PaperlayerView exact revision on arXiv

Source-linked AI summary

Digital Twin-Conditioned RSS-Fingerprint Localization in Cell-Free Millimeter-Wave Networks

Varun S. Advani, Khalid Kanaan, Ahmed Nasser, Mohamed Y. Selim, Ahmed M. Eltawil

arXiv:2610.20933v1cs.NIeess.SP

TL;DR

Dense synthetic DT fingerprints could reduce the costly physical measurement burden, but the sim-to-real gap limits their direct use for cell-free mmWave localization. DTCond fuses real and DT fingerprints as complementary inputs, and on a real 28 GHz testbed its deployable pipeline improves mean error over real-only k-NN while oracle input yields a lower error.

  • Problem

    Ray-traced DT fingerprints can be generated densely, but a persistent sim-to-real gap limits their direct use for cell-free mmWave localization.

    Source: §I · p. 1

  • Method

    DTCond processes real and DT beam-domain fingerprints through separate encoders and learnable AP attention, outputting position estimates with calibrated uncertainty.

    Source: §I · p. 1

  • Results

    0.284 m mean error for the deployable pipeline versus 0.313 m for real-only k-NN, and 0.186 m mean error with oracle DT input.

    Source: §I · p. 2

  • Takeaways & Limitations

    DT conditioning can use the twin as a complementary localization input, with the paper reporting tighter positioning bounds when DT spatial structure is preserved.

    Source: §I · pp. 1–2

    Experiments cover a single indoor environment with 3 APs, 13 trajectories, and a 28 GHz carrier.

    Source: K. Discussion and Design Insights · p. 15

Abstract

from arXiv · show

Digital twins (DTs) can generate dense synthetic fingerprints for localization via ray tracing, yet the sim-to-real domain gap limits their direct use, particularly in cell-free millimeter-wave (mmWave) deployments where distributed geometries and blockage-induced sparsity widen the mismatch. We propose DT-conditioned (DTCond), a framework that fuses real and DT beam-domain fingerprints as complementary inputs through per-domain encoders, learnable per-access point (AP) attention, and calibrated uncertainty. We derive oracle and pipeline Cram\'er-Rao bounds (CRBs) for DT-aided fingerprint localization, proving that DT information strictly tightens the positioning bound whenever spatial structure is preserved, with a heteroscedastic refinement that tightens the bound by a further 9.1%. On a real 28 GHz cell-free testbed, the deployable two-stage pipeline, which reads the DT fingerprint at a coarse k-nearest neighbor (k-NN) estimate, achieves 0.284 m mean error against 0.313 m for real-only k-NN. With the DT fingerprint read at the true position (oracle input), DT conditioning achieves 0.186 m mean error, validated through a ten-method ablation against domain-adaptation (DA) and transfer-learning baselines, and a 48% improvement on unseen regions. Multi-user self-attention provides 31-41% per-user gain for emulated simultaneous users, and progressive calibration reduces the measurement budget by 50%. As a use case, localization drives network configuration in closed loop. Between beam sweeps, a DT updated from measured RSS and read at the tracked position estimate selects the 3 of 81 beam pairs that each AP trains. With 49 calibration anchors in the update, the mean beam-selection loss stays below 1 dB over 2 m of motion, whereas reusing the last sweep loses 2.7 dB after 1 m.

I. INTRODUCTION

Cell-free mmWave localization can exploit distributed AP fingerprints, but dense physical fingerprint collection is costly and ray-traced DT fingerprints face a substantial sim-to-real gap. DTCond treats real and DT fingerprints as complementary inputs; the paper develops bounds, localization methods, and closed-loop uses around this design.

B. Localization in Cell-Free and mmWave Systems

  • Fingerprint localization uses RSS-only beam-domain patterns to map positions and exploits spatial diversity across distributed APs without inter-AP time synchronization or phase coherence.Building a physical fingerprint database is costly because measurement requirements scale with service-area size and AP count.Source: §I · p. 1, A. Cell-Free mmWave Network Model · p. 4

A. Digital Twins for Wireless Networks

  • Ray tracing can generate dense synthetic fingerprints without physical data collection, but imperfect environment models, unmodeled scattering, and hardware differences create a domain gap that makes direct simulated-data deployment unreliable.Prior DT-aided localization has used twins as replacement databases, training sources, or positional references.Source: §I · p. 1, A. Digital Twins for Wireless Networks · p. 3

I. INTRODUCTION

  • DTCond fuses real and DT fingerprints through separate domain encoders and learnable AP attention, producing position estimates and calibrated uncertainty.The framework treats DT fingerprints as complementary conditioning inputs, not as pre-training data or a domain-alignment target.Source: §I · pp. 1–2
  • DT information strictly tightens the positioning bound when spatial structure is preserved, while the heteroscedastic refinement further tightens the oracle bound where local per-AP domain-gap variance is below its pooled value.DT information is most valuable along weak real-only Fisher-information eigendirections, motivating per-AP attention.Source: §I · p. 2
  • 0.284 m mean error for the deployable two-stage pipeline versus 0.313 m for real-only k-NN; oracle-input DT conditioning reaches 0.186 m mean error.The pipeline reads the DT fingerprint at a coarse real-only k-NN estimate; the oracle reads it at the true position.Source: §I · p. 2
  • 31–41% reduction in mean per-user error over the single-user baseline for emulated simultaneous users using DT-mediated cross-user self-attention.The DT supplies shared spatial context that enables cross-user information exchange regardless of physical inter-user distance.Source: §I · p. 2
  • The twin-in-the-loop calibration strategy uses spatially diverse measurements to halve the real-measurement budget, and tracked position estimates support DT-driven network configuration between beam sweeps.The DT selects the 3 of 81 beam pairs each AP trains; with 49 calibration anchors, beam-selection loss stays below 1 dB over 2 m of motion, versus 2.7 dB after 1 m when reusing the last sweep.Source: §I · p. 2, Figure 1 · p. 3

C. DA for Wireless Systems

  • Standard domain-adaptation methods assume structurally similar domains with a distributional shift, whereas real measurements and deterministic ray tracing arise from different observation processes.The paper states that forcing distributional alignment removes spatial structure contributed by the DT.Source: C. DA for Wireless Systems · p. 3

B. Digital Twin Model and Domain Gap

The DT produces deterministic beam-domain fingerprints at arbitrary spatial density, while real fingerprints differ through a spatially varying domain gap and measurement noise. The paper distinguishes absolute fingerprint mismatch from preservation of spatial variation, which determines whether DT fingerprints retain positioning information.

B. Digital Twin Model and Domain Gap

  • DT fingerprints are deterministic and can be generated at arbitrary spatial density without physical measurements.The ray-tracing DT produces a beam-domain fingerprint for each position and AP.Source: B. Digital Twin Model and Domain Gap · p. 4
  • Real fingerprints decompose in dBm as the DT fingerprint plus a position- and AP-dependent domain gap and measurement noise.The gap captures systematic differences from material-property errors, unmodeled scattering, and hardware imperfections; its Gaussian noise approximation is empirically validated.Source: B. Digital Twin Model and Domain Gap · p. 4
  • A large absolute domain gap does not rule out useful spatial structure: the DT's fingerprint gradient can correlate with the real gradient even when absolute power differs substantially.The spatial mean gap biases absolute power but has zero spatial derivative; the paper illustrates this distinction with measured and DT beam patterns.Source: B. Digital Twin Model and Domain Gap · p. 4, Figure 2 · p. 5
  • A DT with near-zero spatial gradient provides no positioning benefit regardless of calibration, whereas large systematic bias can still leave substantial information when spatial variation is rich.The analysis therefore motivates exploiting spatial structure rather than absolute power.Source: B. Digital Twin Model and Domain Gap · p. 4
  • The gradient-preservation condition bounds alignment between the DT and noise-free real Jacobians when the gap-gradient norm is smaller than the DT-gradient norm.The examples contrast small-gradient cable, path-loss, and reflection errors with an unmodeled blocker whose shadow edge can violate the condition.Source: B. Digital Twin Model and Domain Gap · pp. 4–5

C. Problem Formulation

The CRB analysis formalizes how spatially varying DT fingerprints add localization information and how retrieval mismatch affects that benefit. It also motivates position-dependent AP weighting and per-AP uncertainty modeling.

C. Problem Formulation

  • The problem formulation maps paired real and DT fingerprints to a two-dimensional position estimate and per-coordinate uncertainty.Inference applies the learned function to new fingerprint pairs, including positions absent from the training set.Source: C. Problem Formulation · p. 5
  • The observation model treats real measurements as the DT fingerprint plus a spatially varying domain gap and independent measurement noise.The DT fingerprint is an auxiliary observation with effective noise variance representing the real–DT discrepancy; the formulation identifies separate-domain statistics and a limited measurement budget as challenges.Source: §IV · p. 5, C. Problem Formulation · p. 5

IV. CRAM´ER–RAO BOUND FOR DT-AIDED LOCALIZATION

  • The oracle CRB is no greater than the real-only CRB, and is strictly lower whenever the DT fingerprint varies spatially.The result assumes the real-only Fisher information matrix is positive definite.Source: §IV · p. 6
  • 73% of the DT’s CRB reduction on the testbed comes from the weak eigendirection of the real-only Fisher information matrix.This directional complementarity motivates position-dependent AP weighting.Source: §IV · p. 6
  • The per-AP marginal DT utility score measures each AP’s contribution to oracle CRB reduction, weighted by the real-only information geometry.Learned AP attention is designed as a data-driven proxy for this score; geometrically diverse APs can contribute even with low absolute DT fidelity.Source: §IV · p. 6
  • The DT is most valuable when real measurement noise is large relative to the domain gap, with improvement also depending on Jacobian alignment.The alignment factor is estimated from finite data and compared with measured CRB reduction.Source: §IV · p. 6
  • The mean heteroscedastic CRB is 0.162 m, 9.1% tighter than the uniform bound of 0.178 m.The heteroscedastic bound is tighter at 97.1% of test positions; per-AP precision weights can approach it where the stated condition holds.Source: §IV · p. 7
  • The pipeline CRB models retrieval mismatch by treating the DT fingerprint as read at a coarse estimated position rather than the true position.The model assumes independent Gaussian retrieval error and uses a first-order Taylor approximation of the DT fingerprint.Source: §IV · p. 7

which satisfies the sandwich inequality

The pipeline bound accounts for error in the coarse position used to retrieve the DT fingerprint. Its position between the oracle and real-only bounds quantifies the cost of that mismatch.

which satisfies the sandwich inequality

  • The pipeline CRB lies between the oracle CRB and the real-only CRB, even when the DT fingerprint is retrieved at a coarse estimate.The bound approaches the oracle when the coarse estimate is accurate or the DT varies slowly, and approaches the real-only bound when retrieval mismatch dominates the domain gap.Source: which satisfies the sandwich inequality · p. 7
  • Increasing coarse-stage error cannot lower the pipeline bound, while zero retrieval error gives the oracle bound and unbounded error approaches the real-only bound.These relationships follow from the retrieval-mismatch model.Source: which satisfies the sandwich inequality · p. 7
  • The ratio of retrieval-mismatch effects to domain-gap effects diagnoses whether improving the coarse stage or the DT is the more useful target.When the ratio is small, the pipeline approaches oracle performance; when large, improving the coarse stage yields higher returns than improving the DT.Source: which satisfies the sandwich inequality · p. 7
  • A sparser coarse-stage site survey enlarges retrieval error covariance and does not lower the pipeline bound.The standard CRB assumes Gaussian observation noise; the paper reports that mild departures from Gaussianity do not materially affect the bound.Source: which satisfies the sandwich inequality · p. 7

V. DT-CONDITIONED LOCALIZATION FRAMEWORK

DTCond preserves the distinct statistical characteristics of real and DT fingerprints while using DT spatial structure as complementary localization information.

V. DT-CONDITIONED LOCALIZATION FRAMEWORK

  • DTCond processes real and DT fingerprints through separate encoders, fuses them with learnable AP attention, and outputs position estimates with learned uncertainty.The design is motivated by CRB analysis of DT information through spatial structure rather than absolute accuracy.Source: §V · p. 7

A. Data Preprocessing Pipeline

The preprocessing pipeline converts power measurements to dBm, balances AP contributions, and normalizes the real and DT domains separately.

A. Data Preprocessing Pipeline

  • Raw linear power measurements are converted to dBm using 10 log10(max(P, ϵ)), with ϵ > 0 preventing a logarithmic singularity.The architecture caption identifies per-domain encoders, DT-driven AP attention, and heteroscedastic position output.Source: A. Data Preprocessing Pipeline · p. 7, Figure 3 · p. 8
  • Per-AP offsets balance which AP supplies the strongest beam pair across positions, preventing a proximate AP from masking spatial information from more distant APs.The reported strongest-pair shares change from 6.2%, 88.0%, and 5.7% to 32.3%, 34.9%, and 32.8% for APs 1–3.Source: A. Data Preprocessing Pipeline · p. 7
  • Each domain is z-score normalized using its own per-AP statistics; sharing statistics degrades accuracy because the DT’s different dynamic range distorts real-signal statistics.The offsets and normalization statistics use fingerprints without position labels.Source: A. Data Preprocessing Pipeline · p. 7

B. Per-Domain Encoders

DTCond encodes real and DT fingerprints separately, weights AP contributions from the DT input, and predicts position with spatially varying uncertainty. Its two-stage training first stabilizes position estimates, then calibrates uncertainty.

B. Per-Domain Encoders

  • Separate per-domain encoders produce compact representations of each AP’s normalized real and DT fingerprints, sharing encoder weights across APs but not across domains.Sharing across APs reduces encoder sets from O(M) to O(1), while domain separation accommodates their different distributional characteristics.Source: B. Per-Domain Encoders · p. 8

C. Learnable AP Attention

  • Position-dependent AP attention weights are computed exclusively from DT fingerprints, allowing the model to learn which APs are informative in each region.This also permits attention computation where real measurements are unavailable during progressive calibration.Source: C. Learnable AP Attention · p. 8

D. Fusion and Heteroscedastic Uncertainty

  • The fusion network combines real- and DT-domain features to predict position and per-coordinate uncertainty that varies with location.The predicted uncertainty is smaller in well-covered regions and larger in undersampled or ambiguous areas.Source: D. Fusion and Heteroscedastic… · p. 8

E. Two-Stage Training

  • Two-stage training establishes position estimates with an MSE warmup before heteroscedastic NLL jointly refines position accuracy and calibrates uncertainty.The sequence prevents uncertainty collapse and lets the uncertainty head learn spatially varying confidence correlated with actual error.Source: E. Two-Stage Training · p. 9

F. Multi-User Localization via Self-Attention

The method extends DTCond to jointly localize users through self-attention over DT-mediated features, and deploys it with coarse-to-refined inference and progressive real-data calibration. Calibration measurements are selected for spatial coverage.

F. Multi-User Localization via Self-Attention

  • For simultaneous users, scaled dot-product self-attention exchanges spatial context between DT-mediated user features while residual connections preserve each user’s individual information.The evaluation emulates user groups from single-user measurements because copresent users affect one another’s mean fingerprint only through mutual blockage.Source: F. Multi-User Localization via… · p. 9

G. Inference Procedure

  • Deployment first estimates position with real-fingerprint k-NN, then queries the DT at that estimate and refines position and uncertainty with DTCond.Training also substitutes nearby DT-grid fingerprints to improve robustness to coarse-estimate perturbations.Source: G. Inference Procedure · p. 9

A. Calibration Framework

  • Twin-in-the-loop calibration combines dense DT coverage with surveyed real-measurement anchors, with localization error decreasing as the calibration set grows.The calibration anchors provide measured fingerprints and known ground-truth positions.Source: A. Calibration Framework · p. 9

B. Progressive Data Collection

  • Progressive calibration varies the available real training data from 5% to 100%, recomputing normalization statistics and retraining DTCond while keeping the DT available.Evaluation uses a fixed test set; only real measurements are limited.Source: B. Progressive Data Collection · p. 9

C. Spatially Diverse Measurement Selection

  • With a fixed calibration-measurement budget, the method selects positions by a maximin criterion that maximizes spatial coverage.The evaluation compares this spatially diverse selection with random and uncertainty-guided position selection.Source: C. Spatially Diverse Measurement… · p. 10

D. Localization-Driven Network Configuration

Localization estimates and RSS measurements drive closed-loop network configuration between full beam sweeps. The DT is updated from reports, and the resulting beam-selection loss is tied to both DT and localization error.

D. Localization-Driven Network Configuration

  • The uncorrected ray-traced DT ranks the strongest measured beam pair first at only 27.5% of positions, so configuration uses the updated DT read at the tracked estimate.Each AP trains only its candidate beam pairs until the next full sweep, and the serving AP uses its strongest trained pair.Source: D. Localization-Driven Network… · p. 10
  • The DT update uses LMMSE estimation, or Gaussian-process regression, from calibration anchors and localized measurement reports, with localization uncertainty down-weighting each report.With fixed positive observation variances, adding observations makes the model-predicted DT mean-square error non-increasing at every grid node.Source: D. Localization-Driven Network… · p. 10
  • The beam-selection loss bound connects DT error and localization error, with accurate localization reducing the localization-error contribution.The twin update never increases the model-predicted bound over the grid.Source: D. Localization-Driven Network… · p. 10

VII. EXPERIMENTAL EVALUATION

The evaluation uses a real indoor 28 GHz cell-free testbed and a ray-tracing DT, with real and synthetic fingerprints collected at matched positions. It assesses the domain gap and compares DTCond with non-parametric, neural, and domain-adaptation baselines.

A. Measurement Campaign and Dataset

  • The testbed has three distributed APs, each using 81 beam pairs, and covers a trapezoid approximately 9.6 m deep.The dataset includes 1,400 positions on 13 walking trajectories, with 20 repeated beam-domain measurements per position; the DT fingerprints are generated at the same positions.Source: A. Measurement Campaign and Dataset · pp. 10–11, Figure 4 · p. 11
  • Per-AP Pearson correlations between real and DT fingerprints are 0.17, 0.34, and 0.33, indicating a substantial domain gap.The effective DT domain gap variance is 0.932 dB^2, and its ratio to per-snapshot measurement noise is 2.73.Source: A. Measurement Campaign and Dataset · p. 11

B. Baselines and Metrics

  • The comparison includes real-only, DT-only, and concatenated-fingerprint k-NN baselines, neural baselines, and three domain-adaptation methods, using mean Euclidean error on a 280-position test set.The reported metrics also include median error, P90, and standard deviation across five random seeds for neural methods.Source: B. Baselines and Metrics · p. 11

C. Localization Accuracy Comparison

DT conditioning improves localization accuracy over real-only baselines, while CRB analyses quantify the benefit and limits of DT information. The results also validate tighter heteroscedastic bounds and examine pipeline retrieval mismatch.

C. Localization Accuracy Comparison

  • 0.186 ± 0.014 m: DTCond’s mean error is below 0.313 m for k-NN Real in the ten-method ablation.The ablation reports the mean and standard deviation across five seeds.Source: C. Localization Accuracy Comparison · p. 11, Figure 5 · p. 12
  • 12%: DTCond improves over NN Concat on the split, with a statistically significant difference (p-value = 0.022).The comparison holds with the same inputs; DTCond adds per-AP attention.Source: C. Localization Accuracy Comparison · p. 12
  • DANN, CORAL, and MMD reach 0.431 ± 0.023 m, 0.418 ± 0.038 m, and 0.418 ± 0.021 m, respectively, worse than k-NN Real.The reported paired tests find these DA baselines worse than k-NN Real (p-value < 0.01).Source: C. Localization Accuracy Comparison · p. 12
  • 0.284 m: the deployable pipeline’s mean error compares with 0.313 m for k-NN Real and 0.345 m for the same pipeline without augmentation.The gap from the nonaugmented oracle (0.186 m) is attributed to augmentation cost and retrieval mismatch.Source: C. Localization Accuracy Comparison · p. 12

D. CRB Validation

  • 0.178 m: the mean oracle joint CRB is 34.9% lower than the 0.274 m real-only CRB.The reduction varies by less than ±1.5% across the tested Jacobian-estimation neighborhood sizes.Source: Table IV · p. 12, D. CRB Validation · p. 12
  • The misspecified CRB changes the joint improvement over the Gaussian CRB by only 0.3 percentage points despite a rejection of exact Gaussianity.The reported departures are mild: skewness < 0.21 and excess kurtosis ≈ −0.2.Source: D. CRB Validation · p. 12
  • 0.162 m: allowing per-AP gap variance tightens the bound by 9.1% over the uniform bound, and it is tighter at 97.1% of test positions.Fig. 6 presents the per-position comparison.Source: D. CRB Validation · p. 12, Figure 6 · p. 12
  • Per-AP Jacobian cosine similarities of 0.52–0.63 exceed the 0.17–0.34 Pearson correlations; AP 1 has highest DT utility at 19% of positions despite lowest fidelity.AP 1’s Jacobian complements those of APs 2–3 along a weak real-only FIM eigendirection.Source: D. CRB Validation · p. 13

E. Spatial Generalization

DTCond generalizes to held-out trajectories and remains effective under tested DT imperfections and emulated blockage. Calibration, closed-loop beam selection, and emulated multi-user evaluations explore its performance across deployment conditions.

F. Robustness to DT Imperfections and Emulated Blockage

  • Across re-traced DTs, DTCond errors remain 0.169–0.245 m; blockage-aware training reaches 0.205 m under the emulated blockage condition.Without blockage-aware training, DTCond error grows from 0.186 to 0.280 m when the DT does not model the blocker.Source: F. Robustness to DT Imperfections and… · p. 13

E. Spatial Generalization

  • 0.257 ± 0.119 m: DTCond’s mean error on held-out walking lines is a 48% improvement over 0.495 m for k-NN Real.LOLO evaluation trains on 12 lines and tests on the remaining line across 13 folds; DTCond also has the lowest cross-line standard deviation.Source: Figure 7 · p. 13, E. Spatial Generalization · p. 13

G. Progressive Calibration and Data Efficiency

  • 0.226 ± 0.019 m: DTCond with 50% of real training data outperforms k-NN Real with 100% by 28%.The authors report this as effectively halving the measurement budget.Source: G. Progressive Calibration and Data… · p. 13
  • Below 20% data, NN Concat outperforms DTCond; at 5%, their errors are 0.69 m and 0.919 m, respectively.The learnable AP attention mechanism requires at least 20% spatial coverage to learn meaningful per-AP weights.Source: G. Progressive Calibration and Data… · p. 14
  • At a 25% budget, spatially diverse selection achieves 0.293 m versus 0.350 m for random selection and 0.593 m for uncertainty-guided selection.The reported advantage grows at smaller budgets.Source: G. Progressive Calibration and Data… · p. 14

H. Closed-Loop Localization-Driven Configuration

  • With 49 anchors, tracked DT selection stays at 0.93–0.98 dB through 2.0 m of motion, while reusing the last sweep loses 2.74 dB after 0.98 m.For a 1 dB target, the last sweep must be repeated every 0.38 m; tracked DT selection with 49 anchors needs at least five times fewer full sweeps.Source: H. Closed-Loop Localization-Driven… · p. 14
  • With 977 anchors, mean localization errors below 0.47 m keep beam-selection loss below 1 dB; feedback from 98 anchors lowers loss from 1.48 to 1.32 dB.At the sweep position, DT loses 1.8 dB with 10 anchors versus 3.0 dB for d0.Source: H. Closed-Loop Localization-Driven… · p. 14

I. Multi-User Localization (Emulated Users)

  • Cross-user self-attention reaches 0.160 m at Ku = 2, 0.141 m at Ku = 3, and 0.138 m at Ku = 4; the reported gains are 31–40.5%.The DT raises the multi-user benefit 1.8-fold at Ku = 2 and 2.5-fold at Ku = 3; gains span 26–36% across inter-user distance bins.Source: §I · pp. 14–15

J. Trajectory Quality

DTCond achieves the lowest reported trajectory path error and smoothest trajectories, alongside fast inference and uncertainty that tracks prediction difficulty. The conclusion reports improved localization with deployable and oracle-input pipelines, fewer calibration measurements, and low-loss beam configuration between sweeps.

J. Trajectory Quality

K. Discussion and Design Insights

VIII. CONCLUSION

  • Progressive calibration reduces measurements by 50%, while re-traced DTs keep DTCond within 0.169–0.245 m; between beam sweeps, tracked-position configuration holds beam-selection loss below 1 dB over 2 m with 49 anchors.Source: §VIII · p. 16
  • Between beam sweeps, configuration driven by the tracked position estimate keeps beam-selection loss below 1 dB over 2 m of motion, with 49 anchors in the update.Source: §VIII · p. 16

Related papers

Loading 2610.20933v1…