Embedding Space

All feature vectors extracted from the same physical transmitter must cluster tightly together in the embedding space, regardless of minor variations in transmission content, temperature, or channel conditions.

• Minimizes the False Rejection Rate (FRR) by ensuring legitimate variations in a device's signal do not push its embedding outside the acceptance boundary
• Achieved through contrastive loss functions that explicitly penalize distance between samples from the same emitter
• Example: A transmitter's vectors should remain within a tight hypersphere even as its power amplifier warms up over a 30-minute transmission session

Embeddings from different transmitters must be pushed far apart in the vector space, creating clear decision boundaries between device identities.

• Maximizes the margin between clusters to reduce the False Acceptance Rate (FAR)
• Triplet loss and arcface loss are commonly used to enforce angular separation between classes
• Critical for distinguishing devices from the same manufacturer batch that share nearly identical hardware impairment profiles
• Example: Two identical-model SDRs should map to well-separated regions despite having only subtle I/Q imbalance differences

The embedding must remain stable across varying multipath environments and propagation conditions. A device's vector representation should be determined by its hardware impairments, not the room it is transmitting in.

• Domain adversarial training forces the encoder network to strip channel-specific information from the embedding
• Data augmentation with simulated channel models (Rayleigh, Rician fading) during training improves robustness
• Example: A transmitter moved from an anechoic chamber to a reflective warehouse should produce a nearly identical embedding

The embedding space must encode not only known device identities but also a notion of 'unknownness.' Vectors from emitters never seen during training should fall into low-density regions far from all enrolled clusters.

• Enables open set recognition where the system can confidently reject unauthorized or novel transmitters
• Techniques include angular margin penalties that force known classes into tight, non-overlapping cones, leaving the remainder of the hypersphere for unknowns
• Example: A rogue transmitter attempting to spoof a known device will produce an embedding in an unpopulated region, triggering an anomaly alert

The geometric relationships between vectors should reflect meaningful hardware similarities. Devices with similar impairment profiles (e.g., same oscillator type) should be closer than devices with fundamentally different architectures.

• Allows for zero-shot generalization where a new device from a known hardware family can be authenticated without explicit enrollment
• Hierarchical embedding structures can encode manufacturer, model, and individual device identity at different scales
• Example: Two transmitters using the same Texas Instruments DAC should share a region of the space distinct from Analog Devices-based transmitters

The embedding must accommodate the slow, inevitable drift of analog components due to aging and thermal cycling while still distinguishing this natural variation from a true device change.

• Kalman filter-based embedding trackers maintain a moving baseline that follows legitimate drift
• Exponential moving average updates to the enrollment centroid prevent catastrophic authentication failures as hardware ages
• Example: A transmitter's embedding should smoothly translate through the space over months of operation, not jump discontinuously, allowing the system to distinguish drift from device replacement