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C$^2$T-OpenMax: A Novel Open-Set WiFi RF Fingerprinting Method via Center Constrained Learning and Confidence-Guided Tail Modeling
Yuanyu Zhang, Junjie Yang, Ji He, Shuangrui Zhao, Lele Zheng, Yulong Shen
TL;DR
Cross-environment open-set WiFi fingerprinting remains difficult because augmented representations can yield unreliable class statistics for OpenMax. C2T-OpenMax combines center-constrained learning with confidence-guided tail modeling, improving accuracy by 12.31 percentage points, AUROC by 0.0887, and OSCR by 0.0856 over the base model.
Problem
Cross-environment WiFi fingerprinting must recognize authorized devices reliably while detecting unknown devices despite channel variations and unreliable augmented class representations.
Method
C2T-OpenMax combines center-constrained learning for intra-class compactness with confidence-guided screening of correctly classified, high-confidence samples for MAV and Weibull tail modeling.
Results
12.31 percentage points, 0.0887 AUROC, and 0.0856 OSCR improvements over the base model demonstrate the strongest performance from combining both components.
Takeaways & Limitations
The two components have complementary roles: center loss changes feature geometry, while confidence screening refines the samples used for class-wise statistical modeling.
Takeaways & Limitations
Confidence screening is confined to offline OpenMax construction, while inference uses a separate rejection threshold.
Abstract
from arXiv · showhide
Radio frequency fingerprinting (RFF) enables device authentication from transmitter-specific hardware imperfections, but practical deployment requires cross-environment open-set recognition. Data augmentation improves environmental generalization, yet may yield dispersed, low-confidence known-class representations that distort the class statistics used by OpenMax. To address this problem, we propose C$^2$T-OpenMax, an enhanced OpenMax framework combining center-constrained learning with confidence-guided tail modeling. The former improves intra-class compactness, making class-wise representations more suitable for distance-based modeling. The latter retains only correctly classified, high-confidence logits for mean activation vector estimation and Weibull fitting, reducing bias from ambiguous boundary samples. Together, the two modules refine representation geometry and OpenMax construction while preserving augmentation benefits. Experiments on a public WiFi CSI dataset show that C$^2$T-OpenMax achieves the highest open-set accuracy in seven of eight location groups and outperforms all baselines in area under the receiver operating characteristic curve (AUROC) and open-set classification rate (OSCR) across every tested openness level. Under the largest-openness setting, it improves accuracy by 12.31%, AUROC by 0.0887, and OSCR by 0.0856 over the augmented OpenMax baseline.
Introduction
The introduction motivates open-set WiFi RFF recognition under changing environments, where augmentation can produce dispersed, low-confidence known-class representations that undermine OpenMax modeling. It proposes C2T-OpenMax, combining center-constrained learning with confidence-guided tail modeling to improve class compactness and construct more representative OpenMax statistics.
- Motivation: Open-set recognition must identify authorized devices across changing environments while detecting unknown devices, because channel changes can resemble device differences.An unknown device may be incorrectly accepted as authorized, while an authorized device may be misclassified or rejected.
- Motivation: Data augmentation improves environmental generalization but can generate correctly classified, low-confidence samples that distort known-class modeling.Such samples may enlarge acceptance regions, increase inter-device confusion, and shift class representations away from typical patterns.
- Proposed method: C2T-OpenMax combines center-constrained learning with confidence-guided tail modeling to address unreliable OpenMax construction.Center-constrained learning improves within-class compactness, while confidence-guided tail modeling uses correctly classified, high-confidence samples for mean activation vectors and Weibull tail distributions.
- Contributions: The introduction identifies low-confidence correctly classified samples as a source of unreliable known-class modeling and proposes screening them during OpenMax construction.The stated contributions analyze augmented WiFi RFF with OpenMax and introduce both center-constrained learning and confidence-guided tail modeling.
Related Work
Prior RFF research has improved channel robustness and closed-set recognition, while OSR studies have focused mainly on unknown rejection. This work instead highlights the underexplored reliability of augmented known-class activation vectors used to construct OpenMax statistical models.
- RFF and channel robustness: CSI-based RFF uses fine-grained amplitude and phase responses, but environmental channel effects make models sensitive to location, multipath, noise, and acquisition conditions.Existing methods address these variations through feature purification, augmentation, auxiliary objectives, or contrastive learning.
- Open-set recognition: OSR approaches mainly use confidence scoring, distribution modeling, reconstruction, or discriminative boundary learning to reject previously unseen classes.Reconstruction methods use mismatch with known-class patterns, whereas boundary-based methods separate known classes from open space.
- RFF-oriented OSR: Existing RFF-oriented OSR studies primarily improve unknownness scores, decision boundaries, nuisance-feature suppression, or inference-time adaptation.The passage contrasts these directions with examining correctly classified training activation vectors used to estimate OpenMax MAVs and Weibull tails.
- Research gap: Augmentation broadens channel variation exposure and improves cross-environment generalization, but augmented correctly classified samples can differ in confidence and representativeness of known-class structure.These differences matter when activation vectors estimate class MAVs and upper-tail distributions, even if they have limited effect on closed-set decisions.
- Research gap: The intersection of representation robustness and known-sample reliability for tail-distribution modeling remains less explored.The work addresses this gap through representation-level compactness optimization and confidence-guided refinement of OpenMax construction samples.
Problem Formulation and Motivation
The paper formulates WiFi radio-frequency fingerprinting as an open-set task involving known and previously unseen devices. It motivates C^2T-OpenMax by identifying representation dispersion and unreliable correctly classified samples as challenges for OpenMax statistical modeling.
- Open-Set WiFi RFF Setting: At test time, CSI samples belong either to known-device labels YK or disjoint unseen-device labels YU, with unknown output required for unseen devices.OpenMax excludes unseen samples from MAV estimation, Weibull fitting, and model construction.
- Tail-Modeling Challenge: OpenMax models each known class using correctly classified training logits and fits a Weibull distribution to upper-tail distances from the class mean logit vector.Correct classification is defined by the predicted class maximizing p(j | x).
- Tail-Modeling Challenge: Correctly classified samples may still have low confidence, lie near decision boundaries, or poorly represent the class core.These limitations arise because correct classification only requires the ground-truth class to receive the largest prediction score.
- Tail-Modeling Challenge: Including ambiguous correctly classified samples can shift the class mean away from representative high-confidence samples and distort OpenMax construction.The supplied passage identifies these effects as consequences of treating all correctly classified samples as equally reliable.
- Tail-Modeling Challenge: Confidence screening defines Sk = {x ∈ Ck | p(k | x) > δ}, retaining correctly classified samples whose class confidence exceeds threshold δ.The screened subset satisfies Sk ⊆ Ck.
- Tail-Modeling Challenge: Screening refines the samples used to summarize augmented known-class representations during offline OpenMax construction without removing samples from closed-set training.It does not question the benefit of augmentation.
- Design Objectives: A reliable open-set extension requires compact known-device representations and reliable class representatives for MAV estimation and upper-tail distance modeling.Center-constrained learning changes feature geometry, whereas confidence screening changes only the subset used for MAV estimation and Weibull fitting.
Method
C2T-OpenMax retains DeepCRF’s augmentation and Stage I supervised contrastive learning, adds center loss in Stage II, and applies confidence screening during offline OpenMax construction. These components compact known-device representations and refine the samples used for MAV estimation and Weibull tail fitting.
- Representation learning: C2T-OpenMax keeps channel-oriented augmentation and Stage I supervised contrastive learning from DeepCRF, introducing center loss during joint Stage II optimization.The Stage II objective combines cross-entropy and center loss as Lhybrid = Lce + λLcenter.
- Representation learning: Center loss reduces within-class variation and promotes compact class-wise logit distributions, stabilizing MAV estimation and distance-based tail modeling.Its effect propagates from intermediate features to the classifier outputs used by OpenMax.
- Offline OpenMax construction: Confidence screening retains correctly classified samples whose ground-truth class probability exceeds δ, without altering closed-set training or the trained feature extractor.The screened subset is used only for offline OpenMax construction.
- Offline OpenMax construction: The retained logits determine each class’s MAV, mixed Euclidean–cosine distances, and upper-distance tail for class-specific Weibull fitting.Distances are sorted in descending order, and the largest proportion r forms the tail set; the implementation uses δ = 0.8 and r = 0.05.
- OpenMax inference: At inference, Weibull outlier weights discount known-class scores and transfer removed score mass to the unknown class, with rejection controlled by γ selected on known-device validation data.γ is chosen according to classification accuracy without using unknown-device samples.
Experiments
Experiments evaluate C2T-OpenMax across locations, openness levels, and component ablations using open-set accuracy, AUROC, and OSCR. The method consistently improves recognition and unknown-device separability, with complementary gains from center-constrained learning and confidence-guided sample screening.
- Cross-location evaluation: C2T-OpenMax achieves the best open-set accuracy at seven of eight location groups and outperforms original OpenMax across all locations.At P1–P2, accuracy rises from 85.90% to 95.70%.
- Cross-location evaluation: 21.08 and 18.34 percentage points are the gains over original OpenMax at P5 and P8, respectively.Improvements are also observed at P6, P7, and P9 under substantial channel variations.
- Openness evaluation: C2T-OpenMax achieves higher AUROC and OSCR than all compared methods across every reported openness setting.Performance generally decreases or fluctuates as unknown devices increase from 1 to 7, because unknown devices differ in similarity to known classes.
- Ablation study: 12.31 percentage points, 0.0887, and 0.0856 are the improvements in accuracy, AUROC, and OSCR over the base model when both components are combined.The ablation uses 12 known and 7 unknown devices, with test samples from all locations combined.
- Ablation study: Confidence-guided sample screening alone increases accuracy by 7.13 percentage points, AUROC by 0.0733, and OSCR by 0.0740.Center-constrained learning alone increases accuracy from 83.60% to 88.25%, while confidence screening refines the samples used for MAV estimation and Weibull fitting.
Conclusion
C2T-OpenMax extends an augmented closed-set WiFi RFF model to open-set recognition by combining center-constrained learning with confidence-guided tail modeling. Experiments across locations, openness settings, ablations, and fitting-sample visualizations demonstrate complementary effects from the two components.
- Conclusion: C2T-OpenMax combines center-constrained learning and confidence-guided tail modeling to extend augmented closed-set WiFi RFF models to open-set recognition.Center-constrained learning improves intra-class compactness, while confidence-guided tail modeling refines logits for MAV estimation and Weibull tail fitting.
- Conclusion: Center-constrained learning improves intra-class compactness, and confidence-guided tail modeling refines training logits used for MAV estimation and Weibull tail fitting.
- Conclusion: Experiments across locations, openness settings, ablations, and fitting-sample visualizations demonstrate the two components’ complementary effects.