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Low-Complexity Pilot-Aided Doppler Ambiguity Estimation for OTFS Parametric Channel Estimation

Bo-Yuan Chen, Hsuan-Jung Su

TL;DR

This paper tackles Doppler ambiguity in OTFS systems operating in high-mobility NTN links, where true Doppler shifts exceed the fundamental grid. It derives the aliasing-induced phase effects in the DD-domain I/O and shows that ambiguity manifests as a residual fast-time phase, rendering standard MLE ineffective. A low-complexity pilot-aided framework is proposed, featuring pairwise differential processing and majority voting to reliably estimate the ambiguity integer, followed by refined MLE for fractional Doppler and path gains; two pilot strategies (EP-GZ and DSP) balance interference suppression and spectral efficiency. Simulation results demonstrate that the proposed method eliminates the error floor, achieving BER and NMSE close to the exhaustive Extended MLE and Perfect CSI benchmarks while maintaining comparable complexity to conventional MLE. The approach thus extends OTFS applicability to extreme mobility scenarios, offering practical gains for LEO satellite communications.

Abstract

Orthogonal Time Frequency Space (OTFS) modulation offers robust performance in high-mobility scenarios by transforming time-varying channels into the delay-Doppler (DD) domain. However, in high-mobility environment such as emerging 5G Non-Terrestrial Networks (NTN), the extreme orbital velocities of Low Earth Orbit (LEO) satellites frequently cause the physical Doppler shifts to exceed the fundamental grid range. This Doppler ambiguity induces severe model mismatch and renders traditional MLE channel estimators ineffective. To address this challenge, this paper proposes a novel low-complexity pilot-aided Doppler ambiguity detection and compensation framework. We first mathematically derive the OTFS input-output relationship in the presence of aliasing, revealing that Doppler ambiguity manifests itself as a distinct phase rotation along the delay dimension. Leveraging this insight, we developed a two-stage estimator that utilizes pairwise phase differences between pilot symbols to identify the integer ambiguity, followed by a refined Maximum Likelihood Estimation (MLE) for channel recovery. We investigate two pilot arrangements, Embedded Pilot with Guard Zone (EP-GZ) and Data-Surrounded Pilot (DSP), to analyze the trade-off between interference suppression and spectral efficiency. Simulation results demonstrate that the proposed scheme effectively eliminates the error floor caused by ambiguity, achieving Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) performance comparable to the exhaustive search benchmark while maintaining a computational complexity similar to standard MLE.

Low-Complexity Pilot-Aided Doppler Ambiguity Estimation for OTFS Parametric Channel Estimation

TL;DR

This paper tackles Doppler ambiguity in OTFS systems operating in high-mobility NTN links, where true Doppler shifts exceed the fundamental grid. It derives the aliasing-induced phase effects in the DD-domain I/O and shows that ambiguity manifests as a residual fast-time phase, rendering standard MLE ineffective. A low-complexity pilot-aided framework is proposed, featuring pairwise differential processing and majority voting to reliably estimate the ambiguity integer, followed by refined MLE for fractional Doppler and path gains; two pilot strategies (EP-GZ and DSP) balance interference suppression and spectral efficiency. Simulation results demonstrate that the proposed method eliminates the error floor, achieving BER and NMSE close to the exhaustive Extended MLE and Perfect CSI benchmarks while maintaining comparable complexity to conventional MLE. The approach thus extends OTFS applicability to extreme mobility scenarios, offering practical gains for LEO satellite communications.

Abstract

Orthogonal Time Frequency Space (OTFS) modulation offers robust performance in high-mobility scenarios by transforming time-varying channels into the delay-Doppler (DD) domain. However, in high-mobility environment such as emerging 5G Non-Terrestrial Networks (NTN), the extreme orbital velocities of Low Earth Orbit (LEO) satellites frequently cause the physical Doppler shifts to exceed the fundamental grid range. This Doppler ambiguity induces severe model mismatch and renders traditional MLE channel estimators ineffective. To address this challenge, this paper proposes a novel low-complexity pilot-aided Doppler ambiguity detection and compensation framework. We first mathematically derive the OTFS input-output relationship in the presence of aliasing, revealing that Doppler ambiguity manifests itself as a distinct phase rotation along the delay dimension. Leveraging this insight, we developed a two-stage estimator that utilizes pairwise phase differences between pilot symbols to identify the integer ambiguity, followed by a refined Maximum Likelihood Estimation (MLE) for channel recovery. We investigate two pilot arrangements, Embedded Pilot with Guard Zone (EP-GZ) and Data-Surrounded Pilot (DSP), to analyze the trade-off between interference suppression and spectral efficiency. Simulation results demonstrate that the proposed scheme effectively eliminates the error floor caused by ambiguity, achieving Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) performance comparable to the exhaustive search benchmark while maintaining a computational complexity similar to standard MLE.
Paper Structure (19 sections, 24 equations, 3 figures, 1 table)

This paper contains 19 sections, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. SFFT-based OTFS Architecture
  4. DD Domain Input-Output Relation
  5. Doppler Ambiguity Analysis
  6. Physical Constraints on Unambiguous Doppler
  7. Mathematical Modeling of Doppler Ambiguity
  8. Proposed Pilot-Aided Doppler Ambiguity Estimation and Channel Estimation
  9. Pilot Arrangement Strategies
  10. Received Pilot Signal Model and Phase Analysis
  11. Proposed Pairwise Difference and Voting Algorithm
  12. Pairwise Differential Processing
  13. Ambiguity Resolution and Majority Voting
  14. Parametric Channel Estimation and Data Detection
  15. Computational Complexity Analysis
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Illustration of the proposed pilot arrangement strategies in the DD domain: (a) Embedded Pilot with Guard Zone (EP-GZ); (b) Data-Surrounded Pilot (DSP).
  • Figure 2: Average Doppler Ambiguity Detection Probability for different PDR and pilot arrangement.
  • Figure 3: System simulation results with PDR = 25 dB: (a) Bit Error Rate, (b) Channel estimation NMSE, and (c) Effective Spectral Efficiency.