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A Deep Iterative Refinement Receiver for OTFS Symbol Detection in Doubly-Dispersive Channels

Efe Ispir, Ian P. Roberts

arXiv:2609.00465v1eess.SP

TL;DR

Reliable OTFS detection is difficult in doubly-dispersive channels because delay and Doppler dispersion create structured interference. The paper proposes a channel-aware initializer followed by iterative refinement, and reports consistent gains over conventional and learning-based detectors across varied conditions.

  • Problem

    Doubly-dispersive channels create structured delay–Doppler interference that complicates reliable OTFS symbol recovery.

  • Method

    A two-stage detector combines explicit delay–Doppler channel conditioning in initialization with gated iterative refinement using received-signal and estimate feedback.

  • Results

    The proposed receiver achieves lower BER than MMSE, MP, and single-shot CNN detectors across a wide variety of channel conditions.

  • Takeaways & Limitations

    Explicit channel structure and iterative refinement improve robustness, generalization to unseen channels, and residual-interference suppression in OTFS detection.

Abstract

from arXiv · show

Orthogonal time frequency space (OTFS) modulation has emerged as a promising candidate for high-mobility wireless communication systems due to the diversity it offers across both time and frequency. Reliable OTFS detection, however, remains challenging under doubly-dispersive channels, where delay and Doppler dispersion induce structured interference between transmitted symbols and complicate symbol recovery. To address these challenges, we propose a two-stage iterative OTFS detector that integrates a physics-informed learned initializer with an iterative refinement network, enabling progressively more accurate symbol estimates in doubly-dispersive channels. The initializer incorporates the known delay-Doppler input-output relationship to produce a robust first-stage estimate, while the refinement stage iteratively suppresses residual symbol interference in the delay-Doppler domain. Simulation results demonstrate that the proposed detector achieves consistent performance gains over conventional and existing learning-based detectors across a variety of channel conditions. These results highlight the effectiveness of incorporating known channel structure into the detection process and using iterative refinement for improved and robust OTFS detection.

I. INTRODUCTION

High mobility creates doubly-dispersive channels that challenge conventional modulation and make reliable OTFS detection difficult. The paper addresses these challenges with a channel-aware, iterative two-stage CNN detector.

  • High mobility introduces delay and Doppler spreading, while Doppler spread degrades OFDM through intercarrier interference.
  • OTFS multiplexes symbols in the delay–Doppler domain to exploit channel diversity, but detection becomes harder as delay and Doppler spreading increase.
  • MAP/ML detection becomes impractical for large OTFS frames because exhaustive search complexity grows exponentially.
  • Linear LS and MMSE equalizers avoid exhaustive search but require matrix inversions whose complexity becomes significant for practical frame sizes.
  • Model-based detectors rely on channel and interference assumptions, whereas data-driven CNNs can learn complex input–output relationships directly from data.
  • The proposed detector combines channel-conditioned initialization with gated iterative refinement, progressively reducing residual errors and improving BER across channel conditions.

II. SYSTEM MODEL

The system models OTFS frames on a discrete delay–Doppler grid and represents the doubly-dispersive channel as multipath components with distinct gains, delays, and Doppler shifts. The received signal is then formed through this channel with additive noise.

  • The considered OTFS system uses N time slots and M subcarriers, with frame duration Tf = TN and bandwidth B = ∆fM.
  • OTFS arranges MN information symbols on an M × N delay–Doppler grid before mapping them to the time–frequency domain with the ISFFT.
  • A Heisenberg transform using the transmit pulse produces the continuous-time transmit signal from time–frequency samples.
  • The doubly-dispersive channel is modeled with P propagation paths, each characterized by a complex gain, delay, and Doppler shift.
  • The channel parameters include integer delay and Doppler indices plus a fractional Doppler component κi satisfying −0.5 < κi ≤ 0.5.
  • The received signal is generated from the delay–Doppler channel representation and additive noise w(t).

C. OTFS Received Signal Model

Receiver processing obtains a time–frequency representation through a cross-ambiguity function, samples it, and transforms it back to delay–Doppler coordinates. Fractional Doppler causes Doppler-domain spreading that creates inter-Doppler interference.

  • The receiver obtains the time–frequency representation using the cross-ambiguity function between the matched filter and received signal.
  • The continuous time–frequency representation is sampled before further receiver processing.
  • Applying the SFFT to the sampled time–frequency representation produces the delay–Doppler-domain signal.
  • Fractional Doppler spreads each transmitted symbol along the Doppler dimension, causing inter-Doppler interference.

III. PROPOSED TWO-STAGE FRAMEWORK

The proposed OTFS detector combines channel-conditioned initialization with iterative refinement to address structured interference in doubly-dispersive channels. Its initialization explicitly organizes received delay–Doppler information according to supported channel shifts before refinement produces the final estimate.

  • Two-stage framework: The framework first uses channel-conditioned initialization, then iteratively refines the resulting symbol estimates with an IRN.The initialization produces an initial estimate and detection state for subsequent refinement.
  • Two-stage framework: Unlike single-shot detectors, the proposed design progressively corrects residual errors through repeated refinement of the detection result.The iterative stage follows the initial symbol estimate rather than operating only once.
  • Evaluation: The framework is evaluated under varied channel conditions and is reported to improve upon conventional and single-shot CNN-based detectors.The supplied passage states the comparison but provides no numerical performance values.
  • Channel-Conditioned Initialization: Align-Combine constructs aligned copies by applying predetermined circular shifts for supported integer delay–Doppler displacements.The shifts use the channel’s maximum delay and Doppler support and correspond to inverse delay–Doppler displacements.
  • Channel-Conditioned Initialization: The aligned copies are concatenated into a real-valued extended tensor, with real and imaginary components treated as separate features.The resulting stack organizes the received signal according to the shift structure induced by supported channel taps.
  • Channel-Conditioned Initialization: Channel-conditioned convolution uses 1 × 1 kernels for integer Doppler and larger spatial kernels for fractional Doppler leakage.The kernel choice reflects whether the channel response is an exact shift or spreads energy across neighboring Doppler bins.

1) Integer Doppler Kernel Generation:

The detector generates channel-conditioned kernels for integer and fractional Doppler cases, then integrates them with aligned inputs to initialize symbol estimates. The resulting features are processed by an RDN and classifier head.

  • Integer Doppler Kernel Generation: The integer-Doppler representation concatenates real and imaginary components of the estimated tap gains into a 2C-dimensional input.This input is denoted h_in ∈ R^2C.
  • Integer Doppler Kernel Generation: Integer-Doppler channel taps are grouped by shared delay–Doppler indices before forming the channel representation.The grouping uses the path set P_c for each integer delay–Doppler tap.
  • Kernel Generation: A three-layer MLP maps the channel representation to the corresponding 1 × 1 convolution kernel.
  • Fractional Doppler Kernel Generation: For fractional Doppler, a real-valued tensor represents gain-weighted Doppler spread, and MLP/CNN processing captures tap-wise feature interactions.The tensor concatenates real and imaginary components across taps before 1 × 1 convolutions process feature channels.
  • Initialization Pipeline: The generated kernels convolve the extended input, after which the RDN produces the initial detection state and the classifier maps it to symbol estimates.The classifier head uses the detection state to produce the initial symbol probabilities.
  • Initialization Pipeline: The overall module combines alignment, channel-conditioned kernel generation, convolution, RDN processing, and classification.The components are represented by T(·), f_θ(·), F_W(·), G_ϕ(·), and the classifier head.

B. Iterative Refinement Network

The iterative refinement network updates a detection state across multiple steps using prior symbol probabilities, reconstructed signals, the received observation, and explicit residual information. Each iteration applies learned residual correction before producing refined symbol probabilities.

  • Motivation: The refinement stage addresses residual noise and interference left by the single-shot channel-conditioned initializer.
  • Iterative Updates: Each iteration updates the detection state through a learned residual correction and produces symbol probabilities for the next step.Refinement parameters are not shared across iterations, allowing distinct corrections at different steps.
  • Iteration Inputs: The iteration input includes previous symbol probabilities, which carry current symbol-level detection beliefs forward.Soft symbol estimates are computed from those probabilities.
  • Signal Reconstruction: Soft estimates reconstruct the received signal and an extended per-tap representation, whose fixed channels correspond to physical delay–Doppler shifts.The reconstruction is used to calculate E = Y − Ŷ.
  • Residual Features: The refinement input retains the original received signal and explicitly supplies the residual and its magnitude.The residual exposes observation–reconstruction mismatch, while |E| indicates mismatch severity.
  • Refinement Architecture: Residual dense blocks jointly process heterogeneous inputs while preserving feature reuse through dense and residual connections.
  • Classification: The updated detection state is passed to a classifier head that produces the iteration’s symbol probability estimates.

C. Training

The detector is trained on synthetically generated OTFS frames over doubly-dispersive channels with cross-entropy supervision at initialization and every refinement stage. Uniform weighting encourages accurate estimates throughout the iterative process.

  • Training Setup: Training uses synthetic OTFS frames with 1800 channel realizations, 65 frames per realization, and SNR uniformly sampled from 5–25 dB.Transmitted symbols are uniformly sampled from the modulation alphabet.
  • Training Objective: Cross-entropy supervision is applied to symbol probability estimates from the initialization stage and all subsequent refinement stages.
  • Training Objective: Fig. 4 compares initialization-stage cross-entropy loss with and without the Align–Combine module for 16-QAM.
  • Training Objective: The objective uses uniform weighting across stages rather than explicitly prioritizing a particular refinement stage.

IV. SIMULATION RESULTS

Simulations evaluate the proposed receiver under a specified OTFS channel configuration and architectural variants. Results show that channel-aware initialization improves unseen-channel generalization and accelerates refinement, while per-tap reconstruction gives the strongest convergence and BER behavior.

  • Simulation Setup: The simulations use a 32 × 32 delay–Doppler grid, 4 GHz carrier, 15 kHz subcarrier spacing, and five multipath components.Unless otherwise specified, maximum delay and Doppler indices are 3 and 2.
  • Architectural Evaluation: Removing Align–Combine severely limits the RDN’s ability to generalize to unseen channels.The comparison feeds the raw received signal to the same RDN architecture without alignment or channel-conditioned combination.
  • Architectural Evaluation: At Eb/N0 = 15 dB and Eb/N0 = 20 dB, the proposed initialization achieves lower early-iteration BER and faster convergence than the IRN-only baseline.Both variants approach similar error floors at higher iteration counts, but the proposed initialization needs fewer iterations for a given BER.
  • Reconstruction Decomposition: The reconstruction study compares full, per-tap, and per-symbol decompositions of the reconstructed signal.Per-tap decomposition separates contributions across delay–Doppler channel taps.
  • Reconstruction Decomposition: Per-tap decomposition achieves faster convergence and a lower BER floor than full and per-symbol reconstructions at both SNR levels.Its fixed feature-channel-to-tap mapping preserves the delay–Doppler channel structure.

B. Detection Performance

The proposed iterative detector is evaluated against model-based and single-shot learned baselines under integer and fractional Doppler, varying path counts, and power-delay profiles. Iterative refinement improves BER and maintains robustness across these channel conditions.

  • Integer Doppler: The proposed detector improves with iteration count and, beyond four iterations, outperforms all baselines across the entire SNR range under integer Doppler.
  • Fractional Doppler: Under fractional Doppler, four refinement iterations consistently outperform RDN, RCAN, MP, and MMSE, with further iterations producing progressively lower BER.
  • Doppler robustness: The proposed detector maintains nearly identical performance across integer and fractional Doppler, indicating robustness to fractional-Doppler energy spreading.
  • Multipath variations: As propagation paths increase, the proposed detector gains more over RCAN, suggesting iterative refinement better exploits additional multipath diversity than single-shot detection.
  • Multipath variations: The detector remains robust to varying multipath counts and consistently outperforms the considered baselines across the reported range.

D. Robustness to Power Delay Profile Variations

The detector is tested across power-delay profiles, standardized unseen channel distributions, user velocities, and Doppler conditions. It preserves reliable detection across these variations, although generalization degrades for sufficiently distant Doppler regimes.

  • Power-delay profiles: Training with constant and randomized exponential power-delay profiles enables reliable detection across the tested channel conditions, with gradual degradation as α increases.
  • Unseen channels: On unseen EVA and ETU channel distributions, the proposed model performs comparably to oracle models across the evaluated SNR range and slightly better at high SNR.
  • Velocity variations: The proposed detector maintains nearly constant BER across the considered velocity range at Eb/N0 = 15 dB and 20 dB.
  • Doppler generalization: A model trained at kmax = 5 generalizes well to nearby lower-Doppler regimes, but performance degrades more noticeably at kmax = 2 and kmax = 1.

G. Complexity

The paper evaluates runtime, BER, and computational behavior for the proposed method, MP, and MMSE detectors. The proposed method has approximately linear per-iteration runtime and a favorable complexity–performance tradeoff, while its broader scope includes robust detection and future joint refinement.

  • Runtime: Under single-sample inference, the proposed method’s runtime increases approximately linearly with iterations, reflecting a uniform per-iteration computational cost.
  • Runtime and BER: MP decreases from 2.2 × 10−1 at 5 iterations to 2.3 × 10−3 at 15 iterations, requiring significantly more iterations to approach convergence.
  • Batched inference: At 10 iterations, the proposed method requires 106.6 ms per batch for B = 32 versus 108.8 ms for B = 1, indicating effective GPU parallelism.
  • Design scope: The proposed receiver combines explicit delay–Doppler structure with channel-conditioned kernels and iterative refinement for robust OTFS detection.
  • Scope boundary: The current framework treats the available channel estimate as fixed during iterative detection, motivating future joint channel-and-symbol refinement.

+ 2CRDB

The appendix decomposes the computational costs of the proposed network and baseline detectors into FLOP components. It specifies costs for alignment, feature construction, refinement, MP updates, and MMSE equalization.

  • RDN complexity: The RDN uses NRDB stacked residual dense blocks followed by feature-fusion convolution, with cost parameterized by the RDB complexity and network dimensions.
  • Classifier complexity: The classifier head costs 128MN(Cstate + Q) FLOPs.
  • IRN complexity: One IRN iteration includes soft symbol estimation, signal reconstruction, feature refinement, and gated state updating.
  • MP complexity: MP complexity is expressed using the nonzero channel-matrix entries per row or column, with separate mean, variance, and probability-update costs.
  • MMSE complexity: MMSE complexity is dominated by complex matrix multiplication and inversion, with numerical FLOP comparisons evaluated at M = N = 32, Q = 16, Ni = 10, and P = 5.
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