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RF-Diffusion: Radio Signal Generation via Time-Frequency Diffusion

Guoxuan Chi, Zheng Yang, Chenshu Wu, Jingao Xu, Yuchong Gao, Yunhao Liu, Tony Xiao Han

arXiv:2404.09140v1cs.LGcs.ITeess.SPmath.IT

TL;DR

Existing RF generators struggle to produce high-quality raw time-series signals and do not fully capture their time, frequency, and complex-valued characteristics. RF-Diffusion adapts diffusion with Time-Frequency Diffusion and a Hierarchical Diffusion Transformer, reporting strong Wi-Fi and FMCW synthesis results and gains in downstream wireless tasks.

  • Problem

    Existing RF-oriented generators struggle to precisely generate raw signals and versatile time-series data, while diffusion models must address RF signals’ temporal, frequency, and complex-valued information.

    Source: §1 · p. 2

  • Method

    RF-Diffusion combines Time-Frequency Diffusion, which alternates time-domain noise addition and frequency-domain blurring, with a Hierarchical Diffusion Transformer for reverse generation.

    Source: §1 · p. 2, §2 · p. 3

  • Results

    RF-Diffusion achieved 81% average structural similarity relative to ground truth for Wi-Fi and FMCW synthesis, exceeding DDPM, DCGAN, and CVAE by over 18.6%.

    Source: §1 · pp. 2–3

  • Takeaways & Limitations

    Reported downstream results include 4%–11% higher Wi-Fi gesture-recognition accuracy and a 5.97 dB SNR improvement in channel estimation over state-of-the-arts.

    Source: §1 · p. 3

    The paper’s downstream-task exploration specifically includes RF-Diffusion for Wi-Fi gesture-recognition augmentation.

    Source: §9 · p. 13

Abstract

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Along with AIGC shines in CV and NLP, its potential in the wireless domain has also emerged in recent years. Yet, existing RF-oriented generative solutions are ill-suited for generating high-quality, time-series RF data due to limited representation capabilities. In this work, inspired by the stellar achievements of the diffusion model in CV and NLP, we adapt it to the RF domain and propose RF-Diffusion. To accommodate the unique characteristics of RF signals, we first introduce a novel Time-Frequency Diffusion theory to enhance the original diffusion model, enabling it to tap into the information within the time, frequency, and complex-valued domains of RF signals. On this basis, we propose a Hierarchical Diffusion Transformer to translate the theory into a practical generative DNN through elaborated design spanning network architecture, functional block, and complex-valued operator, making RF-Diffusion a versatile solution to generate diverse, high-quality, and time-series RF data. Performance comparison with three prevalent generative models demonstrates the RF-Diffusion's superior performance in synthesizing Wi-Fi and FMCW signals. We also showcase the versatility of RF-Diffusion in boosting Wi-Fi sensing systems and performing channel estimation in 5G networks.

1 INTRODUCTION

Existing RF generators struggle to produce accurate, versatile raw time-series signals, while RF data carries important temporal, frequency, and phase information. RF-Diffusion adapts diffusion to these characteristics and reports results on signal synthesis and wireless tasks.

1 INTRODUCTION

  • Existing approaches face complementary limits: environment models are costly and sometimes require stationary receivers, while data-driven models struggle with raw-signal fidelity and versatility.Source: §1 · pp. 1–2
  • RF signals encode dynamics over time, frequency-domain details such as Doppler shift and chirp, and complex-valued amplitude and phase.Source: §1 · p. 2
  • Time-Frequency Diffusion alternates time-domain noise addition and frequency-domain blurring to destruct and restore RF signals.Source: §1 · p. 2
  • 81% average structural similarity relative to ground truth was reported for synthesized Wi-Fi and FMCW signals, exceeding DDPM, DCGAN, and CVAE by over 18.6%.Source: §1 · pp. 2–3
  • Wi-Fi gesture-recognition accuracy improved 4%–11%, while channel estimation gained 5.97 dB SNR over state-of-the-arts.Source: §1 · p. 3
  • RF-Diffusion pairs that theory with a hierarchical, attention-based, complex-valued transformer, and its code and pretrained model are publicly available.Source: §1 · pp. 2–3

2 OVERVIEW

RF-Diffusion combines Time-Frequency Diffusion with a Hierarchical Diffusion Transformer. Its forward process degrades signals through time-domain noise and frequency-domain blurring, while the learned reverse process restores them.

2 OVERVIEW

  • RF-Diffusion uses Time-Frequency Diffusion to guide state transitions in both the forward and reverse processes, with HDT as the reverse-generation model.Source: §2 · p. 3
  • The forward process gradually adds Gaussian noise in time and blurs the spectrum in frequency until the original RF signal degrades into noise.Source: §2 · p. 3
  • HDT learns restoration by separating Gaussian-noise denoising from spectral deblurring, taking a destructed signal as input and the previous diffusion-step signal as its supervised output.Source: §2 · p. 3

3 TIME-FREQUENCY DIFFUSION

Time-Frequency Diffusion (TFD) handles both amplitude distortion and spectral aliasing in RF signals by modeling destruction and restoration across time and frequency. The section describes how this process supports conditional signal generation.

3 TIME-FREQUENCY DIFFUSION

  • TFD addresses both amplitude distortion and spectral aliasing, so restoration targets sample amplitudes and time-series spectral resolution.The process jointly eliminates the original data distribution in time and frequency before fitting a reverse process.Source: §3 · pp. 3–4

3.1 Forward Destruction Process

  • RF-Diffusion’s forward process combines frequency-domain spectral blurring with complex Gaussian noise to progressively destroy the signal.The blur is applied to the Fourier-transformed signal, and the result is transformed back before noise is added.Source: §3.1 · p. 4

3.2 Reverse Restoration Process

  • The reverse process restores the data distribution by fitting a model to predict each preceding diffusion step from the current one.The paper describes the reverse process as Gaussian Markov and states that fitting its mean is optimized using mean squared error.Source: §3.2 · pp. 4–5

3.3 Conditional Generation

  • Conditional generation uses a condition label to guide iterative synthesis of a signal from sampled noise.Conditions can specify rooms, Tx-Rx deployments, activities, or bandwidths; one model can generate different categories from condition combinations.Source: §3.3 · p. 5

4 HIERARCHICAL DIFFUSION TRANSFORMER

The Hierarchical Diffusion Transformer (HDT) translates TFD into a practical generative model through a hierarchical architecture, attention-based blocks, complex-valued operations, and phase modulation encoding.

4 HIERARCHICAL DIFFUSION TRANSFORMER

  • HDT is the proposed practical generative model that bridges time-frequency diffusion theory and RF signal generation.Its design includes a hierarchical architecture, an attention-based diffusion block, complex-domain transformer operations, and phase modulation encoding.Source: §4 · p. 6

4.1 Hierarchical Architecture

  • HDT separates restoration into spatial denoising and time-frequency deblurring stages to handle distinct components of non-isotropic noise.It denoises each sample independently before concatenating the results for sequence-level deblurring.Source: §4.1 · p. 6

4.2 Attention-based Diffusion Block

  • The attention-based diffusion block jointly analyzes the noisy input, condition, and diffusion step.Its self-attention extracts signal features, cross-attention models input-condition associations, and adaptive normalization embeds the diffusion step.Source: §4.2 · p. 7

4.3 Complex-Valued Module Design

  • Complex-valued modules adapt HDT’s attention and feed-forward operations to RF signals represented in complex space.Attention uses a Hermitian inner product and applies softmax to the dot-product magnitude while retaining phase; feed-forward activation acts separately on real and imaginary parts.Source: §4.3 · p. 7

4.4 Phase Modulation Encoding

  • Phase modulation encoding provides HDT with positional information in the complex domain, allowing attention to recover relative offset m−n.The encoded query-key attention operation is equivalent to attention on the unencoded vectors with the relative position offset.Source: §4.4 · p. 7

5 IMPLEMENTATION

The implementation specifies the training setup, diffusion schedules, and input preprocessing used for RF-Diffusion.

5 IMPLEMENTATION

  • RF-Diffusion was implemented in PyTorch and trained on 8 NVIDIA GeForce 3090 GPUs with exponential moving average at a decay rate of 0.999.The final layers were zero-initialized before the residual, while other layers used Xavier uniform initialization.Source: §5 · p. 8
  • Training used AdamW with an initial learning rate of 1 × 10^-3, a step scheduler decay factor of 0.5, and dropout of 0.1.The diffusion process used 300 steps, with the noise coefficient and frequency-domain Gaussian-kernel standard deviation increasing across steps.Source: §5 · p. 8
  • Each signal sequence was interpolated or downsampled to length 512 and normalized by its average signal power before input.The noise coefficient increased from 10^-4 to 0.03, while the frequency-domain Gaussian kernel standard deviation increased from 10^-3 to 0.3.Source: §5 · p. 8

6 EVALUATION

The evaluation compares RF-Diffusion with representative generators on Wi-Fi and FMCW data, then tests its diffusion and network designs. RF-Diffusion leads the reported generation-quality comparisons, and the component studies favor time-frequency diffusion and the hierarchical transformer.

6.1 Experiment Design

  • The dataset covers three scenarios with varying rooms, device locations, and human factors; it contains more than 20,000 Wi-Fi and 13,000 FMCW sequences with condition labels.Labels include room, device placement, human identity, location, orientation, and activity.Source: §6.1.1 · p. 8, Figure 5 · p. 9

6.1.2 Comparative Methods.

  • The evaluation compares against DDPM, DCGAN, and CVAE, re-implementing the models with complex-valued neural networks for RF signals.The compared approaches use diffusion, adversarial generation, and conditional variational autoencoding, respectively.Source: §6.1.2 · p. 8

6.1.3 Evaluation Metrics.

  • The evaluation uses complex-domain SSIM and FID, with a pretrained STFNets model extracting features for FID.The paper notes that no definitive gold standard for generative-model evaluation has been established.Source: §6.1.3 · p. 8

6.2 Overall Generation Quality

  • Wi-Fi RF-Diffusion reaches average SSIM 0.81 and FID 4.42; FMCW reaches average SSIM 0.75 and average FID 6.10, outperforming comparative methods.The Wi-Fi comparison reports SSIM gains over DDPM, DCGAN, and CVAE of 25.4%, 18.6%, and 71.3%, respectively.Source: Figure 6 · p. 9, Figure 7 · p. 9, §6.2 · p. 9

6.3 Micro-benchmarks

  • The evaluation presents FMCW signal-generation quality in Figure 7, while the authors state they retained RF-Diffusion’s network-model architecture to validate their proposed time-frequency diffusion theory.Source: Figure 7 · p. 9, §6.3.1 · p. 9

6.3.2 Impact of Network Design.

  • The hierarchical diffusion transformer reaches SSIM 0.81, compared with 0.75 for SDT and 0.68 for U-Net, and leads both on FID.HDT decouples non-isotropic noise in two sequential stages; its transformer architecture distinguishes signal characteristics at different times.Source: §6.3.2 · pp. 9–10, Figure 9 · p. 10

6.3.1 Impact of Diffusion Methods.

  • Time-frequency diffusion achieves SSIM 0.81, versus 0.71 for Gaussian diffusion and 0.45 for blur diffusion, and leads both alternatives on FID.The authors attribute its advantage to combining diffusion methods on orthogonal spaces for complementary benefits.Source: §6.3.1 · p. 9, Figure 8 · p. 10

6.3.2 Impact of Network Design.

  • Increasing RF-Diffusion’s model parameters and computation correlates strongly with better FID performance across nine tested model sizes.The study varies attention-based diffusion blocks and hidden dimensions, and anticipates further improvement from increasing model size.Source: §6.3.3 · p. 10

7 CASE STUDY

The case studies use RF-Diffusion to augment Wi-Fi gesture-recognition training and to estimate 5G FDD downlink channels from uplink CSI. Reported results include cross-domain recognition gains and higher channel-estimation SNR than comparative methods.

7.1 Wi-Fi Gesture Recognition

  • RF-Diffusion generates condition-guided synthetic Wi-Fi signals, which are combined with the original real-world data to train existing sensing models without changing their structure.The baseline and augmented solution use the same real-world dataset, without extra data.Source: §7.1 · p. 10, §7 · p. 10

7 CASE STUDY

  • Cross-domain Wi-Fi augmentation improves accuracy by 4.7% for Widar3.0 and 11.5% for EI; channel estimation reaches average SNR 27.01, leading the compared methods.The channel-estimation result is 34.6% above NeRF2 and 77.5% above FIRE, with more than 5× performance gain over codebook.Source: Figure 11 · p. 10, §7.1.2 · p. 10, Figure 13 · p. 11

7.1.4 Impact of Synthesized Data Ratio.

  • Recognition accuracy peaks and then declines as synthetic-data volume increases, with the best tested ratios varying by model and domain.Widar3.0 peaks at 92.7% with +100% synthetic data cross-domain and 93.4% with +50% in-domain; EI peaks at 83.8% with +125% cross-domain and 89.1% with +75% in-domain.Source: Figure 12 · p. 10, §7.1.4 · p. 11

7.1.1 Experiment Design.

  • The gesture-recognition evaluation uses the public Widar3.0 dataset and considers both Widar3.0 and the end-to-end EI model.Widar3.0 extracts physical features before recognition; EI takes raw signals as input.Source: §7.1.1 · p. 10

7.1.2 Cross-domain Evaluation.

  • Cross-domain gains are larger for EI than Widar3.0; DDPM yields smaller gains, while DCGAN or CVAE can reduce recognition accuracy.The authors relate EI’s larger improvement to sensitivity to data volume and diversity, while Widar3.0 may not fully exploit generated signals after conversion to physical features.Source: §7.1.2 · p. 11

7.1.3 In-domain Evaluation.

  • In-domain augmentation improves accuracy by 1.8% for Widar3.0 and 8.7% for EI, with smaller gains than in the cross-domain setting.The authors attribute the modest gains to synthetic-data diversity having limited impact within the same domain.Source: §7.1.3 · p. 11

7.2 5G FDD Channel Estimation

  • For FDD channel estimation, downlink CSI is the generation target and uplink CSI is the condition; the approach assumes both channels share propagation paths.The evaluation uses Argos MIMO data, assigning the first 26 of 52 subcarriers to uplink and the remaining 26 to downlink.Source: §7.2 · p. 11, §7.2.1 · pp. 11–12

7.2.2 Channel Estimation Accuracy.

  • RF-Diffusion’s estimated downlink CSI closely aligns with ground truth and achieves the highest SNR among the compared channel-estimation methods.The authors attribute NeRF2’s underperformance to its time-invariant propagation-space treatment, and describe FIRE and codebook as less able to characterize fine-grained channel-state distributions.Source: §7.2.2 · p. 12

8 RELATED WORK

Prior work spans diffusion models and wireless signal-generation approaches, including simulation, learned environment models, and task-specific generative models. The paper positions RF-Diffusion as a general wireless-signal generator combining temporal and spectral modeling.

Diffusion probabilistic models

  • Diffusion models have been applied to image, point-cloud, text, and audio generation; DDIM [44] accelerates reverse sampling, while LDM [54] performs diffusion in latent space.DDPM progressively adds Gaussian noise and learns to reverse the process [60].Source: §8 · p. 12

RF-Diffusion

  • RF-Diffusion is presented as a versatile wireless-signal generator that models temporal and spectral details through time-frequency diffusion and generates high-fidelity signals in dynamic scenarios.The paper highlights Wi-Fi sensing and 5G channel estimation as applications.Source: §8 · pp. 12–13

Signal generation in wireless systems

  • Wireless signal generation includes ray-traced environment simulation, vision-based human reconstruction, and learned approaches such as NeRF2 [76], VAEs, and GANs.The passage describes NeRF2 as limited to specific static scenarios and less effective in dynamic real-world scenarios.Source: §8 · pp. 12–13

9 DISCUSSION AND FUTURE WORK

The discussion considers RF-Diffusion for downstream data-driven tasks and as a signal-simulation alternative, while identifying limits in simulation stability and variable-length generation.

9 DISCUSSION AND FUTURE WORK

  • Synthetic samples can extend beyond the dataset’s initial scope, potentially improving downstream-model generalization; the paper demonstrates this for Wi-Fi gesture recognition.The discussion says the approach can apply to wireless communication and sensing tasks more broadly.Source: §9 · p. 13
  • RF-Diffusion needs no propagation assumptions or environment pre-modeling, but may be less stable and precise than traditional simulators in some scenarios.It is presented as a complementary data-driven approach, particularly for complex, dynamic environments where accurate modeling is difficult.Source: §9 · p. 13
  • Because RF-Diffusion processes time series as a unified entity, variable-length sequences require downsampling and interpolation, limiting versatility.The discussion contrasts this with autoregressive models, which it says improve length adaptability and enable exploration of temporal correlations.Source: §9 · p. 13

10 CONCLUSION

The conclusion presents RF-Diffusion as a diffusion model for RF signals, built on a time-frequency process and a hierarchical diffusion transformer. It highlights high-fidelity time-series generation and potential applications in wireless sensing and channel estimation.

10 CONCLUSION

  • The paper presents RF-Diffusion as a pioneering generative diffusion model designed for RF signals.It is described as generating high-fidelity time-series signals.Source: §10 · p. 13
  • A time-frequency diffusion process captures RF signal characteristics across spatial, temporal, and frequency domains.The theory is translated into a practical generative model based on a hierarchical diffusion transformer.Source: §10 · p. 13
  • The conclusion identifies wireless sensing accuracy and channel-state estimation as potential applications of RF-Diffusion.The stated scope ranges from wireless sensing to communication systems.Source: §10 · p. 13

A CONVERGENCE OF FORWARD DESTRUCTION PROCESS

The appendix states that the forward process converges to a distribution independent of the original signal as T grows, and gives a sufficient condition for this convergence.

A CONVERGENCE OF FORWARD DESTRUCTION PROCESS

B REVERSE PROCESS DISTRIBUTION

The appendix introduces a reverse-process distribution derivation using Bayes’ theorem and a combination of Eqn. 2 and Eqn. 3.

B REVERSE PROCESS DISTRIBUTION

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