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DFT-Spread Orthogonal Time Frequency Space System with Superimposed Pilots for Terahertz Integrated Sensing and Communication

Yongzhi Wu, Chong Han, Zhi Chen

arXiv:2202.10035v2eess.SP

TL;DR

THz ISAC faces Doppler-related communication and sensing challenges, as well as PAPR-related limits on PA efficiency. The paper proposes DFT-s-OTFS with superimposed pilots and develops sensing estimation and iterative receiver methods. Simulations report improved PA efficiency, accurate range and velocity estimation, and BER performance not degraded by Doppler effects.

  • Problem

    In THz ISAC, severe Doppler effects influence communication and sensing, while high PAPR degrades power-amplifier efficiency.

    Source: A. Related Work · p. 3

  • Method

    The paper combines DFT-s-OTFS with superimposed pilots, a two-phase sensing estimator, and iterative channel estimation and data detection.

    Source: B. Our Contributions · p. 3

  • Results

    DFT-s-OTFS improves PA efficiency by 7% for class A PA and 10% for class B PA compared with OTFS, while simulations report millimeter-level range accuracy, decimeter-per-second-level velocity accuracy, and BER not degraded by Doppler effects.

    Source: §VII · p. 14

  • Takeaways & Limitations

    The simulations support DFT-s-OTFS as a candidate waveform for 6G sub-THz/THz ISAC with sensing and communication functionality.

    Source: B. Our Contributions · p. 3, §VII · p. 14

Abstract

from arXiv · show

Terahertz (THz) integrated sensing and communication (ISAC) is a promising interdisciplinary technology that realizes simultaneously transmitting Terabit-per-second (Tbps) and millimeter-level accurate environment or human activity sensing. However, both communication performance and sensing accuracy are influenced by the Doppler effects, which are especially severe in the THz band. Moreover, peak-to-average power ratio (PAPR) degrades the THz power amplifier (PA) efficiency. In this paper, a discrete Fourier transform spread orthogonal time frequency space (DFT-s-OTFS) system with superimposed pilots is proposed to improve the robustness to Doppler effects and reduce PAPR for THz ISAC. Then, a two-phase sensing parameter estimation algorithm is developed to integrate sensing functionality into the DFT-s-OTFS waveform. Meanwhile, a low-complexity iterative channel estimation and data detection method with a conjugate gradient based equalizer is proposed to recover the data symbols of DFT-s-OTFS. The proposed DFT-s-OTFS waveform can improve the PA efficiency by 10% on average compared to OTFS. Simulation results demonstrate that the proposed two-phase sensing estimation algorithm for THz DFT-s-OTFS systems is able to realize millimeter-level range estimation accuracy and decimeter-per-second-level velocity estimation accuracy. Moreover, the effectiveness of the iterative method for data detection aided by superimposed pilots in DFT-s-OTFS systems is validated by the simulations and the bit error rate performance is not degraded by the Doppler effects.

I. INTRODUCTION

THz ISAC promises high-rate communication and accurate sensing, but severe Doppler effects and high PAPR challenge waveform design. The paper introduces DFT-s-OTFS with superimposed pilots and develops sensing and receiver methods for this setting.

I. INTRODUCTION

  • THz ISAC combines the prospect of Tbps links and highly accurate sensing, but Doppler effects and stringent PAPR requirements challenge communication, sensing, and PA efficiency.The introduction identifies Doppler-induced ICI as a source of communication and sensing error, while high PAPR constrains THz PA efficiency.Source: §I · p. 1

A. Related Work

  • Existing OTFS approaches leave open needs for lower PAPR, reduced pilot overhead, low-complexity processing, and channel estimation and detection with fractional delay and Doppler.Prior superimposed-pilot methods cited here either assume integer delay and Doppler or do not address fractional parameters.Source: A. Related Work · pp. 2–3

B. Our Contributions

  • The paper proposes a THz ISAC DFT-s-OTFS framework with superimposed pilots, fractional-parameter sensing, and iterative channel estimation and data detection.It also develops pilot/data power allocation and a conjugate-gradient-based equalizer.Source: A. Related Work · p. 3, B. Our Contributions · p. 3

II. SYSTEM FRAMEWORK

  • The system supports active sensing from returned signals and joint passive sensing and data detection from communication-path signals.The active receiver uses the transmitted signal to estimate target parameters; the passive receiver uses pilot knowledge while detecting data.Source: §II · p. 3

A. Transmitter Design and Processing

  • DFT spreading precedes delay-Doppler mapping, where a pilot is superimposed on data at one grid point rather than assigned a dedicated pilot region.The design is described as reducing pilot overhead and improving spectral efficiency relative to embedded pilots with guard regions.Source: A. Transmitter Design and Processing · p. 4

B. Continuous-Delay-and-Doppler-Shift Channel Impulse Response

This section models the channel using continuous-valued delay and Doppler shifts, including fractional values that are relevant to high-accuracy THz ISAC. It derives the corresponding sampled signal relationship for the system.

B. Continuous-Delay-and-Doppler-Shift Channel Impulse Response

  • The channel comprises P paths with complex gains, continuous delays, and Doppler shifts, with path separability specified by delay or Doppler spacing.For active sensing, the round-trip delay and Doppler relations include an extra factor of two.Source: B. Continuous-Delay-and-Doppler-Shift… · p. 5
  • Because fractional delay and Doppler remain challenging for DFT-s-OTFS with rectangular pulses, the paper derives a continuous-delay-and-Doppler-shift channel matrix.The integer-grid case is presented separately as r = Hs + w.Source: B. Continuous-Delay-and-Doppler-Shift… · p. 5
  • The continuous-time received signal is sampled and represented in vector form using delay and Doppler operators to describe each channel path.The resulting baseband input-output relation is stated for the CDDS channel.Source: B. Continuous-Delay-and-Doppler-Shift… · pp. 5–6

C. Receiver Design and Processing

The receiver transforms the received signal into the delay-Doppler domain and represents it using an effective channel matrix. This representation supports active sensing or joint passive sensing and data detection.

C. Receiver Design and Processing

  • The receiver applies the Wigner transform and SFFT to obtain the received delay-Doppler-domain vector.With rectangular pulses, the Wigner transform is equivalent to a DFT.Source: C. Receiver Design and Processing · p. 6
  • The received vector is expressed as the effective channel acting on data and pilot vectors, plus transformed noise.The effective channel matrix depends on the path gains, delays, and Doppler shifts.Source: C. Receiver Design and Processing · p. 6
  • The receiver supports active estimation of delay and Doppler from known transmitted and received vectors, or joint passive estimation and data recovery using pilots and the received vector.The passive task estimates channel parameters and recovers the data symbols.Source: C. Receiver Design and Processing · p. 6

III. ACTIVE SENSING PARAMETER ESTIMATION

For active sensing, the receiver uses the transmitted signal to estimate target parameters. The proposed estimator turns a difficult multi-target continuous search into two-dimensional searches, first coarse on-grid and then refined off-grid.

B. Two-Phase Sensing Parameter Estimation Method

  • The two-phase method first performs low-complexity on-grid coarse estimation, then off-grid search to refine the result.The method is based on the maximum-likelihood estimator and targets super-resolution accuracy with low complexity.Source: §III · p. 6, A. Maximum Likelihood Estimator · p. 6

A. Maximum Likelihood Estimator

  • The maximum-likelihood estimator estimates each target’s channel coefficient, delay, and Doppler shift for calculating range and velocity.A direct search over all 3P parameters in a continuous domain is high-complexity and intractable for multi-target sensing.Source: A. Maximum Likelihood Estimator · p. 6

B. Two-Phase Sensing Parameter Estimation Method

  • For multi-target estimation, previously estimated targets’ interference is subtracted before estimating the next target.The estimator searches for each target’s delay and Doppler parameters in a two-dimensional region.Source: B. Two-Phase Sensing Parameter… · pp. 6–7

1) Phase I:

The estimator brackets target delay and Doppler on a grid, then refines the search off-grid. The two phases trade a low-complexity coarse search for sharper parameter estimates.

1) Phase I:

  • Phase I searches a discretized delay-Doppler grid, using the 2D circular-shift relation when delay and Doppler are resolution-aligned.It estimates integer delay and Doppler components to establish the uncertainty region for Phase II.Source: 1) Phase I:  · p. 7, 2) Phase II · p. 7

2) Phase II:

  • Phase II applies off-grid search within the Phase I region using a 2D golden-section method to refine delay and Doppler estimates.The target’s range and velocity are calculated from the estimated delay and Doppler.Source: 2) Phase II · p. 7
  • Phase I’s coarse profile has a flat peak around the 10 m target, while Phase II’s super-resolution profile has a steep peak at the ground truth.The coarse estimate narrows the search region before refinement.Source: 2) Phase II · pp. 7–8, Figure 3 · p. 7

C. Complexity Analysis

The estimator uses circular shifts and FFT-based operations to reduce computation. Its stated overall complexity is O(MN log(MN)), rather than direct matrix-vector multiplication.

C. Complexity Analysis

  • Phase I computes the needed operation through a 2D circular shift, while Phase II avoids direct multiplication of the channel matrix and vector.Direct multiplication has complexity O(M^2N^2).Source: C. Complexity Analysis · p. 8
  • The two-phase estimator has overall computation complexity O(MN log(MN)).The Phase II calculation uses diagonal-matrix multiplications, cyclic shifts, and DFT/IDFT operations implemented with FFT.Source: C. Complexity Analysis · p. 8
  • Compared with the whole-domain direct off-grid search in, the method narrows the search first and uses FFT-based computation for the off-grid stage.The cited direct matrix-vector calculation multiplies an MN × MN channel matrix by an MN × 1 vector.Source: C. Complexity Analysis · p. 8

IV. JOINT PASSIVE SENSING AND DATA DETECTION

The passive receiver estimates channel parameters from received signals and pilots, then alternates data detection with data-aided channel refinement. A conjugate-gradient equalizer provides the channel equalization step.

A. Coarse Channel Estimation using Superimposed Pilots

  • Pilot-aided coarse channel estimates treat the received signal induced by unknown data symbols as interference.Because only superimposed pilots are used, these estimates are less accurate than estimates using full data and pilot information, but can initialize approximate data recovery.Source: A. Coarse Channel Estimation using… · p. 8

B. Iterative Channel Estimation and Data Detection

  • Each iteration equalizes the received signal, detects data symbols, and uses the detected data with pilots to refine channel estimates.The process repeats until detected symbols match those from the previous iteration.Source: B. Iterative Channel Estimation and… · pp. 8–9
  • The CG-based time-domain equalizer solves a regularized least-squares problem using efficient computations of Hs and HHs.Direct matrix inversion requires O((MN)^3); block-circulant methods do not apply to fractional-delay-and-Doppler channels.Source: B. Iterative Channel Estimation and… · pp. 8–9
  • The iterative channel-estimation and data-detection algorithm converges within 2 to 5 iterations in simulations, with CG equalization complexity O(MN log(MN)).FFT computes the required Hs and HHs operations.Source: B. Iterative Channel Estimation and… · pp. 9–10

V. OPTIMAL POWER ALLOCATION BETWEEN PILOT AND DATA SYMBOLS

Pilot and data power must be balanced: stronger pilots improve channel estimation, while stronger data allocation supports detection. The section derives an effective SINR and uses it to formulate the power allocation under an average transmit-power constraint.

V. OPTIMAL POWER ALLOCATION BETWEEN PILOT AND DATA SYMBOLS

  • Pilot power trades channel-estimation accuracy against data-detection performance; insufficient pilot power can make estimation inaccurate enough to prevent iterative-method convergence.The allocation is optimized to maximize SINR using pilot- and data-aided channel estimation, which minimizes BER.Source: §V · p. 10
  • A nonzero pilot occupies one delay-Doppler grid point, while the remaining pilot symbols are set to zero before pilots are superimposed on data.The derivation also includes the error in estimated channel coefficients obtained through pilot-aided channel estimation.Source: §V · p. 10
  • The optimal pilot–data allocation is formulated from the derived effective SINR subject to an average transmit-power constraint.The effective SINR derivation uses the received vector, pilot elimination, and data-aided channel estimation; it accounts for errors in equalized data symbols and pilot-aided channel coefficients.Source: §V · p. 10

VI. SIMULATION RESULTS

The simulation section evaluates DFT-s-OTFS with superimposed pilots for THz ISAC, covering PAPR, BER, and sensing accuracy against OFDM, DFT-s-OFDM, and OTFS.

VI. SIMULATION RESULTS

  • The simulations assess PAPR, BER, and sensing accuracy for DFT-s-OTFS with superimposed pilots and compare it with OFDM, DFT-s-OFDM, and OTFS.The simulation parameters are designed for THz and compatible with 5G numerology.Source: §VI · p. 10

A. PAPR and PA Efficiency

In simulations, DFT-s-OTFS retains BER under strong Doppler, reduces PAPR relative to OTFS, and lowers out-of-band leakage relative to OFDM-family waveforms. Pilot power also affects PAPR and BER, with its optimal allocation varying with SNR.

A. PAPR and PA Efficiency

B. Out-of-Band Emission

C. BER Performance

  • For 16-QAM, pilot power 0.04 gives the best BER at 15 dB SNR, while 0.08 gives the lowest BER at 21 dB; optimal values are 0.0403 and 0.0633, respectively.The optimal pilot power decreases with SNR at low SNR and increases at high SNR, producing a saddle point at about 10 dB.Source: C. BER Performance · pp. 11–12, Figure 9 · p. 12
  • DFT-s-OTFS BER is not degraded by Doppler in the evaluated high-mobility channel, and the optimal pilot-power allocation is near optimal.At low SNR, the allocation from the derived scheme performs worse than pilot powers 0.06, 0.14, and 0.18 because the derivation invokes approximations.Source: C. BER Performance · p. 12, Figure 10 · p. 12

D. Sensing Accuracy

DFT-s-OTFS combines active and passive sensing with superimposed pilots, and the reported results cover sensing accuracy, Doppler robustness, and PA efficiency. Its two-phase estimator supports range and velocity estimation, while the iterative method supports passive sensing and data recovery.

D. Sensing Accuracy

  • Below 10^-3 m range RMSE is achieved for one active-sensing target above 10 dB SNR; for two or three targets, RMSE can fall below 10^-2 m.Successful-estimation SNR thresholds are -15, -10, and -5 dB for one, two, and three targets, respectively; increased target interference explains the higher threshold with more targets.Source: D. Sensing Accuracy · p. 13, Figure 11 · p. 13
  • Active-sensing velocity estimation reaches decimeter-per-second-level accuracy, with RMSE approaching 10^-1 m/s for two and three targets.More targets increase velocity estimation error; the two-phase algorithm uses an on-grid search in Phase I and an off-grid search in Phase II.Source: D. Sensing Accuracy · p. 13, Figure 12 · p. 13
  • At 300 km/h, OFDM and DFT-s-OFDM sensing accuracy degrades, while OTFS and DFT-s-OTFS RMSE is not influenced; at 30 km/h, the four waveforms have indistinguishable accuracy.The comparison evaluates range and velocity estimation for target velocities of 30 km/h and 300 km/h.Source: Figure 13 · p. 13, Figure 14 · p. 13, D. Sensing Accuracy · p. 14
  • For passive sensing, range estimation error is below 10^-2 at high SNR and has accuracy similar to active sensing for multiple targets.At 3 dB SNR, low pilot power causes inaccurate coarse pilot-aided channel estimation; pilot power allocation σ_p² = 0.14 performs well for passive sensing.Source: D. Sensing Accuracy · p. 14, Figure 15 · p. 14

VII. CONCLUSION

  • The conclusion’s framework supports active sensing and joint passive sensing with data detection, using delay-Doppler superimposed pilots and a two-phase range-and-velocity estimator.Superimposed pilots avoid a dedicated pilot region, improving spectral efficiency relative to embedded-pilot OTFS; pilot/data power allocation is optimized for data recovery.Source: §VII · p. 14
  • 7% for class A PA and 10% for class B PA: DFT-s-OTFS improves PA efficiency over OTFS, with about 3 dB lower transmit-signal PAPR.The conclusion also reports that BER is not degraded in high-mobility scenarios compared with time-invariant channels, and that sensing reaches millimeter-level range and decimeter-per-second-level velocity accuracy.Source: §VII · p. 14

APPENDIX A

The appendix describes channel-estimation and MMSE equalization error expressions in the presence of data interference and noise.

APPENDIX A

  • The channel-estimation mean-square error is expressed using an expectation over noise.The supplied passage names the quantity as σ_0² but does not provide the complete expression.Source: Appendix A · p. 14
  • The covariance of the data-interference-plus-noise term is used in the pilot-aided channel-estimation error analysis.The term is identified as w_d = Ω_d α + ẇ.Source: Appendix A · p. 14
  • With pilot-based channel coefficients, the appendix proceeds to the MMSE equalization error and then an error expression using both pilot and data.The passages identify these as successive error calculations without giving the complete expressions.Source: Appendix A · pp. 14–15
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