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Low-Complexity Iterative Detection for Orthogonal Time Frequency Space Modulation

P. Raviteja, Khoa T. Phan, Qianyu Jin, Yi Hong, Emanuele Viterbo

arXiv:1709.09402v1cs.ITmath.IT

TL;DR

OFDM is not robust to time-varying channels with high Doppler, motivating OTFS as an alternative for delay–Doppler channels. The paper derives an uncoded OTFS input–output relation and proposes a sparsity-exploiting message-passing detector adapted to fractional-Doppler interference; simulations report an OTFS advantage over OFDM.

  • Problem

    OFDM is not robust to time-varying channels, especially channels with high Doppler spread.

    Source: §I · p. 1

  • Method

    The paper derives the uncoded OTFS input–output relation and uses a sparse-factor-graph message-passing detector with Gaussian-approximated interference, adapted to fractional Doppler.

    Source: §I · p. 1, A. Low-complexity MP detection… · p. 4

  • Results

    At BER 10^-4, OTFS outperforms OFDM by approximately 15 dB in the reported 4-QAM delay–Doppler-channel comparison.

    Source: §V · p. 6

  • Takeaways & Limitations

    Simulations show significant OTFS BER gains over OFDM under various channel conditions, with the proposed detector mitigating fractional-Doppler interference.

    Source: §VI · p. 6

Abstract

from arXiv · show

We elaborate on the recently proposed orthogonal time frequency space (OTFS) modulation technique, which provides significant advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. We first derive the input--output relation describing OTFS modulation and demodulation (mod/demod) for delay--Doppler channels with arbitrary number of paths, with given delay and Doppler values. We then propose a low-complexity message passing (MP) detection algorithm, which is suitable for large-scale OTFS taking advantage of the inherent channel sparsity. Since the fractional Doppler paths (i.e., not exactly aligned with the Doppler taps) produce the inter Doppler interference (IDI), we adapt the MP detection algorithm to compensate for the effect of IDI in order to further improve performance. Simulations results illustrate the superior performance gains of OTFS over OFDM under various channel conditions.

I. INTRODUCTION

OFDM is not robust to time-varying channels with high Doppler, motivating interest in alternatives such as OTFS. This paper derives an uncoded OTFS input–output relation and proposes sparse-channel message-passing detection, including adaptation for fractional-Doppler interference.

I. INTRODUCTION

  • OFDM is not robust to time-varying channels, especially those with high Doppler, while OTFS was proposed with advantages over OFDM in delay–Doppler channels.Source: §I · p. 1
  • The paper derives the uncoded OTFS input–output relation and proposes low-complexity message-passing detection that exploits channel sparsity and compensates for fractional-Doppler interference.The introduction also notes that the detector can be applied to OFDM to compensate for Doppler effects.Source: §I · p. 1

II. OTFS MODULATION/DEMODULATION

  • The OTFS modulator and demodulator are introduced as the subject of the paper's signal-processing framework.Source: §II · p. 1, Figure 1 · p. 2

B. OTFS modulation

OTFS maps information symbols from a delay–Doppler grid to a time–frequency grid, then forms the transmitted waveform. That waveform passes through a time-varying channel characterized by delay and Doppler, with additive receiver noise.

B. OTFS modulation

  • OTFS maps delay–Doppler information symbols to time–frequency symbols using the inverse symplectic finite Fourier transform, then maps them to a transmitted waveform.Source: B. OTFS modulation · p. 2

C. Wireless transmission and reception

D. OTFS demodulation

The receiver applies a matched filter and samples its output to obtain time–frequency observations, then applies the SFFT. The stated channel relation assumes ideal bi-orthogonal pulses, a condition the text says practical pulses such as rectangular pulses do not satisfy.

D. OTFS demodulation

A. Sparse representation of the delay–Doppler channel

The delay–Doppler channel is represented by paths with delay and Doppler taps, and fractional Doppler can spread a transmitted symbol across neighboring Doppler taps. The resulting inter Doppler interference is modeled using a finite set of significant neighboring values.

A. Sparse representation of the delay–Doppler channel

IV. MESSAGE PASSING DETECTION ALGORITHM FOR OTFS

The section proposes a message passing (MP) detection algorithm for OTFS using the input-output relation in (13).

IV. MESSAGE PASSING DETECTION ALGORITHM FOR OTFS

  • The section proposes a message passing (MP) detection algorithm for OTFS using the input-output relation in (13).Source: §IV · p. 4

A. Low-complexity MP detection algorithm for OTFS

The algorithm uses a sparse factor graph to approximate symbol-by-symbol MAP detection with message passing, reducing the complexity of joint MAP detection, which is exponential in NM.

A. Low-complexity MP detection algorithm for OTFS

  • The delay–Doppler channel matrix H has S nonzero entries in each row and column, enabling a sparsely connected factor graph.The graph has NM variable nodes and NM observation nodes, connected according to the nonzero positions of H.Source: A. Low-complexity MP detection… · p. 4
  • The proposed MP detector has complexity linear in NM, unlike joint MAP detection, whose complexity is exponential in NM.The detector isolates each symbol from other interference terms and approximates those terms as Gaussian noise with computable mean and variance.Source: A. Low-complexity MP detection… · p. 4
  • The detector approximates symbol-by-symbol MAP detection assuming equally likely transmitted symbols and approximately independent received components given each symbol.The independence approximation is attributed to the sparsity of H.Source: A. Low-complexity MP detection… · p. 4
  • Messages from observation nodes to variable nodes use Gaussian approximations of interference-plus-noise, while reverse messages carry symbol-alphabet probability mass functions.The transmitted symbols are assumed i.i.d. and independent of noise.Source: A. Low-complexity MP detection… · p. 4
  • The probability-message update uses damping with Δ∈(0, 1] to improve convergence rate.Source: A. Low-complexity MP detection… · pp. 4–5
  • Each iteration has complexity O(NMS|A|), giving overall per-symbol complexity O(niterS|A|); simulations typically converged within 20 iterations.The channel sparsity is identified as key to reducing decoder complexity.Source: A. Low-complexity MP detection… · p. 5

B. Application of MP detection algorithm for OFDM over delay–Doppler channels

The OTFS MP detector is applied to OFDM because its frequency-domain channel matrix is also sparse, with off-diagonal values decaying away from the diagonal.

B. Application of MP detection algorithm for OFDM over delay–Doppler channels

  • The OFDM signal path replaces the OTFS Heisenberg and Wigner transforms with IFFT/FFT processing and cyclic-prefix and serial/parallel conversion steps.For OFDM, N is set to 1.Source: B. Application of MP detection… · p. 5
  • The OFDM frequency-domain channel matrix is diagonally dominant, with off-diagonal values in each row decaying away from the diagonal, so the OTFS MP detector can be applied to OFDM.The passage attributes the matrix structure to sparsity and says it enables low-complexity MP detection.Source: B. Application of MP detection… · p. 5
  • Unlike OTFS, OFDM symbols experience distinct channel gains at different subcarriers because of the FFT operation on Ht.In OTFS, all transmitted symbols experience the same channel gain, independent of k and l.Source: B. Application of MP detection… · p. 5

V. ILLUSTRATIVE RESULTS

Simulations compare OTFS and OFDM across Doppler conditions and show OTFS gains, while examining how interference-term count and damping affect MP detection.

V. ILLUSTRATIVE RESULTS

  • Both systems use the Extended Vehicular A model for path delays in the BER simulations.The passage identifies this as the channel delay model.Source: §V · p. 5
  • BER improves significantly through E=10 and then saturates; considering 5–10 neighboring interference terms is sufficient.This result is for 4-QAM at 18 dB and 120 km/h.Source: §V · p. 5, Figure 3 · p. 6
  • At 4-QAM, 18 dB, and 120 km/h, BER is nearly unchanged through Δ=0.7 and worsens above; Δ=0.7 uses the fewest iterations.The authors select Δ=0.7 as the optimum damping factor.Source: §V · pp. 5–6, Figure 4 · p. 6
  • OTFS outperforms OFDM by approximately 15 dB at BER 10^-4 across tested Doppler frequencies.The comparison uses 4-QAM at UE speeds of 30, 120, and 500 km/h.Source: §V · p. 6

VI. CONCLUSION

The paper derives an OTFS input–output relation, proposes sparsity-exploiting MP detection with IDI mitigation, and reports BER gains over OFDM.

VI. CONCLUSION

  • Simulations show significant BER gains for OTFS over OFDM under various channel conditions.Fig. 5 compares their BER performance at different Doppler frequencies.Source: §VI · p. 6, Figure 5 · p. 6
  • The proposed linear-complexity MP detector exploits channel sparsity and is adapted to mitigate fractional-Doppler IDI.Source: §VI · p. 6
  • The paper analyzes the OTFS modulation and demodulation input–output relation using a sparse delay–Doppler channel representation.Source: §VI · p. 6
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