over-the-Air Computation Design for Time-Varying Channels

Xinyu Huang, Henrik Hellström, Carlo Fischione

TL;DR

This work addresses AirComp for high-mobility devices over multipath time-varying channels by employing OTFS to render the DD-domain channel quasi-static and robust to Doppler. It proposes three schemes: S1 optimizes transmit powers and a denoising factor to minimize MSE; S2 adds zero-padding with SIC-based interference cancellation to further reduce MSE while lowering complexity; and S3 formulates a matrix-based, iterative design that jointly optimizes device precoders and FC receivers. Numerical results show S3 achieves the best error performance at higher complexity, S2 offers a favorable MSE-CPU trade-off, and S1 remains robust with low complexity, particularly at low SNR. These findings highlight practical paths for efficient AirComp in dynamic wireless environments, with implications for IoT, federated learning, and integrated sensing-communication systems.

Abstract

This paper investigates over-the-air computation (AirComp) over multiple-access time-varying channels, where devices with high mobility transmit their sensing data to a fusion center (FC) for averaging. To combat the Doppler shift induced by time-varying channels, each device adopts orthogonal time frequency space (OTFS) modulation. Our objective is minimizing the mean squared error (MSE) for the target function estimation. Due to the multipath time-varying channels, the OTFS-based AirComp not only suffers from noise but also interference. Specifically, we propose three schemes, namely S1, S2, and S3, for the target function estimation. S1 directly estimates the target function under the impacts of noise and interference. S2 mitigates the interference by introducing a zero padding-assisted OTFS. In S3, we propose an iterative algorithm to estimate the function in a matrix form. In the numerical results, we evaluate the performance of S1, S2, and S3 from the perspectives of MSE and computational complexity, and compare them with benchmarks. Specifically, compared to benchmarks, S3 outperforms them with a significantly lower MSE but incurs a higher computational complexity. In contrast, S2 demonstrates a reduction in both MSE and computational complexity. Lastly, S1 shows superior error performance at small SNR and reduced computational complexity.

Low-Complexity OTFS-Based Over-the-Air Computation Design for Time-Varying Channels

TL;DR

This work addresses AirComp for high-mobility devices over multipath time-varying channels by employing OTFS to render the DD-domain channel quasi-static and robust to Doppler. It proposes three schemes: S1 optimizes transmit powers and a denoising factor to minimize MSE; S2 adds zero-padding with SIC-based interference cancellation to further reduce MSE while lowering complexity; and S3 formulates a matrix-based, iterative design that jointly optimizes device precoders and FC receivers. Numerical results show S3 achieves the best error performance at higher complexity, S2 offers a favorable MSE-CPU trade-off, and S1 remains robust with low complexity, particularly at low SNR. These findings highlight practical paths for efficient AirComp in dynamic wireless environments, with implications for IoT, federated learning, and integrated sensing-communication systems.

Abstract

This paper investigates over-the-air computation (AirComp) over multiple-access time-varying channels, where devices with high mobility transmit their sensing data to a fusion center (FC) for averaging. To combat the Doppler shift induced by time-varying channels, each device adopts orthogonal time frequency space (OTFS) modulation. Our objective is minimizing the mean squared error (MSE) for the target function estimation. Due to the multipath time-varying channels, the OTFS-based AirComp not only suffers from noise but also interference. Specifically, we propose three schemes, namely S1, S2, and S3, for the target function estimation. S1 directly estimates the target function under the impacts of noise and interference. S2 mitigates the interference by introducing a zero padding-assisted OTFS. In S3, we propose an iterative algorithm to estimate the function in a matrix form. In the numerical results, we evaluate the performance of S1, S2, and S3 from the perspectives of MSE and computational complexity, and compare them with benchmarks. Specifically, compared to benchmarks, S3 outperforms them with a significantly lower MSE but incurs a higher computational complexity. In contrast, S2 demonstrates a reduction in both MSE and computational complexity. Lastly, S1 shows superior error performance at small SNR and reduced computational complexity.
Paper Structure (21 sections, 2 theorems, 60 equations, 11 figures, 1 algorithm)

This paper contains 21 sections, 2 theorems, 60 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. OTFS Modulation & Demodulation
  4. OTFS-based AirComp System
  5. OTFS-Based AirComp Design
  6. Problem Formulation
  7. Optimization of $p_u$ and $\eta$
  8. Interference Cancellation for ZP-Assisted OTFS-Based AirComp
  9. ZP-Assisted OTFS
  10. Algorithm for Interference Cancellation
  11. Different $l_i$ associated to each path
  12. At least two paths share the same $l$
  13. Iterative Estimation for OTFS-Based AirComp
  14. Problem Formulation
  15. Optimization of $\boldsymbol{B}_u$ and $\boldsymbol{V}$
  16. ...and 6 more sections

Key Result

Theorem 1

The optimal $p_u$ and $\eta$ that jointly minimize $\mathcal{P}1$ are given by and

Figures (11)

  • Figure 1: Illustration of the OTFS-based AirComp system.
  • Figure 2: DD domain input-output relation for $N=M=8$, $R_u=4$, $l_u=[0,1,2,3]$, and $k_u=[0,1,2,3], \forall u\in\mathcal{U}$.
  • Figure 3: Illustration of the process for determining $\theta_m$ and $m^*$. (a): $\mathcal{L}_u=[0,2,4,5], m^*=5$. (b): $\mathcal{L}_u=[0,0,4,5]$, $m^*=4$. (c): $\mathcal{L}_u=[0,2,2,5]$, $m^*=3$.
  • Figure 4: MSE versus SNR for S1 and S2, where different transmission power policies are applied.
  • Figure 5: MSE versus SNR for S1, S2, and benchmarks.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • Theorem 2