I/Q Constellation Morphology

The geometric deformation of an ideal constellation diagram into a non-uniform shape, such as a parallelogram or ellipse, caused by the combined effects of I/Q gain and phase imbalances. This warping is a deterministic, device-specific signature.

• Gain Imbalance: Stretches the constellation along one axis, turning a square grid into a rectangle.
• Quadrature Skew: Shears the constellation, transforming a rectangle into a parallelogram.
• Combined Effect: Produces a unique, repeatable 2D distortion pattern that serves as a robust fingerprint.

The statistical dispersion of measured signal points around an ideal constellation locus, forming a 'cloud' rather than a single point. This dispersion is caused by additive noise, phase noise, and inter-symbol interference.

• Cluster Variance: The spread of points, indicating noise power.
• Cluster Skewness: Asymmetry in the point distribution, revealing non-linear distortion.
• Cluster Kurtosis: The 'tailedness' of the distribution, sensitive to impulsive noise sources.
• Shape Analysis: The specific 2D shape of the cloud (e.g., circular vs. elliptical) is a key morphological feature.

The displacement of the constellation diagram's center from the ideal (0,0) coordinate. This is primarily caused by DC offset and local oscillator leakage in the transmitter's analog stages.

• Static Component: A fixed voltage error from DAC offsets.
• LO Leakage: Creates a carrier spur that manifests as a DC offset in the baseband constellation.
• Fingerprinting Value: The magnitude and phase of this offset vector are highly unique to each device and relatively stable over time.

A measure of how much a nominally circular constellation point cluster has been stretched into an ellipse. This is a direct indicator of the specific ratio between I/Q gain imbalance and phase imbalance.

• Major/Minor Axis Ratio: Quantifies the severity of the combined imbalance.
• Tilt Angle: The angular orientation of the ellipse's major axis provides a sensitive measure of the phase imbalance between the I and Q channels.
• Feature Vector: Ellipticity and tilt angle form a powerful 2D feature for distinguishing emitters with similar gain errors but different phase errors.

Quantitative descriptors of the shape of a constellation point distribution beyond simple variance. These moments capture non-Gaussian characteristics of the impairment signature.

• Skewness (3rd Order): Measures asymmetry in the point cloud, indicating non-linear distortion like amplifier compression.
• Kurtosis (4th Order): Measures the 'tailedness' of the distribution, highly sensitive to impulsive noise and jitter.
• Robustness: These moments are often more robust to Gaussian channel noise than raw point locations, making them valuable features for machine learning classifiers.

The process of calculating the geometric center of a cluster of measured constellation points for each specific symbol. The vector offset of this centroid from the ideal symbol location quantifies the static I/Q imbalance for that symbol.

• Symbol-Dependent Offset: The centroid offset can vary slightly for different symbols due to non-linear DAC behavior.
• Drift Monitoring: Tracking the slow movement of centroids over time enables compensation for temperature and aging effects.
• Multi-Point Profile: The set of all symbol centroid offsets creates a high-dimensional distortion profile unique to the transmitter.

The calculated geometric center of a cluster of measured constellation points for a specific symbol. The vector offset of this centroid from the ideal symbol location directly quantifies the static I/Q imbalance and DC offset for that specific modulation state. Analyzing centroid displacement across all symbols in a constellation provides a multi-dimensional feature vector that is highly unique to the transmitter's analog front-end.

A measure of how much a nominally circular constellation point cluster has been stretched into an ellipse. This deformation is a direct consequence of the interaction between I/Q gain imbalance and quadrature skew. The ratio of the major to minor axis length serves as a sensitive, frequency-dependent identifier, as it captures the specific mismatch in the analog low-pass filters and mixer stages.

The angular orientation of the major axis of an elliptical constellation point cluster relative to the ideal I/Q axes. This tilt is a precise indicator of phase imbalance between the I and Q channels. Unlike magnitude-based metrics, the tilt angle is often robust to linear amplification changes, making it a stable feature for drift compensation algorithms in long-term device authentication.

Quantitative descriptors of the shape of a constellation point distribution beyond simple variance. These include:

• Skewness: Measures the asymmetry of the point cloud, indicating non-linear distortion.
• Kurtosis: Measures the 'tailedness' of the distribution, sensitive to intermittent phase noise or jitter. These higher-order moments form a robust feature set for deep learning signal identification models.

A multi-parameter characterization of a transmitter's unique impairment fingerprint. This profile maps the specific gain error, phase error, and DC offset not just at one power level, but across the device's entire dynamic range and frequency hopping pattern. The resulting multi-dimensional matrix captures the non-linear behavior of the power amplifier and mixer, forming a highly unclonable hardware signature.

The slow, temporal variation of a transmitter's I/Q impairment signature due to environmental factors like temperature change and component aging. This drift causes the constellation morphology to evolve, challenging static fingerprint databases. Mitigation requires adaptive tracking algorithms and channel-robust feature learning to update the reference signature without requiring full device re-enrollment.