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OTFS-based Robust MMSE Precoding Design in Over-the-air Computation

Dongkai Zhou, Jing Guo, Siqiang Wang, Zhong Zheng, Zesong Fei, Weijie Yuan, Xinyi Wang

TL;DR

This work investigates an OTFS-based AirComp system in the presence of time-frequency dual-selective channels and proposes a robust precoding matrix aiming at minimizing mean square error, which takes into account the estimation error from the receiver noise and the outdated CSI.

Abstract

Over-the-air computation (AirComp), as a data aggregation method that can improve network efficiency by exploiting the superposition characteristics of wireless channels, has received much attention recently. Meanwhile, the orthogonal time frequency space (OTFS) modulation can provide a strong Doppler resilience and facilitate reliable transmission for high-mobility communications. Hence, in this work, we investigate an OTFS-based AirComp system in the presence of time-frequency dual-selective channels. In particular, we commence from the development of a novel transmission framework for the considered system, where the pilot signal is sent together with data, and the channel estimation is implemented according to the echo from the access point to the sensor, thereby reducing the overhead of channel state information (CSI) feedback. Hereafter, based on the CSI estimated from the previous frame, a robust precoding matrix aiming at minimizing mean square error in the current frame is designed, which takes into account the estimation error from the receiver noise and the outdated CSI. The simulation results demonstrate the effectiveness of the proposed robust precoding scheme by comparing it with the non-robust precoding. The performance gain is more obvious in a high signal-to-noise ratio in case of large channel estimation errors.

OTFS-based Robust MMSE Precoding Design in Over-the-air Computation

TL;DR

This work investigates an OTFS-based AirComp system in the presence of time-frequency dual-selective channels and proposes a robust precoding matrix aiming at minimizing mean square error, which takes into account the estimation error from the receiver noise and the outdated CSI.

Abstract

Over-the-air computation (AirComp), as a data aggregation method that can improve network efficiency by exploiting the superposition characteristics of wireless channels, has received much attention recently. Meanwhile, the orthogonal time frequency space (OTFS) modulation can provide a strong Doppler resilience and facilitate reliable transmission for high-mobility communications. Hence, in this work, we investigate an OTFS-based AirComp system in the presence of time-frequency dual-selective channels. In particular, we commence from the development of a novel transmission framework for the considered system, where the pilot signal is sent together with data, and the channel estimation is implemented according to the echo from the access point to the sensor, thereby reducing the overhead of channel state information (CSI) feedback. Hereafter, based on the CSI estimated from the previous frame, a robust precoding matrix aiming at minimizing mean square error in the current frame is designed, which takes into account the estimation error from the receiver noise and the outdated CSI. The simulation results demonstrate the effectiveness of the proposed robust precoding scheme by comparing it with the non-robust precoding. The performance gain is more obvious in a high signal-to-noise ratio in case of large channel estimation errors.
Paper Structure (9 sections, 1 theorem, 25 equations, 6 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 25 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Network Model
  4. Proposed OTFS-based Transmission Framework
  5. Robust Precoding Design for OTFS
  6. Channel Estimation and Error Modeling
  7. Robust MMSE Precoder for OTFS
  8. Simulation Results
  9. Conclusions

Key Result

Proposition 1

For our proposed transmission framework of the OTFS-based AirComp system, the robust MMSE precoder of the $q$-th sensor at the current frame is given by

Figures (6)

  • Figure 1: The illustration of the transmission framework of the sensor in the considered system.
  • Figure 2: The schematic diagram of the frame structure of the OTFS-based signal.
  • Figure 3: Computation NMSE versus SNR under different estimation errors for integer Doppler case and fractional Doppler case when delay taps and Doppler taps are accurate.
  • Figure 4: Computation NMSE versus SNR under different channel estimation noise in the case of integer Doppler case when delay taps and Doppler taps are imperfect.
  • Figure 5: Computation NMSE versus the ratio of data power and pilot power under different noise levels when $\rho=0.99$.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Remark 1
  • Remark 2