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Unique Word Channel Estimation for Oversampled OTFS

Radim Zedka, Roman Marsalek, Marek Bobula, Arman Farhang

TL;DR

This work addresses the practical challenge of data-to-pilot energy leakage in oversampled, pulse-shaped OTFS systems by first analyzing the leakage in CP-OTFS and then introducing UW-OTFS, which places the CSI pilot in the oversampled time domain to avoid leakage. The authors develop a unified GCE-BEM/LMMSE-based framework for CSI and data estimation applicable to both CP-OTFS and UW-OTFS, with UW-OTFS achieving lower OOB emissions and a 36% gain in spectral efficiency. They propose two pilot designs—Dirac impulses (optimal but wideband) and a practical UW pilot with spectral shaping—plus an Arbitrary UW pilot generalization, and provide a thorough complexity and memory footprint analysis. Numerical results show leakage-free performance and enhanced spectral efficiency for UW-OTFS in fractional Doppler channels, at the expense of higher receiver complexity. The practical impact lies in enabling more efficient, robust OTFS-based communication in high-mobility scenarios while offering a clear design path for CSI estimation in oversampled, pulse-shaped waveforms.

Abstract

Practical aspects of orthogonal time frequency space (OTFS), such as channel estimation and its performance in fractional delay-Doppler (DD) channels, are a lively topic in the OTFS community. Oversampling and pulse shaping are also discussed in the existing literature, but not in the context of channel estimation. To the best of our knowledge, this paper is the first to address the problem of data-to-pilot and vice versa energy leakage caused by oversampling and pulse shaping in OTFS. Theoretical analysis is performed on an oversampled, pulse-shaped OTFS implementing the embedded pilot channel estimation technique, revealing a trade-off between the amount of energy leakage and excess bandwidth introduced by the pulse shape. Next, a novel variant of OTFS is introduced, called UW-OTFS, which is designed to overcome the leakage problem by placing the pilot in the oversampled time domain instead of the DD domain. The unique structure of UW-OTFS offers 36 percent higher spectral efficiency than the OTFS with embedded pilot. UW-OTFS also outperforms traditional OTFS in terms of bit error ratio and out-of-band emissions.

Unique Word Channel Estimation for Oversampled OTFS

TL;DR

This work addresses the practical challenge of data-to-pilot energy leakage in oversampled, pulse-shaped OTFS systems by first analyzing the leakage in CP-OTFS and then introducing UW-OTFS, which places the CSI pilot in the oversampled time domain to avoid leakage. The authors develop a unified GCE-BEM/LMMSE-based framework for CSI and data estimation applicable to both CP-OTFS and UW-OTFS, with UW-OTFS achieving lower OOB emissions and a 36% gain in spectral efficiency. They propose two pilot designs—Dirac impulses (optimal but wideband) and a practical UW pilot with spectral shaping—plus an Arbitrary UW pilot generalization, and provide a thorough complexity and memory footprint analysis. Numerical results show leakage-free performance and enhanced spectral efficiency for UW-OTFS in fractional Doppler channels, at the expense of higher receiver complexity. The practical impact lies in enabling more efficient, robust OTFS-based communication in high-mobility scenarios while offering a clear design path for CSI estimation in oversampled, pulse-shaped waveforms.

Abstract

Practical aspects of orthogonal time frequency space (OTFS), such as channel estimation and its performance in fractional delay-Doppler (DD) channels, are a lively topic in the OTFS community. Oversampling and pulse shaping are also discussed in the existing literature, but not in the context of channel estimation. To the best of our knowledge, this paper is the first to address the problem of data-to-pilot and vice versa energy leakage caused by oversampling and pulse shaping in OTFS. Theoretical analysis is performed on an oversampled, pulse-shaped OTFS implementing the embedded pilot channel estimation technique, revealing a trade-off between the amount of energy leakage and excess bandwidth introduced by the pulse shape. Next, a novel variant of OTFS is introduced, called UW-OTFS, which is designed to overcome the leakage problem by placing the pilot in the oversampled time domain instead of the DD domain. The unique structure of UW-OTFS offers 36 percent higher spectral efficiency than the OTFS with embedded pilot. UW-OTFS also outperforms traditional OTFS in terms of bit error ratio and out-of-band emissions.
Paper Structure (40 sections, 81 equations, 12 figures, 5 tables, 2 algorithms)

This paper contains 40 sections, 81 equations, 12 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notation
  3. Basic Definition of OTFS
  4. OTFS with Pulse Shaping
  5. CP-OTFS Transmitter
  6. Linear Time-Variant Channel Model
  7. CP-OTFS - Basic Receiver Processing
  8. Delay Leakage Analysis
  9. Embedded Impulse Pilot
  10. Leakage Analysis
  11. Proposed UW-OTFS
  12. Transmitter
  13. Equivalent Channel Matrix
  14. Data Estimation
  15. Proposed Pilot Design and CSI Estimation
  16. ...and 25 more sections

Figures (12)

  • Figure 1: Waveform diagrams of: a) the data part of UW-OTFS, b) the UW pilot of UW-OTFS, c) CP-OTFS.
  • Figure 2: Embedded pilot PSD comparison (top) and energy dispersion in the DD domain (bottom) for various values of the roll-off factor.
  • Figure 3: Illustration of the delay dimension leakage in the energy of $\mathbf{\hat{D}}$.
  • Figure 4: Transmitter structures of CP-OTFS and UW-OTFS (UW pilot omitted).
  • Figure 5: PSD comparison of the UW-OTFS data transmission $s_{\rm d}(.)$ in \ref{['eq_TX_s_0_waveform_1']} with the Dirac UW pilot \ref{['eq_TX_s_u_ideal_waveform_1']}, with the proposed UW pilot \ref{['eq_TX_s_u_waveform_1']} and without the pilot.
  • ...and 7 more figures