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OTFS Channel Estimation and Detection for Channels with Very Large Delay Spread

Preety Priya, Yi Hong, Emanuele Viterbo

TL;DR

The paper addresses OTFS channel estimation and detection in overspread channels where $\tau_{\max}\nu_{\max}>1$, causing aliasing that defeats conventional CE. It introduces a two-stage CE based on a DD-domain training frame with a dual-chirp and a high-power pilot, combining DD-domain embedded-pilot estimation for aliased delays/Dopplers with time-domain chirp-correlation to recover actual path parameters, plus optional refinements to resolve ambiguities. A modified low-complexity MRC detector for overspread channels (RZP-OTFS) is proposed, including complexity considerations and convergence behavior. Simulation results show substantial NMSE reduction and BER performance approaching that of more complex detectors, with refinement steps rarely invoked, validating the approach for low-latency, high-mobility scenarios. The work advances practical OTFS in overspread environments and highlights potential extensions to fractional Doppler.

Abstract

In low latency applications and in general, for overspread channels, channel delay spread is a large percentage of the transmission frame duration. In this paper, we consider OTFS in an overspread channel exhibiting a delay spread that exceeds the block duration in a frame, where traditional channel estimation (CE) fails. We propose a two-stage CE method based on a delay-Doppler (DD) training frame, consisting of a dual chirp converted from time domain and a higher power pilot. The first stage employs a DD domain embedded pilot CE to estimate the aliased delays (due to modulo operation) and Doppler shifts, followed by identifying all the underspread paths not coinciding with any overspread path. The second stage utilizes time domain dual chirp correlation to estimate the actual delays and Doppler shifts of the remaining paths. This stage also resolves ambiguity in estimating delays and Doppler shifts for paths sharing same aliased delay. Furthermore, we present a modified low-complexity maximum ratio combining (MRC) detection algorithm for OTFS in overspread channels. Finally, we evaluate performance of OTFS using the proposed CE and the modified MRC detection in terms of normalized mean square error (NMSE) and bit error rate (BER).

OTFS Channel Estimation and Detection for Channels with Very Large Delay Spread

TL;DR

The paper addresses OTFS channel estimation and detection in overspread channels where , causing aliasing that defeats conventional CE. It introduces a two-stage CE based on a DD-domain training frame with a dual-chirp and a high-power pilot, combining DD-domain embedded-pilot estimation for aliased delays/Dopplers with time-domain chirp-correlation to recover actual path parameters, plus optional refinements to resolve ambiguities. A modified low-complexity MRC detector for overspread channels (RZP-OTFS) is proposed, including complexity considerations and convergence behavior. Simulation results show substantial NMSE reduction and BER performance approaching that of more complex detectors, with refinement steps rarely invoked, validating the approach for low-latency, high-mobility scenarios. The work advances practical OTFS in overspread environments and highlights potential extensions to fractional Doppler.

Abstract

In low latency applications and in general, for overspread channels, channel delay spread is a large percentage of the transmission frame duration. In this paper, we consider OTFS in an overspread channel exhibiting a delay spread that exceeds the block duration in a frame, where traditional channel estimation (CE) fails. We propose a two-stage CE method based on a delay-Doppler (DD) training frame, consisting of a dual chirp converted from time domain and a higher power pilot. The first stage employs a DD domain embedded pilot CE to estimate the aliased delays (due to modulo operation) and Doppler shifts, followed by identifying all the underspread paths not coinciding with any overspread path. The second stage utilizes time domain dual chirp correlation to estimate the actual delays and Doppler shifts of the remaining paths. This stage also resolves ambiguity in estimating delays and Doppler shifts for paths sharing same aliased delay. Furthermore, we present a modified low-complexity maximum ratio combining (MRC) detection algorithm for OTFS in overspread channels. Finally, we evaluate performance of OTFS using the proposed CE and the modified MRC detection in terms of normalized mean square error (NMSE) and bit error rate (BER).
Paper Structure (14 sections, 31 equations, 5 figures, 2 tables, 2 algorithms)

This paper contains 14 sections, 31 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Channel Estimation for overspread channels
  4. Proposed Training Frame Arrangement
  5. Proposed Two-Stage CE
  6. First Stage CE using Embedded Pilot
  7. Second Stage CE using Dual Chirps
  8. Error correction in Doppler when $|\mathcal{K}_{{\hat{\ell}}}|>1$
  9. Error correction when path is unrecognized due to same Doppler
  10. Complexity
  11. MRC Detection for OTFS in Overspread Channels
  12. Detection Complexity and Convergence
  13. Results and Discussions
  14. Conclusion

Figures (5)

  • Figure 1: DD received pilot echos with $M=8,N=6$ with 9 paths $(l_i,k_i)=\{(0,0),(9,4), (2,1),(10,3),(4,2),(12,2)$, $(20,5),(14,1),(30,1) \}$. The path index $i=0,\ldots, 8$ is given in each cell, X represents an underspread path ($l_i<M$) and O an overspread path ($l_i\geq M$).
  • Figure 2: Flow Chart of Two-Stage CE
  • Figure 3: NMSE vs $\text{SNR}_{\rm p}$.
  • Figure 4: BER vs $\text{SNR}_{\rm d}$, for $\text{SNR}_{\rm p}=30$ dB and $\text{SNR}_{\rm c}=23$ dB using the proposed CE and MRC detection.
  • Figure 5: BER vs $\text{SNR}_{\rm d}$ comparison between MRC and MP $(M=N=32, L=4$, 4-QAM).