Modulation-Domain Fingerprinting

Every transmitter's analog impairments—I/Q imbalance, DC offset, and phase noise—produce a unique, repeatable warping of the ideal symbol constellation. This card examines how the measured scatter plot of demodulated symbols deviates from the theoretical grid. By modeling the spatial distribution of received symbols around each ideal constellation point, a distinctive signature emerges. Key metrics include:

• Cluster centroid displacement: The shift of the mean symbol location from the ideal point
• Cluster ellipticity: The non-circular spread caused by gain imbalance
• Cluster rotation: The angular skew induced by quadrature error These geometric distortions are stable over time and independent of the transmitted data payload, making them ideal for persistent device authentication.

Error Vector Magnitude (EVM) is the distance between an actual transmitted symbol and its ideal reference position. While aggregate EVM is a standard quality metric, the statistical distribution of the error vector—its magnitude, phase, and temporal correlation—constitutes a powerful fingerprint. A transmitter's power amplifier non-linearity creates a characteristic EVM pattern that varies with signal amplitude. By profiling:

• The probability density function of EVM magnitudes
• The phase distribution of error vectors
• The amplitude-dependent EVM (AM-AM distortion mapping) a model can distinguish between devices with identical aggregate EVM scores but different underlying impairment structures.

The phase trajectory traces the signal's instantaneous phase as it transitions between consecutive symbols. In an ideal transmitter, this path follows a smooth, mathematically defined curve. Hardware impairments—particularly local oscillator leakage and pulse shaping filter imperfections—introduce subtle, repeatable deviations. Key fingerprinting features include:

• Overshoot and ringing at symbol transitions
• Asymmetric rise and fall times in phase changes
• Phase memory effects where the current trajectory depends on prior symbols These transient behaviors between constellation points often carry more identifying information than the steady-state symbol positions themselves, especially in high-order modulation schemes like 64-QAM or 256-QAM.

Rather than analyzing individual symbols in isolation, this technique models the conditional probability distributions of symbol transitions. A transmitter's power amplifier memory effect causes the distortion of the current symbol to depend on the sequence of previously transmitted symbols. By constructing a transition matrix that captures the statistical relationship between consecutive symbol pairs, a unique behavioral fingerprint emerges. Features include:

• Markov chain models of symbol-to-symbol distortion patterns
• N-gram analysis of symbol sequences and their associated EVM values
• Trellis-based modeling of state-dependent impairment trajectories This approach is particularly effective for identifying devices using burst-mode transmissions where preamble-based techniques are insufficient.

Different modulation schemes stress transmitter hardware in distinct ways, revealing unique impairment signatures. Phase Shift Keying (PSK) schemes expose phase noise and I/Q phase imbalance, while Quadrature Amplitude Modulation (QAM) reveals amplitude non-linearity and gain imbalance. Key modulation-domain features include:

• PSK: Circular constellation warping, phase offset, and phase noise skirts
• QAM: Rectangular grid distortion, amplitude compression at high power levels
• OFDM: Subcarrier-specific impairment patterns and pilot tone deviations
• FSK: Frequency deviation asymmetry and inter-symbol transition timing jitter A comprehensive fingerprinting system extracts features across multiple modulation domains, creating a multi-dimensional signature that is robust to changes in the transmission scheme.

This technique removes the influence of the unknown transmitted data by analyzing the difference between consecutive received symbols rather than the absolute symbol positions. By computing the differential error vector—the deviation between the actual and ideal symbol transitions—the fingerprint becomes independent of the specific data payload. Benefits include:

• Data-agnostic feature extraction: No need for known training sequences
• Channel resilience: Differential operation mitigates slow-varying channel effects
• Blind identification: Operates without demodulating or decoding the payload The differential constellation trace forms a secondary scatter plot whose shape and statistical properties are determined solely by the transmitter's hardware impairments, providing a robust, payload-independent biometric.