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ALF: Spectrally Anchored Latent Flow Matching for Wireless Signal Generation

Yiyang Li, Sai Shankar Narasimhan, Priam Alataris, Avi Bagchi, Kaushik Chowdhury, Sanjay Shakkottai

arXiv:2609.36385v2eess.SP

TL;DR

RF signals’ spectral constraints create time-domain structure that makes long, coherent generation challenging. ALF conditions latent flow on labels and trains it to predict spectrogram representations. Across held-out channels and evaluated lengths, it reports 84.5% average TSTR accuracy, a 38.02% relative improvement over Time Weaver, and 100× faster generation.

  • Problem

    RF generation must preserve engineered waveform structure, while prior approaches do not use the frequency domain as an intermediate reasoning space for long-range coherence.

    Source: §1 · pp. 1–2

  • Method

    ALF is a label-conditioned latent flow model trained to predict spectrogram latents that guide generation of time-domain IQ signals.

    Source: §1 · p. 2

  • Results

    Across held-out channels and evaluated lengths, ALF reaches 84.5% average TSTR accuracy, improves 38.02% over Time Weaver, and generates records 100× faster on average.

    Source: §7 · p. 10

  • Takeaways & Limitations

    ALF improves spectral fidelity and downstream utility without adding inference-time computation.

    Source: §7 · p. 10

    Evaluation on over-the-air recordings, including receiver-level validation under hardware and environmental impairments, remains future work.

    Source: §7 · p. 10

Abstract

from arXiv · show

Wireless time-series generation is useful for emerging applications that will drive the adoption and integration of machine learning tasks within next-generation networks, such as waveform classification in shared spectrum bands and interpretation of the physical world through integrated sensing and communications. Unlike a generic time series, wireless signals have time-frequency duality, where a frequency domain bandwidth constraint implicitly imposes latent structural constraints on the evolution of the time-domain sequence. In this paper, we develop Anchored Latent Flow (ALF), a latent space flow model for label-conditioned signal generation that exploits this duality. Our flow model "reasons'" through a spectrogram, which is a 2-D representation of the signal constructed by applying a windowed Fast Fourier Transform to successive, overlapping signal segments and mapping their frequency-domain power components across time. Specifically, we shape the latent space of the flow model through a training-time auxiliary objective that is supervised by the (latent) spectrogram (i.e., anchoring through the spectrogram). By guiding the flow field to reason through a spectrogram, the generated sequence maintains long-range coherence across time and greatly improves the signal quality at inference. Empirically, ALF exhibits state-of-the-art generation quality and reconstruction error across various signal lengths, waveform classes, signal-to-noise ratio (SNR), and channel conditions, reaching a train on synthetic, test on real (TSTR) accuracy of 84.5%, a 1.9X average memory reduction, and 100X average compute speedup over existing models. Our design further enables downstream tasks, including style transfer and data augmentation, and has broad utility for the wireless community.

1 Introduction

RF generation must capture engineered signal structure, including spectral constraints that shape plausible time-domain waveforms. ALF uses spectrogram supervision to guide latent flow generation and reports improved generation and efficiency.

1 Introduction

  • RF generation must model amplitude, frequency, phase, long-sample coherence, and cross-antenna correlations under bandwidth constraints.Time-frequency duality means spectral constraints induce structure in the time domain.Source: §1 · p. 1
  • Prior RF generation work uses spectral information but does not use the frequency domain as an intermediate reasoning space, motivating spectrogram-based anchoring.The paper proposes WaveScene, a dataset with 7.82 million IQ recording-label pairs across waveform classes, propagation environments, and sequence lengths.Source: §1 · p. 2
  • ALF reports a 38.02% relative improvement in TSTR waveform-classification accuracy over the closest baseline, with 100× compute speedup and 1.9× memory reduction.The design also supports native style transfer and autoregressive capabilities.Source: §1 · p. 2
  • ALF is a label-conditioned latent flow model that predicts spectrogram latents to guide time-domain signal generation and improve long-range coherence.Its flow transports an aligned, condition-aware signal latent space to a reconstruction-oriented space.Source: §1 · p. 2

2 Related Work

Related work spans diffusion for images, audio, video, and time-series, alongside RF-specific generation methods. The paper identifies long-range coherent IQ generation as a gap and introduces spectral anchoring as an RF-oriented inductive bias.

2 Related Work

3 Background

The paper formulates conditional generation of receiver-side IQ waveforms and builds on rectified flow to learn a transport from a tractable source distribution to the target conditional data distribution.

3 Background

  • An IQ waveform stacks synchronized receiver-side I and Q samples across antennas, and each waveform is paired with heterogeneous conditioning information.Labels are mapped to fixed-dimensional real representations, such as one-hot encodings for categorical variables.Source: §3 · p. 3
  • The learning dataset treats waveform-label pairs as i.i.d. samples from the empirical joint distribution p_data(X_IQ, Y).The dataset is defined as paired IQ waveforms and labels.Source: §3 · p. 3
  • The objective is to learn conditional generation matching p(X_IQ|Y), using rectified flow to transport samples from a tractable source distribution to target data.Rectified flow interpolates linearly between source and target samples, with a constant velocity along each sampled path.Source: §3 · p. 3
  • At inference, the learned conditional velocity field is integrated from t = 0 to t = 1, starting from a source sample, to obtain a generated sample.The training objective regresses the field using uniformly sampled times and learns the conditional mean transport across paths.Source: §3 · p. 3

4 WaveScene Dataset

WaveScene is a large synthetic corpus of labeled, receiver-side IQ waveforms designed to cover varied waveform classes, channel conditions, and sequence lengths.

4 WaveScene Dataset

  • The corpus covers 32 waveform classes and 1,066 parameterized variants, with four-antenna SIMO recordings at five sequence lengths from 2,048 to 32,768 samples.The variants span generic modulations, standardized communication protocols, and radar emissions.Source: §4 · p. 3
  • WaveScene uses geometry-based stochastic channels across urban microcell, urban macrocell, rural macrocell, and indoor hotspot environments.Propagation states include LOS, NLOS, and O2I; channel generation follows 3GPP TR 38.901.Source: §4 · pp. 3–4
  • WaveScene contains approximately 7.82 million recording-label pairs, including shared-channel and channel-held-out sets.The channel-held-out test set contains 300K recordings with unseen channel realizations.Source: §4 · p. 4
  • Training uses six complementary labels, combining categorical waveform, scene, and propagation attributes with continuous spectral occupancy, SNR, and RMS delay spread.The label representation has 42 dimensions.Source: §4 · p. 4

5 Anchored Latent Flow

ALF uses a two-stage latent flow approach to address inference costs and weak long-range spectral coherence in long IQ generation. It first builds label-aligned, reconstruction-aware IQ latents, then spectrally anchors flow matching to guide global structure.

5 Anchored Latent Flow

  • ALF addresses high inference costs and weak long-range spectral coherence in long IQ generation with a two-stage training setup.Source: §5 · p. 4

5.1 Stage 1: Label-Aligned Reconstruction-Aware Encoding

  • Stage 1 fuses raw-IQ and spectral patch representations, mixes them across patches, and aligns record-level embeddings with labels while supporting waveform reconstruction.The encoder produces patch-level latents and a record-level summary; the decoder reconstructs the four-antenna waveform.Source: §5.1 · p. 4

5.2 Stage 2: Spectrally Anchored Latent Flow Matching

  • Stage 2 supervises an intermediate flow representation to predict a spectrogram latent, encouraging generated waveforms to follow global spectral structure such as occupied bandwidth.A frozen spectral autoencoder supplies the target latent, and a prediction head attaches after the flow network’s sixth Transformer block.Source: §5.2 · pp. 5–6
  • At inference, the generated IQ latent is reconstructed with the frozen IQ decoder, while the spectral autoencoder and anchor head are omitted.Source: §5.2 · p. 6

6 Results

ALF provides downstream utility on frequency-dependent tasks and improves RF-specific metrics, while spectral anchoring shapes latent representations and supports coherent, efficient generation. The reported results also demonstrate style transfer and autoregressive long-sequence generation, with limitations on scene- and propagation-centered tasks and in the simulated-channel evaluation scope.

Downstream utility

  • 38.02% TSTR and 102.88% TRTS performance improvements are reported for waveform classification, with additional utility on bandwidth, sample-rate, and unseen carrier-frequency tasks.The authors interpret TSTR as corpus generality and TRTS as recording-level specificity.Source: §6 · p. 6, Table 2 · p. 7

Anchoring ablations

  • ALF outperforms label-source initialization and base LF on TSTR and RF amplitude properties, while anchoring slows generation collapse for low-density samples.The reported RF metrics include PSD, PAPR, and envelope CV; Table 3 compares anchored and unanchored ablations and low-density reclassification.Source: §6 · pp. 6–7, Table 3 · p. 7

Latent-space inspection

  • ALF produces an identifiable Costas hopping pattern in decoded intermediate spectrograms, while the unanchored LF baseline remains ambiguous.Sharper frequency patterns increasingly constrain time-domain generation as lengths scale, compounding sample-coherence advantages.Source: §6 · p. 7, Figure 3 · p. 8

Inference efficiency

  • Two orders of magnitude lower inference time than Time Weaver makes 100k+ sample generations feasible in fractions of a second.Inference complexity remains subject to attention scaling laws.Source: §6 · p. 8, Table 4 · p. 9

Style transfer

  • RF-Inversion denoises near- or below-noise-floor recordings while preserving FHFM hopping information, despite marginally decreasing generated SNR.The paper contrasts this controlled approach with naive resampling, which produces less similar FHFM outputs.Source: §6 · pp. 8–9, Figure 4 · p. 8

Autoregressive generation

  • Autoregressive generation demonstrates 327k-sample sequences with waveform shifts and single-condition continuity.Suffix generation flows new patches alongside previously generated tokens, conditioned on the target label and signal context.Source: Figure 5 · p. 9, §6 · p. 9

Limitations

  • ALF shows no improvement on scene- or propagation-centered tasks, and WaveScene uses simulated channels that remain static within recordings.The evaluation also omits mobility, Doppler evolution, hardware impairments, interference, and other variability in real transmissions.Source: §6 · p. 9

7 Conclusion

The conclusion presents ALF as a latent flow framework for generating long, multi-antenna IQ recordings and pairs it with WaveScene. The overview argues that spectral anchoring reveals band-limit structure implicit in time-domain samples.

7 Conclusion

  • ALF is a latent flow-matching framework for conditional generation of long, multi-antenna IQ recordings, paired with WaveScene, a dataset spanning waveform classes, propagation conditions, and record lengths.Source: §7 · p. 9

A.2 Setup

  • A length-n signal generally has n degrees of freedom, while band limitation to k frequency bins exposes structure in its DFT.Source: §A.1 · p. 14

A.1 Overview

  • Spectral anchoring exposes band-limit constraints directly, revealing dependencies across time-domain samples and reducing the parameter complexity needed relative to an unstructured time-domain representation.Source: §A.1 · p. 14

A.3 Unanchored Parameter Count

  • Without a spectral anchor, the model must represent any distribution over D^n, with a conditioning-table row for every prefix and d − 1 free parameters per row.Source: §A.3 · p. 15

A.4 Anchored Parameter Count

This appendix examines ALF’s spectral constraints and model complexity, situates the method among related work, and describes WaveScene’s design. It also reports clipping in normalized targets and defines a held-out-channel benchmark for generalization to unseen propagation realizations.

A.4 Anchored Parameter Count

  • For signals with frequency support K, the first |K| time samples uniquely determine all n samples; support-aware anchoring lowers parameter complexity relative to an unstructured time-domain model.A deterministic spectral anchor reveals active frequency bins; full-spectrum and magnitude-spectrum anchors additionally reveal spectral values or magnitudes, respectively.Source: §A.4 · pp. 16–17

A.5 Specializing to a Contiguous Bandwidth Model

  • Each of the n − k frequency bins excluded by an anchor divides the parameter count by d, yielding near-d^n gain for narrowband signals, exponential-in-duration gain for fixed B/fs < 1, and no gain at full band.For a DC signal, the anchored bound is d − 1, independent of n, versus d^n − 1 unanchored.Source: §A.5 · p. 18

B Extended Related Works

  • Prior methods use metadata, observed windows, or frequency information for conditional generation, while ALF uses a learned spectral latent to supervise intermediate flow representations during training and removes the target at inference.Related work also covers IQ embeddings and channel estimation or synthesis; those channel-focused outputs do not model the full received recordings Y ∈ C^4×N considered by ALF.Source: B Extended Related Works · p. 19

C.1 Physical Channel Model and Modeling Challenges

  • WaveScene models up to 32,768 complex samples and four synchronized receive streams, requiring long-context waveform fidelity and preservation of cross-antenna phase, amplitude, and covariance; its channel impulse response is static.The four antennas share transmitted waveform, path delays, and propagation geometry, but have antenna-dependent complex path coefficients and independent receiver noise.Source: §C.1 · pp. 19–20

C.2 Waveform Parameterization and Standards Alignment

  • WaveScene contains 1,066 parameterized waveform variants across 32 classes, uses standards-oriented physical-layer implementations where available, and controls payload bits with a deterministic canonical stream.This design emphasizes waveform morphology and propagation rather than independently varying payloads, so the dataset does not assess generalization to such payload variation.Source: §C.2 · pp. 20–21

C.3 Propagation-State Construction of Shared-Channel Set

  • The 7.52M shared-channel set uses scene-dependent propagation-state proportions rather than independent balancing; for RMa, the in-car deployment share is approximated as outdoor without vehicle penetration loss.UMi and UMa links are initialized as 80% O2I and 20% outdoor, while InH has no O2I state.Source: §C.3 · p. 21

C.4 Label Definitions and Normalization

  • WaveScene defines six learning factors from clean waveform manifests and channel realizations: waveform class, scene, propagation state, spectral occupancy, mean per-antenna pre-combining SNR, and RMS delay spread.Spectral occupancy is the fraction of the sampled spectrum occupied, making it comparable across capture rates.Source: §C.4 · p. 21
  • SNR clipping affected 0.018% of recordings below and 0.102% above the thresholds; delay-spread clipping affected 0.0014% below and fewer than 0.0001% above.No occupancy values were clipped in the 7.52M-recording corpus.Source: §C.4 · p. 22

C.5 Held-Out Channel Benchmark

  • The held-out-channel benchmark contains 300,000 recordings with channel identities absent from the development corpus, jointly holding out scene, topology, stochastic variation, propagation state, and carrier frequency.This prevents evaluation on a previously observed CIR under only a different waveform or noise realization.Source: §C.5 · p. 22
  • The benchmark provides exactly 9,375 recordings per waveform class across 32 classes and is distributed across propagation scenes and carrier frequencies, without a deliberately shifted waveform or label distribution.A deterministic list of selected recording and channel identifiers is distributed with the benchmark.Source: §C.5 · p. 22

C.6 Reproducibility and Limitations

ALF’s frozen encoder achieves high waveform macro-F1 with few labeled recordings, including on channel-held-out data. The section also documents the encoder and evaluation protocols, benchmark boundaries, and embedding geometry.

C.6 Reproducibility and Limitations

  • Dataset generation uses versioned manifests, deterministic seeds, and configuration-bound cache fingerprints; release checks validate 1,066 manifests, while the benchmark excludes mobility and several RF impairments.Other scope boundaries include aligned temporal origins and deterministic communications payloads.Source: §C.6 · pp. 22–23

D.1 Encoder Architecture

  • Stage 1 processes 1,024-sample patches with gated raw-IQ and spectral fusion, Transformer mixing, and dual-path decoding, using waveform, spectral, envelope, covariance, and level reconstruction terms.Its structural objective retains metadata factors and discourages redundant group encoding; the factor probe is discarded after Stage 1.Source: §D.1 · pp. 23–24

D.2 Adaptation of External RF Encoders

  • External encoders retain their native recipes, including 256-sample views, while ALF processes full recordings; long-recording scaling is therefore not an equal-context representation comparison.IQFormer’s waveform result also uses supervised waveform-class pretraining.Source: §D.2 · p. 25

D.3 Frozen-Encoder Probing Protocol

  • Frozen encoders are evaluated with identical one-hidden-layer probes trained on 5M recordings and tested without adaptation on matched seen-channel and channel-held-out sets.Waveform macro-F1, SNR regression, and log10(ns) delay-spread regression are reported across five matched seeds.Source: §D.3 · p. 26, Table 9 · p. 26

D.4 Label efficiency

  • 97.8% seen-channel and 98.3% unseen-channel macro-F1 with 10K recordings; ALF largely saturates by 100K, while external encoders plateau lower and improve through 5M.Figure 7 reports 92.0% and 92.7% macro-F1 with 1K labeled recordings on seen and unseen channels, respectively, and over 99% by 100K.Source: §D.4 · p. 26, Figure 7 · p. 27

D.5 Embedding geometry

  • ALF’s embedding separates waveform-class manifolds while retaining smooth SNR and delay-spread variation; adapted external encoders show more overlapping geometry.The UMAP plots are descriptive; frozen-probe results provide the quantitative comparison.Source: Figure 9 · p. 27, §D.5 · p. 28, Figure 8 · p. 28

D.6 Zero-shot alignment and exact retrieval

The encoder supports zero-shot attribute prediction and exact metadata retrieval, while ALF uses a label-conditioned prior and a training-only spectrogram anchor. The section also specifies generation protocols and a post-decode refiner that improves spectral-error metrics.

D.6 Zero-shot alignment and exact retrieval

  • 72.84% of seen-channel and 72.66% of channel-held-out queries retrieve the complete six-factor metadata configuration within the top 10 of 300K candidates.Conditional zero-shot prediction uses metadata prototypes, while paired retrieval ranks the matching six-label configuration against the test gallery.Source: §D.6 · pp. 28–29, Table 10 · p. 29

E.1 Hyperparameters

  • The edge-refiner gate is at least 30 dB, and the fixed-seed corpus contains 100,000 records generated under held-out test-split conditioning.Unrefined corpora are otherwise identical.Source: §E.1 · p. 31

E.2 Label-Conditioned Gaussian Prior

  • ALF initializes each patch-token trajectory from a Gaussian parameterized by the frozen label tower, conditioned on six RF metadata factors rather than standard-normal noise.Conditioning is injected both through the initial state and through adaptive LayerNorm; conditioning dropout is set to zero.Source: §E.2 · p. 31

E.3 Separate Spectral Autoencoder and Mid-Depth Anchoring

  • A frozen spectral autoencoder supplies clean spectrogram latents for a mid-depth denoising objective, whose anchor head is discarded at inference and adds no generation FLOPs.The anchor loss is ramped to 0.25 over the first two epochs and weighted toward later flow times.Source: §E.3 · p. 31

E.4 Training Consistency and Generation Protocol

  • Generation uses 100,000 records under fixed sampling conditions; baselines differ in length support, with WaveStitch uncoupled across 256-sample windows and RF-Diffusion evaluated only at 2,048 samples.The RF-Diffusion figures are not comparable to the other models’ length-pooled results.Source: §E.4 · p. 32

E.5 Inference

  • Inference follows Sample, Flow, Decode; user-specified target features condition the prior, and the per-patch design supports length-agnostic generation.The passage describes potentially unlimited generation length.Source: §E.5 · p. 33, Figure 11 · p. 33

E.6 Refined vs. Unrefined

  • Per-record smoothing addresses patch-seam fluctuations that create spectral stripes and raise PSD and spectrogram MSE despite preserved overall SNR.The refiner applies only above an SNR threshold to avoid modifying intentionally noisy generations.Source: §E.6 · p. 33
  • Roughly 2 dB PSD MSE and 6.5 dB Spectrogram MSE improvements occur across ablations with the post-decode refiner.The refiner is included for ALF, LF-M, and LF-N in the main comparison.Source: Table 12 · p. 33, §E.6 · p. 33

E.7 Robustness

ALF’s robustness and style-transfer evaluations report slower record collapse and sharper spectral detail with anchoring. Phase and array-level tests show stable behavior across recording lengths, with a qualification in spatial-covariance diversity.

E.7 Robustness

  • ALF slows the record-collapse curve and remains the best-performing model at a single inference step; the trend continues through five steps.The robustness section also reports that TimeWeaver experiences the largest collapse in this region.Source: §E.7 · p. 33, Figure 12 · p. 34, Table 13 · p. 34

E.8 Style Transfer Cont.

  • Unanchored style transfer has less sharp frequency detail, whereas anchored guidance reduces the observed spectrogram blurring.The comparison uses naive sampling with ALF and the unanchored metadata-prior LF-M model.Source: §E.8 · p. 35, Figure 13 · p. 35

E.9 Within-Recording Phase Consistency

  • Generated phase-rate drift was 0.066 rad/sample at 2k and 0.047 at 32k samples, close to reference values of 0.071 and 0.048; CW showed the clearest long-range gap.Local phase-increment concentration remained stable across lengths.Source: §E.9 · p. 36, Figure 14 · p. 36, Figure 15 · p. 37

E.10 Cross-Antenna Consistency

  • ALF has slightly lower spatial-covariance effective rank, indicating modest compression of antenna-specific multipath diversity rather than perfect reproduction of every array statistic.The reported timing and phase-drift behavior nevertheless supports coherent relationships among generated antenna streams over long recordings.Source: §E.10 · p. 38
  • Median adjacent-pair delay spread is zero samples in every length bin, with generated interquartile ranges no larger than one sample; relative phase drift remains low across lengths.Generated drift exceeds reference drift: 0.023 versus 0.0105 cycles at 2k samples, and 0.0055 versus 0.0027 at 32k samples.Source: §E.10 · p. 37, Figure 16 · p. 38

F Autoregressive Post-Training

Because the base model jointly samples at most 32 patches, ALF is post-trained for conditional suffix generation to extend recordings and support label-driven distribution shifts. The post-training uses clean prefix latents as anchors and combines suffix flow matching with continuity losses.

F Autoregressive Post-Training

  • The base model’s maximum generation length is 32,768 samples, motivating conditional suffix generation for longer downstream sequences such as integrated-sensing data.The post-trained model demonstrates arbitrary-length generation and custom label-driven distribution shifts.Source: F Autoregressive Post-Training · p. 39, Figure 17 · p. 39
  • ALF conditions each generated suffix on the last k clean latent patches, using them as anchors for the following patches based on their labels.This windowed conditioning approach is described as preserving RF structure and producing smoother transitions.Source: F Autoregressive Post-Training · p. 39
  • Post-training uses P = 16 and k = 8; continuity training combines suffix flow matching, a zero-velocity prefix pin, and an edge loss with the original generation loss.Figure 17 illustrates noise and waveform shifts alongside a no-transition control.Source: F Autoregressive Post-Training · p. 39, Figure 17 · p. 39

G.1 Distributional Metrics

ALF is significantly superior in PSD MSE and overall better in Spectrogram MSE, while these distributional metrics may not adequately evaluate highly constrained wireless representations. RF Diffusion could not be trained beyond length 2,048 because of memory limitations.

G.1 Distributional Metrics

  • ALF is significantly superior in PSD MSE and overall better in Spectrogram MSE, but distributional alignment is not a fine-grained quality measure for highly constrained wireless representations.Table 14 compares PSD and spectral MSE metrics; the authors note that downstream tasks provide a better quality judgment.Source: Table 14 · p. 40, §G.1 · p. 40
  • RF Diffusion could not be trained on records longer than 2,048 because of memory limitations, so longer generations were not considered.Other models were evaluated on 100k recordings.Source: §G.1 · p. 40

G.2 Other Generation Quality Metrics

Rescaling energy-linked objectives changes their classification quality: performance equalizes across ALF, WaveStitch, and Time Weaver on Indoor/Outdoor and LOS/NLOS tasks, while two other objectives remain barely above chance.

G.2 Other Generation Quality Metrics

  • After rescaling, ALF, WaveStitch, and Time Weaver have equal classification performance on Indoor/Outdoor and LOS/NLOS tasks.Table 15 reports the effect of rescaling on quality metrics for energy-linked objectives.Source: Table 15 · p. 41, §G.2 · p. 41
  • The other two objectives have accuracies barely over chance, and their noise readings indicate more difficult representations.The authors attribute lower utility performance than Time Weaver to the models’ energy-based nature.Source: §G.2 · p. 41
  • Both models output normalized data without attenuation, making scene classifications easier to detect than shape alone.The passage identifies Indoor/Outdoor and LOS/NLOS as the scene classifications affected.Source: §G.2 · p. 41
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