PaperlayerView exact revision on arXiv

Source-linked AI summary

Delay-Doppler Domain Aided OFDM (DD-a-OFDM): Pulsone Pilot and Cross-Domain Iterative Receiver Design

Rongrong Xin, Zhiqiang Wei, Zai Yang

arXiv:2610.29742v1eess.SP

TL;DR

High-mobility channels degrade OFDM, while DDMC offers accurate channel estimation but has higher detection complexity. The paper proposes DD-a-OFDM with a DD-domain pulsone pilot and a cross-domain iterative receiver. Simulations report rapid convergence, Doppler robustness, and better performance than conventional OFDM.

  • Problem

    High mobility causes OFDM channel variation and severe inter-carrier interference, while DDMC's higher detection complexity limits its practical deployment.

    Source: §I · p. 1

  • Method

    The proposed DD-a-OFDM framework uses a DD-domain pulsone pilot and a cross-domain iterative receiver for interference cancellation, channel estimation, and symbol detection.

    Source: §I · p. 2

  • Results

    Simulations show that the algorithm typically converges within 3 iterations and consistently outperforms conventional OFDM while remaining robust to Doppler effects.

    Source: §I · p. 2

  • Takeaways & Limitations

    DD-a-OFDM combines DDMC's precise channel estimation with OFDM's low-complexity equalization for high-mobility environments.

    Source: §I · p. 1

Abstract

from arXiv · show

In high-mobility channels, the widely adopted orthogonal frequency division multiplexing (OFDM) modulation waveform suffers from significant performance degradation due to channel variation and severe inter-carrier interference. Although delay-Doppler (DD) domain multicarrier (DDMC) modulation enjoys a higher channel estimation (CE) accuracy via exploiting the inherent DD-domain channel stability, sparsity, and separability, its high detection complexity limits its practical deployment, making OFDM still a promising waveform candidate for the sixth-generation (6G) cellular networks. To simultaneously harness the complementary strengths of DDMC and OFDM and mitigate their respective limitations, this paper proposes a DD-domain aided OFDM (DD-a-OFDM) framework, including a pulsone pilot (PP) design and a cross-domain iterative receiver design, to enhance the CE and detection performance of OFDM in high-mobility channels. Specifically, a pulsone pilot sequence is periodically inserted before the cyclic prefix (CP) for each OFDM symbol in the time-domain, which is equivalent to a single DD-domain pilot impulse and enables accurate DD-domain CE. Then, we propose a cross-domain iterative receiver in which the time-frequency (TF) domain detection results are transformed into the DD-domain for interference cancellation and CE; in turn, the DD-domain estimated channel is transformed into the TF-domain for channel reconstruction and symbol detection. The proposed cross-domain iterative receiver achieves a higher CE accuracy and detection performance with a much lower pilot overhead, compared to the conventional OFDM system. Simulation results validate the fast convergence and superior performance of the proposed DD-a-OFDM scheme and demonstrate that it maintains a robust CE and detection performance even in high-mobility channels.

I. INTRODUCTION

The paper combines DD-domain channel estimation with OFDM's practical waveform structure to address high-mobility degradation. It introduces a DD-domain pulsone pilot and a cross-domain iterative receiver for channel estimation and symbol detection.

I. INTRODUCTION

  • DD-a-OFDM combines DDMC's precise channel estimation with OFDM's low-complexity equalization to address their respective limitations in high-mobility settings.OFDM suffers from Doppler-induced inter-carrier interference and pilot-intensive estimation, while DDMC offers strong estimation and detection performance at higher detection complexity.Source: §I · p. 1

B. TF-domain Data Symbol and DD-domain Pilot Sym-

  • A single DD-domain pilot maps to a periodic time-domain pulsone sequence and leverages the full TF resources for high-resolution delay-Doppler estimation with low pilot overhead.The design exploits DD-channel stability, sparsity, and separability.Source: §I · p. 2, B. TF-domain Data Symbol and DD-domain… · p. 4

I. INTRODUCTION

  • The proposed framework typically converges within 3 iterations and consistently outperforms conventional OFDM while remaining robust to Doppler effects.The results are validated through numerical simulations.Source: §I · p. 2

II. The proposed Transceiver Architecture and System

A. DD-a-OFDM Transceiver Architecture

  • The receiver processes signals in parallel TF and DD branches for symbol detection and channel estimation, then iteratively cancels DD-domain interference using prior detection and estimation results.The refined outputs are channel estimates and detected TF-domain data symbols.Source: §I · p. 2, A. DD-a-OFDM Transceiver Architecture · p. 3

B. TF-domain Data Symbol and DD-domain Pilot Sym-

C. The Received Signal Model

The received-signal model samples the matched-filter output over extended OFDM symbols and supports DD-domain channel estimation and TF-domain symbol detection. It assumes integer delays, allows fractional Doppler, and processes the first N′ received symbols.

C. The Received Signal Model

  • The model neglects fractional delay and adopts integer-delay paths while accounting for fractional Doppler shifts.The passage motivates neglecting fractional delay by the small sampling interval in wideband systems.Source: C. The Received Signal Model · p. 4
  • After matched filtering, the received signal is sampled at t = n′T + l′Ts, with n′ spanning the received symbols and l′ spanning each extended OFDM symbol.The sampled signal includes discrete noise after matched filtering.Source: C. The Received Signal Model · p. 4
  • The receiver uses the first N′ extended OFDM symbols for channel estimation and detection; larger N′ provides higher Doppler resolution but increases latency.The paper notes that receiving all N transmitted symbols is unnecessary.Source: C. The Received Signal Model · p. 4

A. TF-domain Input-Output Relationship

The TF-domain received signal comprises desired data, effective noise, and a channel response that captures delay and Doppler effects. The CP prevents interference from the DD-domain pilot to TF-domain data, while high mobility makes the effective channel non-diagonal.

A. TF-domain Input-Output Relationship

B. DD-domain Input-Output Relationship

The DD-domain observation combines the pilot’s received signal with data-induced interference and noise. The pilot combines coherently across received symbols, while aggregated data interference behaves approximately as Gaussian noise, supporting accurate channel estimation.

B. DD-domain Input-Output Relationship

  • The N′ received time-domain pulsone pilot signals combine coherently in the DD-domain, retaining much of that gain even with fractional Doppler.For integer Doppler, the received symbol power at the corresponding path bin is N′σ_i^2 Epp.Source: B. DD-domain Input-Output Relationship · p. 6
  • Data-induced interference aggregates contributions from many TF-domain symbols and is modeled as circularly symmetric complex Gaussian noise.The Gaussian behavior follows from the aggregation effect described in the passage.Source: B. DD-domain Input-Output Relationship · pp. 6–7
  • The pilot combines coherently while data symbols spread their energy and behave approximately as Gaussian noise, enhancing the DD-domain pilot-to-interference power ratio for channel estimation.Source: B. DD-domain Input-Output Relationship · pp. 6–7

IV. Cross-Domain Iterative Receiver Design

The receiver iteratively exchanges information between the DD and TF domains: detected TF symbols support DD-domain interference cancellation and channel estimation, and estimated channels feed back to update TF-domain detection. The process begins with DD-domain channel estimation without interference cancellation.

IV. Cross-Domain Iterative Receiver Design

  • The iterative receiver reconstructs and cancels DD-domain interference using prior TF-domain detection and channel-estimation results, then uses the cleaned signal for channel estimation.The receiver starts with DD-domain channel estimation without interference cancellation because no prior data-symbol information is available.Source: §IV · p. 7
  • Estimated DD-domain channels are fed back to the TF-domain to update symbol detection, and cross-domain exchange progressively improves estimation and detection.Source: §IV · p. 7
  • For the integer-delay and integer-Doppler case, the interference term is represented per DD bin, enabling per-bin channel estimation and receiver processing without explicit dependence on the number of propagation paths.The passage describes this simplification for integer delay and Doppler.Source: §IV · p. 7

A. DD-domain Interference Cancellation

DD-domain interference cancellation uses prior-iteration TF symbol estimates to estimate and subtract interference before channel estimation. The residual depends on channel-estimation and symbol-detection errors, while its estimated power can be shared across Doppler bins within each delay tap.

A. DD-domain Interference Cancellation

  • Prior-iteration TF symbol estimates are used to estimate and subtract DD-domain interference before channel estimation.At the initial iteration, interference cancellation is not applied.Source: A. DD-domain Interference Cancellation · p. 7
  • Residual DD-domain interference is governed by channel-estimation error and the previous iteration’s TF symbol-detection error.The derivation neglects a second-order channel-estimation error term.Source: A. DD-domain Interference Cancellation · pp. 7–8
  • Within each delay tap, all Doppler bins share identical residual-interference power, approximated using channel estimates from the previous iteration.The passage says simulations validate the accuracy of this residual-power approximation.Source: A. DD-domain Interference Cancellation · p. 8
  • At initialization, data-symbol interference in the DD domain is approximated as Gaussian, with symbol interference and noise jointly modeled as AWGN.The stated average power is N0 + Es.Source: A. DD-domain Interference Cancellation · p. 8

B. DD-domain Channel Estimation

DD-domain channel estimation adopts low-complexity thresholding based on residual-interference and noise-power analysis. It uses recent channel estimates where true channel values are unavailable and limits retained paths to avoid potential path-miss detection.

B. DD-domain Channel Estimation

  • A low-complexity thresholding method is adopted for DD-domain channel estimation based on residual-interference and noise-power analysis.Source: B. DD-domain Channel Estimation · p. 8
  • Because the true channel coefficient is unavailable, the error variance is not directly evaluated and the most recent channel estimate is substituted in the variance calculation.Source: B. DD-domain Channel Estimation · p. 8
  • Setting Pmax > P is used to avoid potential path-miss detection; when detected paths exceed Pmax, lower-ranked paths by gain are treated as false and zeroed.Source: B. DD-domain Channel Estimation · p. 8

C. TF-domain Symbol Detection

TF-domain detection uses DD-domain channel estimates for channel reconstruction and MMSE equalization, followed by soft demodulation. Detection estimates and their error variances are fed back to the DD domain for the next interference-cancellation and channel-estimation round.

C. TF-domain Symbol Detection

  • DD-domain channel estimates support MMSE channel equalization to obtain TF-domain symbol estimates, followed by soft demodulation to produce posterior symbol distributions.Full-matrix MMSE equalization is adopted to suppress ICI.Source: C. TF-domain Symbol Detection · p. 8
  • Direct DD-domain channel-parameter estimation enables more accurate TF-domain channel reconstruction than interpolation-based methods and characterizes the ICI channel structure.The reconstructed channel supports ICI-aware equalization.Source: C. TF-domain Symbol Detection · p. 9
  • When maximum Doppler is much smaller than the subcarrier spacing, single-tap MMSE equalization can be applied per TF resource element to reduce computational complexity.Source: 2) Single-tap MMSE Equalization · p. 9
  • Probabilistic soft demodulation uses constellation prior information to refine TF-domain symbol estimates and facilitate subsequent iterative interference cancellation and channel estimation.Source: 3) Soft Demodulation · p. 9
  • TF-domain symbol-detection results and their error variances are fed back to the DD domain for the next interference-cancellation and channel-estimation round.Source: 3) Soft Demodulation · p. 9

D. Complexity Analysis

The receiver’s computational cost is dominated by DD-domain interference reconstruction, TF-domain channel reconstruction, and equalization. Equalization cost varies substantially between full-matrix and single-tap MMSE, while simulations report convergence within three iterations.

D. Complexity Analysis

  • O(NM^3) for full-matrix MMSE equalization falls to O(NM) for single-tap MMSE equalization.The single-tap option reduces equalization complexity significantly.Source: D. Complexity Analysis · p. 10
  • Per iteration, DD-domain interference reconstruction costs O(P̂(lmax + 1)(2kmax + 1)MN), while TF-domain channel reconstruction costs O(P̂NM log M).P̂ denotes the number of identified DD-domain paths.Source: D. Complexity Analysis · p. 10
  • Although the receiver is iterative, it usually converges within a few iterations, including three iterations in the reported simulations.The authors note that parallel and pipelined implementations can further accelerate operations.Source: D. Complexity Analysis · p. 10

E. Extension to Fractional Doppler Case

The fractional-Doppler extension replaces per-DD-bin processing with per-delay-tap processing on a virtual Doppler grid. This supports iterative interference cancellation and channel estimation, with grid resolution traded against computational complexity.

E. Extension to Fractional Doppler Case

  • Fractional-Doppler processing uses per-delay-tap rather than per-DD-bin processing, producing DD-channel estimates and estimation errors for feedback to TF-domain symbol detection.The extension replaces the corresponding processing in Sections IV-A and IV-B and feeds the results into the Section IV-C detection stage.Source: E. Extension to Fractional Doppler Case · p. 10
  • The extension formulates an on-grid SSR problem by mapping Doppler shifts onto a virtual sampling grid and representing the channel as a high-resolution sparse vector.The virtual Doppler resolution is 1/(RνN′T); the resulting channel estimates and error covariance are obtained by solving the SSR problem, with LASSO, OMP, or SBL listed as options.Source: E. Extension to Fractional Doppler Case · p. 10
  • The virtual sampling factor Rν sets Doppler-grid resolution; increasing it reduces grid-mismatch error and improves channel representation accuracy, but increases SSR complexity.The paper recommends balancing these costs and notes that off-grid or gridless compressed-sensing methods can alternatively formulate DD-domain CE as SSR problems.Source: E. Extension to Fractional Doppler Case · p. 10
  • The per-delay-tap input-output model separates data symbols and channel, enabling iterative DD-domain interference cancellation and channel estimation.The resulting estimates and associated error covariance support the cross-domain iterative framework for interference cancellation, channel estimation, and symbol detection.Source: E. Extension to Fractional Doppler Case · p. 10

V. NUMERICAL RESULTS

The numerical-results section evaluates the proposed DD-a-OFDM transceiver and CD-IED algorithm. It specifies simulation conditions and compares the proposal with ideal and genie-aided DD-domain CE and classical OFDM baselines.

V. NUMERICAL RESULTS

  • Fig. 6 illustrates iterative DD-domain CE with four channel taps at delays [0, 1, 2, 5] and Dopplers [2, 1, 1, 1].The plane marks the detection threshold and red solid circles mark correctly detected taps.Source: Figure 6 · p. 11

A. Parameter Setting and Baseline Schemes

  • The simulations use uniformly distributed integer delays and, by default, integer Dopplers; fractional Doppler runs use oversampling factor Rν = 10.Path gain decays exponentially with delay.Source: A. Parameter Setting and Baseline… · p. 11
  • The practical PP power is set to the peak power of the transmitted time-domain OFDM signal to support reliable CE while avoiding high PAPR.The paper uses this criterion rather than optimizing PDR because CE, interference cancellation, and symbol equalization are strongly coupled.Source: A. Parameter Setting and Baseline… · p. 11
  • The proposed system is evaluated against ideal DD-domain CE, genie-aided DD-domain CE with perfect interference cancellation, and classical OFDM with pilots on all subcarriers of OFDM symbols 11 and 22.Classical OFDM uses LS channel estimation, linear interpolation, and single-tap equalization; it does not explicitly capture ICI or provide the full effective channel matrix for full-matrix MMSE equalization.Source: A. Parameter Setting and Baseline… · p. 11

B. Simulation Results

The simulations show that DD-a-OFDM maintains robust detection in high-mobility channels, with fast iterative convergence and channel estimation approaching genie-aided performance. Its pulsone pilot and cross-domain receiver also yield low PAPR and compatibility with existing OFDM transmitter architectures.

B. Simulation Results

  • As DD-domain residual interference falls, later iterations reveal weaker channel paths; falsely detected taps from noise and interference can be removed in subsequent iterations.The CE performance approaches genie-aided interference cancellation at t = 3.Source: B. Simulation Results · pp. 11–12
  • Residual interference-plus-noise power falls rapidly across iterations at SNRs of 15 dB and 30 dB, and the analytical estimate closely matches simulation.The paper reports that this analysis supports more accurate DD-domain channel estimation in later iterations.Source: B. Simulation Results · p. 12, Figure 8 · p. 12
  • Within three iterations, CD-IED approaches ideal-CSI and genie-aided detection performance with both single-tap and full-matrix MMSE equalizers.The reported fast convergence stems from the pulsone pilot and ordered path detection and estimation.Source: B. Simulation Results · p. 12, Figure 9 · p. 12
  • TF-domain NMSE decreases with increasing SNR for both equalizers; full-matrix MMSE approaches genie-aided performance, while single-tap errors particularly impair CE at 600 km/h.The paper attributes the difference to full-matrix suppression of mobility-induced ICI and single-tap equalization's inability to mitigate severe ICI.Source: B. Simulation Results · p. 12, Figure 10 · p. 13
  • Above 8 dB PDR, CD-IED SER approaches the corresponding ideal-CSI and genie-aided cases; SER also gradually decreases as PDR increases.The pulsone pilot combines coherently in the DD-domain, unlike data-symbol interference, which combines incoherently across DD grids.Source: B. Simulation Results · p. 13, Figure 13 · p. 13
  • DD-a-OFDM achieves lower PAPR than classical OFDM across PDR settings, and the peak-power-constrained design achieves the lowest PAPR.The peak-power-constrained design improves average signal power while maintaining the original OFDM peak-power level.Source: B. Simulation Results · pp. 13–14, Figure 14 · p. 14
  • In fractional-Doppler tests, CD-IED maintains detection robustness as velocity rises, while classical OFDM degrades; full-matrix MMSE further suppresses ICI.The conclusion also reports robust SER relative to classical OFDM and says the gap between full-matrix and single-tap equalization is more pronounced at higher velocity.Source: Figure 11 · p. 13, B. Simulation Results · p. 14, Figure 15 · p. 14

VI. Conclusion

  • The pulsone pilot maps a single DD-domain impulse to a time-domain pulse train, reducing pilot overhead while preserving low PAPR and OFDM transmitter compatibility.The conclusion presents the framework as a pathway for upgrading existing OFDM infrastructure for high-mobility applications.Source: §VI · p. 14
Loading 2610.29742v1…