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Semantic Communication for Distributed Spectrum Monitoring over Unreliable Links

Samer Lahoud, Kinda Khawam

arXiv:2609.05791v1cs.NI

TL;DR

Distributed emitter counting and localization must work when unreliable shared links erase whole receiver reports, making raw I/Q forwarding impractical. The paper trains compact semantic reports and set-based fusion for partial receiver sets. Experiments report improved robustness under erasure, stronger set-fusion performance than fixed-order concatenation, and sufficiency of four bits per latent component in the tested setting.

  • Problem

    Distributed spectrum monitoring must estimate emitter count and locations despite shared links that can erase whole reports, while forwarding all raw I/Q streams is costly.

    Source: §I · p. 1, E. Contention-Based Access and Report… · p. 3

  • Method

    Each receiver sends a compact task-trained latent with its position, and an end-to-end trained permutation-invariant decoder fuses the surviving set under report erasure and optional quantization.

    Source: §I · p. 1, C. Permutation-Invariant Fusion over… · p. 3

  • Results

    The conclusion reports improved robustness from erasure-aware training, better performance than fixed-order concatenation, cross-count deployment, and sufficiency of four bits per latent component at M = 4.

    Source: §VI · p. 9

  • Takeaways & Limitations

    In the tested setting, a few hundred task-relevant bits per observation window suffice, while increasing bit depth beyond the rate knee does not recover spatial evidence from erased receivers.

    Source: H. Discussion · p. 8

Abstract

from arXiv · show

Distributed spectrum monitoring relies on spatially separated receivers to infer the state of the radio environment. A central task is to determine how many emitters are active and where they are located. Sensors typically report over shared unreliable links, where contention, fading, or energy limits erase whole reports, so forwarding raw I/Q samples from all receivers to a fusion node becomes impractical. This paper formulates distributed emitter counting and localization as a semantic communication problem over unreliable reporting links. Each receiver maps its local time-frequency observation to a compact latent representation and transmits it. The fusion node pairs each surviving latent with the corresponding receiver position and operates on the resulting unordered set, which keeps the fusion rule compatible with variable membership and receiver-count changes. The encoder and decoder are trained end-to-end with report erasure, and optionally finite-rate quantization, inside the task objective. Experiments on synthetic multi-emitter scenes show that channel-aware training improves robustness under erasure, that set fusion is more robust than fixed-order concatenation, and that one trained model operates across receiver counts without retraining. The rate study shows that a few bits per latent component suffice in the tested setting, and that the rate knee remains roughly stable across erasure levels. These results support the feasibility of low-rate semantic reporting for distributed spectrum monitoring over unreliable links.

I. INTRODUCTION

The paper frames emitter counting and localization over unreliable reporting links as task-oriented communication, using compact reports and fusion over surviving receivers. It situates this design among semantic communication, learned wireless sensing, and permutation-invariant set models.

I. INTRODUCTION

  • Forwarding raw I/Q streams from distributed low-cost receivers consumes bandwidth, energy, and access-channel resources, motivating compact task-relevant reports.Whole-report losses and changing report membership also require the scheme to handle partial, variable receiver sets.Source: §I · p. 1
  • The system uses compact task-relevant reports and an unordered, position-tagged set of surviving reports to support variable membership and receiver counts without retraining.Training includes whole-report erasure and optionally finite-rate quantization in the task objective.Source: §I · p. 1
  • Channel-aware training improves erasure robustness, set fusion outperforms fixed-order concatenation, and accurate operation requires only a few bits per latent component.The supplied results also evaluate receiver-count variation.Source: §I · pp. 1–2

II. RELATED WORK

  • Task-oriented communication targets downstream task utility rather than bit-level reconstruction, extending to cooperative inference and rate-distortion formulations.The paper places its work in a distributed setting with unreliable links and variable received-report sets.Source: §II · p. 2
  • Unlike deep joint source-channel coding that maps a source directly to channel symbols, this work retains a digital reporting interface and models whole-report loss directly.The cited distinction is the separate task-oriented reports sent by multiple receivers over unreliable links.Source: §II · p. 2
  • Prior distributed sensing and localization systems often assume reliable delivery, whereas this work learns representations under erasure and rate constraints.It also contrasts with fixed-array, clean-link multi-emitter localization and relates to cooperative sensing, compressive sensing, and in-network aggregation.Source: §II · p. 2
  • Permutation-invariant set models make the decoder invariant to report ordering and compatible with whichever receiver subset survives the channel.The paper draws on Deep Sets and attention-based set pooling while matching fusion to variable receiver membership.Source: §II · p. 2

III. SYSTEM MODEL

The monitoring task estimates the count and locations of emitters from distributed observations, with receiver positions available as side information. Each receiver sends a task-trained latent paired with its position, rather than transmitting raw observations.

A. Monitoring Scenario and Task

  • Receiver positions are known side information and are redrawn across scenes, allowing arbitrary receiver layouts.Positions reach the decoder as slow-varying metadata registered when a receiver joins.Source: A. Monitoring Scenario and Task · p. 2
  • The output is an unordered emitter set with cardinality, scored for both count and localization errors after the best assignment between predicted and true emitters.The task probes reporting-link reliability because every lost report removes a spatial view of the same scene.Source: A. Monitoring Scenario and Task · p. 2

B. Distributed Semantic Encoding

  • Each receiver applies the same encoder to its local observation and sends a compact latent paired with the receiver's known position.The shared encoder avoids tying the model to a particular receiver index or geometry.Source: B. Distributed Semantic Encoding · p. 3
  • The position tag gives each latent its geometric meaning, and end-to-end set-distortion training optimizes it for emitter counting and localization rather than observation reconstruction.The received observations are noisy superpositions; emitter signal parameters remain nuisance variables.Source: A. Monitoring Scenario and Task · p. 2, B. Distributed Semantic Encoding · p. 3

C. Permutation-Invariant Fusion over Surviving Reports

The fusion node receives a channel-determined subset of reports rather than a fixed-length ordered vector. Set-based fusion handles reordering and missing reports while remaining defined for different receiver counts.

C. Permutation-Invariant Fusion over Surviving Reports

  • The decoder is permutation-invariant, so reordering the surviving reports does not change its output.The proposed rule treats the received collection as a set rather than a fixed-order vector.Source: C. Permutation-Invariant Fusion over… · p. 3
  • A lost report simply leaves the input set, matching contention-based and unreliable links that determine which receivers reach the fusion node.This is the central architectural choice for fusion over surviving reports.Source: C. Permutation-Invariant Fusion over… · p. 3
  • The decoder is defined for any surviving subset and can be evaluated with receiver counts different from the training count, unlike fixed-order concatenation.Fixed-order concatenation ties input dimension to a prescribed receiver count and index ordering.Source: C. Permutation-Invariant Fusion over… · p. 3

D. Finite-Rate Semantic Reporting

Receiver latents can be quantized for finite-rate reporting, while shared unreliable links may erase entire reports. The fusion node therefore works with the surviving position-tagged reports.

D. Finite-Rate Semantic Reporting

  • Each latent component is mapped to the unit interval, uniformly quantized to b bits, and mapped back; as b increases, this approaches full precision.The paper uses per-dimension affine min–max calibration.Source: D. Finite-Rate Semantic Reporting · p. 3
  • The semantic payload rate depends on latent dimension d and bit depth b; receiver positions are side information, and the rate study samples b during training.Erasure and fusion comparisons instead use full-precision latents.Source: D. Finite-Rate Semantic Reporting · p. 3

E. Contention-Based Access and Report Erasure

F. Access-Regime Interpretation

The access-regime interpretation relates report erasure to shared-link load while noting that the experiments do not reproduce correlated protocol collisions. The method trains on channel realizations, using shared receiver features and an objective over emitter-set distortion.

F. Access-Regime Interpretation

  • ϵ = 0.3 corresponds to G ≈ 0.36 and ϵ = 0.5 to G ≈ 0.69; both lie below the ALOHA throughput peak at G = 1.The independent-erasure experiments do not reproduce correlated collisions of a specific random-access protocol; ϵ = 0.9 is an overloaded stress test.Source: F. Access-Regime Interpretation · p. 4

G. Channel-Aware Task Objective

  • Training minimizes expected set distortion over random emitter scenes, receiver geometries, and reporting-link realizations; including H makes training channel-aware.The channel-naive baseline is the clean-link case with all reports delivered and full-precision latents.Source: G. Channel-Aware Task Objective · p. 4

IV. METHOD

  • The method encodes each local time-frequency feature, aggregates surviving position-tagged reports as a set, and matches predicted emitter slots to the true set through permutation-invariant distortion.The matching handles an unordered emitter set with variable cardinality.Source: §IV · p. 4

A. Receiver Feature and Shared Encoder

  • Each receiver’s complex baseband window becomes a time-frequency feature; a shared encoder maps that feature to a latent using the same parameters across receivers.The implementation uses a short-time Fourier transform with real and imaginary parts stacked as input channels.Source: A. Receiver Feature and Shared Encoder · pp. 4–5

B. Permutation-Invariant Set-Fusion Decoder

The decoder combines surviving receiver reports through attention pooling over a set, producing candidate emitter slots for count and location estimates.

B. Permutation-Invariant Set-Fusion Decoder

  • Each surviving latent is paired with its receiver’s normalized position, then embedded by a shared multilayer perceptron.The paired report is u_i = (z_i, r_i).Source: B. Permutation-Invariant Set-Fusion… · p. 5
  • Attention pooling aggregates the report embeddings over the surviving set, making the aggregation permutation-invariant; erased latents are excluded from attention weights.If no reports survive, the summary depends on receiver geometry alone; the normalized survivor count is appended to the summary.Source: B. Permutation-Invariant Set-Fusion… · p. 5
  • A final multilayer perceptron maps the pooled representation to Kmax candidate emitter slots, each with an existence logit and predicted location.Locations are normalized during training and converted back to meters for reporting.Source: B. Permutation-Invariant Set-Fusion… · p. 5

C. Permutation-Invariant Set Distortion

Predicted and true emitter slots are matched before set distortion is computed, and the same matching supports reported metrics. Channel-aware training samples erasures, while the fixed-order comparison is not parameter-matched.

C. Permutation-Invariant Set Distortion

  • The loss matches predicted slots to padded ground-truth slots, combining binary cross-entropy for existence with smooth-L1 localization loss gated by real-emitter labels.The optimal assignment is selected over slot permutations; Kmax = 3 makes exhaustive search sufficient in the experiments.Source: C. Permutation-Invariant Set Distortion · p. 5
  • The reported metrics use the same matching: cardinality accuracy and localization RMSE over matched active emitters.Source: C. Permutation-Invariant Set Distortion · p. 5

D. Channel-Aware Training and Baselines

  • Training samples surviving report sets according to the erasure model, realizing the objective’s expectation over channel realizations.The erasure probability is sampled up to ϵmax = 0.5; in the rate study, bit depth is also sampled and a straight-through estimator passes through the quantizer.Source: D. Channel-Aware Training and Baselines · p. 5
  • The fixed-order baseline uses the same encoder, positions, and erasure training as set fusion, but consumes reports in a receiver-count- and ordering-dependent input.The decoders are not parameter-matched: with M = 4 and d = 16, set fusion has 1.9×10^5 parameters versus 1.2×10^5 for fixed-order fusion.Source: D. Channel-Aware Training and Baselines · pp. 5–6

V. EXPERIMENTS AND RESULTS

The evaluation uses synthetic multi-emitter scenes with varied receiver positions, emitter properties, and overlapping spectra. It also describes the receiver observations, task metrics, propagation assumptions, and optional latent quantization.

A. Experimental Setup

  • Scenes contain 4 randomly positioned receivers and 1–3 emitters, with randomized bandwidth, frequency offset, power, and waveform family.Emitter spectra may overlap; the scene-generation description specifies a 40 MHz sampling rate and a 1000 × 1000 m receiver region.Source: A. Experimental Setup · p. 6
  • Each receiver supplies a 1 ms, 40 MHz complex baseband window; the shared encoder outputs a 16-dimensional latent, scored by cardinality accuracy and matched-emitter localization RMSE.The time-frequency feature uses a 256-sample Hann window with hop 160, producing 249 frames.Source: A. Experimental Setup · p. 6

B. Signal Generation and Quantizer

  • The synthetic propagation model uses power-law path loss and shared noise power, with no per-emitter random phase or propagation delay.Localization therefore uses received-power variation across known receiver positions, without time- or phase-difference cues.Source: B. Signal Generation and Quantizer · p. 6
  • Latent components can be uniformly quantized to 2^b levels, with b sampled from 2, 3, 4, 6, and 8 during rate-study training.The bounds are estimated from clean full-precision training latents; out-of-range values are clipped, and gradients use a straight-through estimator.Source: B. Signal Generation and Quantizer · p. 6

C. Architecture and Training

The set decoder pools surviving receiver reports, and the experiments compare channel-aware training with clean-link-only training. Channel-aware training preserves counting accuracy over a wider erasure range and improves localization once erasure is appreciable.

C. Architecture and Training

  • The set decoder embeds surviving reports, applies attention pooling, appends the normalized survivor count, and predicts up to three emitter slots.The receiver encoder is a residual convolutional network; the dataset contains 40,000 training, 4,000 validation, and 4,000 test scenes.Source: C. Architecture and Training · p. 6

D. Channel-Aware Co-Design

  • Channel-aware training preserves counting accuracy over a wider erasure range and yields lower localization error once report loss is appreciable.The channel-naive model performs well on clean links but degrades rapidly as reports are erased; channel-aware localization crosses over at low-to-moderate erasure and remains better thereafter.Source: Figure 3 · p. 7, D. Channel-Aware Co-Design · p. 7

C. Architecture and Training

  • The study uses synthetic propagation, at most three emitters, two waveform families, and identical receiver noise; more realistic propagation and denser scenes remain future work.Geometry-dependent receiver reliability is also left for future work.Source: C. Architecture and Training · pp. 6–7

D. Channel-Aware Co-Design

  • Channel-aware training samples report erasures uniformly from 0 to 0.5, while the channel-naive model trains only on clean links.Both models use the same shared encoder and permutation-invariant decoder and are evaluated under increasing erasure probability.Source: D. Channel-Aware Co-Design · p. 7

E. Set Fusion versus Fixed-Order Concatenation

Set fusion is more robust than fixed-order concatenation under report erasure. The same set-fusion model, trained at four receivers, can be deployed at different receiver counts without retraining, with performance varying by count.

E. Set Fusion versus Fixed-Order Concatenation

  • Across the erasure sweep, set fusion is more robust for cardinality estimation and has lower localization RMSE than fixed-order concatenation.Both models receive receiver positions and train with channel-aware erasure; the localization gap is largest in clean and moderate-erasure regimes and narrows at very high erasure.Source: Figure 4 · p. 7, E. Set Fusion versus Fixed-Order… · p. 7
  • Set fusion treats erased reports as absent set elements, whereas fixed-order concatenation retains an ordered, fixed-dimensional input built for constant membership.The models otherwise hold the encoder, inputs, training channel, and reporting budget fixed.Source: E. Set Fusion versus Fixed-Order… · p. 7

F. Deployment Across Receiver Counts

  • A model trained with M = 4 receivers is evaluated without retraining at M ∈ {2, 3, 4, 6}; fixed-order concatenation cannot accept counts other than four here.Its input dimension and index ordering are tied to the training receiver count.Source: F. Deployment Across Receiver Counts · p. 7, Figure 5 · p. 8
  • Localization improves as receiver count increases, both on clean links and under erasure, with diminishing returns beyond the training count.The improvement is especially clear when increasing from two to four receivers.Source: Figure 5 · p. 8, F. Deployment Across Receiver Counts · p. 8
  • Cardinality accuracy remains high across receiver counts but is best near the training configuration; performance is not identical across counts.The reported drops occur at M = 2 and, more mildly, at M = 6.Source: Figure 5 · p. 8, F. Deployment Across Receiver Counts · p. 8
  • The decoder supports adding, removing, or temporarily losing receivers by processing the surviving report set rather than requiring a fixed input format.Performance follows the spatial information available from the surviving receivers.Source: F. Deployment Across Receiver Counts · p. 8

G. Rate–Reliability

In the tested setting, reporting performance saturates at about four bits per latent component, while erasure changes the achievable performance level more than the rate knee. The discussion and conclusion connect low-rate reporting with channel-aware training and set fusion, while limiting the evaluation to specified synthetic conditions.

G. Rate–Reliability

  • Around 256 bits per window (four bits per component at M = 4, d = 16), performance saturates with little additional gain at higher rates.The study plots cardinality accuracy and localization RMSE against total reporting load.Source: Figure 6 · p. 8, G. Rate–Reliability · p. 8
  • The rate knee remains roughly stable across tested erasure levels, although erasure lowers cardinality accuracy and increases localization error.Beyond the knee, increasing bit depth does not recover missing receiver observations.Source: G. Rate–Reliability · p. 8
  • At four bits per component, semantic reporting uses 256 bits across four receivers versus 5.12 Mbit for forwarding raw I/Q samples.The comparison quantifies payload and does not establish equivalence with a centralized raw-I/Q receiver.Source: G. Rate–Reliability · p. 8

H. Discussion

  • Channel-aware training makes learned reports more useful under partial observation, whereas channel-naive models degrade quickly when reports are lost.The results frame semantic reporting as addressing limited reporting capacity and unreliable links.Source: H. Discussion · p. 8
  • Set fusion operates on the surviving reports and supports receiver counts different from the training count; increasing bit depth beyond the rate knee cannot restore missing spatial evidence.The discussion distinguishes quantization limits on each surviving report from erasure limits on available spatial evidence.Source: H. Discussion · p. 8

VI. CONCLUSION

  • The evaluation uses synthetic propagation, at most three emitters, two waveform families, identical receiver noise, and independent per-node erasures.The conclusion identifies denser scenes, more realistic propagation, correlated or geometry-dependent erasures, and spectral nuisance estimation as future work.Source: §VI · p. 9
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