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Doppler-Resilient LEO Satellite OFDM Transmission with Affine Frequency Domain Pilot

Shuntian Tang, Xiaomei Wu, Xinyi Wang, Le Zhao, Guang Yang, Zilong Liu, Fan Liu, Zesong Fei

TL;DR

This work tackles Doppler-induced degradation in OFDM for high-mobility LEO NTN sub-systems by introducing an AF-domain pilot scheme that enables explicit AF-domain CSI estimation and a transform to the TF domain via $\mathbf{H}_{\text{FD},k}=\mathbf{T}^H\mathbf{H}_{\text{AFD},k}\mathbf{T}$. AF-domain pilots are generated by IDAFT from a single pilot, yielding constant modulus signals and enabling virtual pilots on data-carrying resources. The authors reveal an intrinsic $P$-order AR structure in the received AF-domain pilots and channel, but show that classic AR-based prediction can be unstable; thus, they design a data-driven LSTM-based predictor with a Re-concatenation, Multi-layer LSTM Encoder, and Decoder/Re-mapping to forecast future pilots and CSI offline with MMSE loss. Numerical results on NTN-TDL channels demonstrate that AF-domain pilots with LSTM prediction significantly reduce BER under high residual Doppler, outperforming conventional TF-domain OFDM with interpolation and AF-domain schemes without prediction, and approaching a Perfect CSI baseline at moderate-to-high SNR. The approach offers a practical pathway to robust next-generation NTN communications for LEO satellites by combining structure-exploiting pilot design with deep learning-based channel prediction.

Abstract

Orthogonal frequency division multiplexing (OFDM) based low Earth orbit (LEO) satellite communication system suffers from severe Doppler shifts, while {the Doppler-resilient affine frequency-division multiplexing (AFDM) transmission suffers from significantly high processing complexity in data detection}. In this paper, we explore the channel estimation gain of affine frequency (AF) domain pilot to enhance the OFDM transmission under high mobility. Specifically, we propose a novel AF domain pilot embedding scheme for satellite-ground downlink OFDM systems for capturing the channel characteristics. By exploiting the autoregressive (AR) property of adjacent channels, a long short-term memory (LSTM) based predictor is designed to replace conventional interpolation operation in OFDM channel estimation. Simulation results show that the proposed transmission scheme significantly outperforms conventional OFDM scheme in terms of bit error rate (BER) under high Doppler scenarios, thus paving a new way for the design of next generation non-terrestrial network (NTN) communication systems.

Doppler-Resilient LEO Satellite OFDM Transmission with Affine Frequency Domain Pilot

TL;DR

This work tackles Doppler-induced degradation in OFDM for high-mobility LEO NTN sub-systems by introducing an AF-domain pilot scheme that enables explicit AF-domain CSI estimation and a transform to the TF domain via . AF-domain pilots are generated by IDAFT from a single pilot, yielding constant modulus signals and enabling virtual pilots on data-carrying resources. The authors reveal an intrinsic -order AR structure in the received AF-domain pilots and channel, but show that classic AR-based prediction can be unstable; thus, they design a data-driven LSTM-based predictor with a Re-concatenation, Multi-layer LSTM Encoder, and Decoder/Re-mapping to forecast future pilots and CSI offline with MMSE loss. Numerical results on NTN-TDL channels demonstrate that AF-domain pilots with LSTM prediction significantly reduce BER under high residual Doppler, outperforming conventional TF-domain OFDM with interpolation and AF-domain schemes without prediction, and approaching a Perfect CSI baseline at moderate-to-high SNR. The approach offers a practical pathway to robust next-generation NTN communications for LEO satellites by combining structure-exploiting pilot design with deep learning-based channel prediction.

Abstract

Orthogonal frequency division multiplexing (OFDM) based low Earth orbit (LEO) satellite communication system suffers from severe Doppler shifts, while {the Doppler-resilient affine frequency-division multiplexing (AFDM) transmission suffers from significantly high processing complexity in data detection}. In this paper, we explore the channel estimation gain of affine frequency (AF) domain pilot to enhance the OFDM transmission under high mobility. Specifically, we propose a novel AF domain pilot embedding scheme for satellite-ground downlink OFDM systems for capturing the channel characteristics. By exploiting the autoregressive (AR) property of adjacent channels, a long short-term memory (LSTM) based predictor is designed to replace conventional interpolation operation in OFDM channel estimation. Simulation results show that the proposed transmission scheme significantly outperforms conventional OFDM scheme in terms of bit error rate (BER) under high Doppler scenarios, thus paving a new way for the design of next generation non-terrestrial network (NTN) communication systems.
Paper Structure (13 sections, 3 theorems, 21 equations, 4 figures, 1 table)

This paper contains 13 sections, 3 theorems, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. AF-Domain Pilot Aided OFDM Transmission Scheme
  3. Satellite Communication Channel Model
  4. Doppler-Resilient OFDM Transmission with AF-Domain Pilot
  5. LSTM-based Virtual Received Pilots Prediction based Channel Prediction
  6. AR Property of Received Pilot Sequence
  7. LSTM-based Pilot Prediction Module Design
  8. Re-concatenation Module
  9. Multi-layer LSTM Encoder Module
  10. Decoder and Re-mapping Module
  11. Training Strategy
  12. Numerical Results
  13. Conclusion

Key Result

Lemma 1

Assume that the transmitter sends the same pilot symbol $\mathbf{x}_{\text{p}}$ on each symbol in the AF domain within the channel coherence time and bandwidth. The sequence of received pilot symbols $\{\mathbf{y}_{\text{p},k}\}$ in the AF domain possesses the $P$-order AR property described in (yAR

Figures (4)

  • Figure 1: Block diagram of AF-domain pilot embedding enhanced LEO-OFDM system.
  • Figure 2: Structure of LSTM-based prediction module.
  • Figure 3: BER performance comparison among different schemes.
  • Figure 4: BER performance under different pilot-to-data symbol number ratios.

Theorems & Definitions (5)

  • Remark 1
  • Lemma 1
  • Theorem 1
  • Remark 2
  • Corollary 1