I/Q Constellation Distortion Profile

Quantifies the amplitude mismatch between the I and Q signal paths. This is expressed as the I/Q Gain Ratio, where a value deviating from unity indicates a scaling error along one axis. The profile captures this ratio not as a static number, but as a frequency-dependent vector that varies across the modulation bandwidth. A typical profile might show a gain ratio of 1.02 at the band center, degrading to 1.05 at the band edges due to analog filter roll-off mismatch.

Measures the deviation from the ideal 90-degree separation between the I and Q local oscillator signals. This quadrature skew causes the constellation to shear, transforming a square grid into a parallelogram. The profile records this phase error in degrees, often with sub-degree precision. For example, a consistent 0.8-degree skew across all power levels is a highly distinctive, device-specific trait caused by minute trace length differences in the PCB layout.

Represents the static voltage added to the baseband signal, visualized as an Origin Point Offset in the constellation. The profile decomposes this into two independent components:

• I-path DC Offset: Caused by DAC output errors and baseband amplifier bias.
• Q-path DC Offset: Similarly sourced from the quadrature chain. A correlated component, Local Oscillator Leakage, manifests as a carrier spur and contributes to a shared offset. The profile tracks these offsets in millivolts, noting their drift with temperature.

A critical dimension of the profile is the non-linear behavior of impairments across transmit power levels. A device's I/Q imbalance at 0 dBm output may differ significantly from its imbalance at 20 dBm due to amplifier compression. The profile captures this as a multi-point map, revealing the unique gain compression curve of the power amplifier and its interaction with the modulator. This non-linearity is a rich source of distinguishing features.

Captures how I/Q impairments vary across the operational frequency range of the device. Analog components like mixers and filters have frequency-selective behavior. The profile maps I/Q Gain Ratio and Quadrature Skew at multiple carrier frequencies (e.g., at 2.400 GHz, 2.440 GHz, and 2.480 GHz for a Wi-Fi device). The resulting curve of impairment vs. frequency is a highly stable, device-specific signature rooted in the physical tolerances of the RF front-end.

Beyond simple error vectors, the profile includes higher-order statistical descriptors of the Constellation Cloud for each symbol point:

• Ellipticity: The ratio of the major to minor axis of the point cluster, indicating the combined gain/phase imbalance.
• Tilt Angle: The rotation of the cluster's major axis, a sensitive measure of phase error.
• Kurtosis: Describes the 'tailedness' of the distribution, revealing intermittent impairments like burst noise. These morphological features provide a rich, multi-dimensional vector for deep learning classifiers.

A hardware impairment in direct-conversion transmitters where the in-phase (I) and quadrature (Q) signal paths exhibit mismatched amplitude (gain imbalance) or non-orthogonal phase (quadrature skew). This mismatch creates a unique, identifiable distortion in the constellation diagram, forming the foundation of the distortion profile. The I/Q Gain Ratio and Quadrature Skew are the two primary parameters that define this impairment.

A constant voltage added to the baseband signal, primarily caused by Local Oscillator Leakage and DAC Offset Error. This displaces the entire constellation diagram from the (0,0) origin. The Origin Point Offset is a critical fingerprinting parameter because it is highly device-specific and independent of the modulation scheme, providing a stable identifier even during idle transmission periods.

The geometric deformation of an ideal constellation into a non-uniform shape—typically a parallelogram or ellipse—caused by the combined effects of I/Q gain and phase imbalances. Constellation Morphology studies the shape, symmetry, and statistical structure of point clusters to extract a multi-dimensional feature vector. Key metrics include:

• Constellation Ellipticity: Stretching of a circular cluster into an ellipse
• Constellation Tilt Angle: Angular orientation of the elliptical major axis

A comprehensive metric quantifying the deviation of measured constellation points from their ideal reference positions. EVM is calculated as the root-mean-square (RMS) magnitude of the error vector, normalized to the ideal symbol magnitude. While EVM provides a single aggregate measure of modulation accuracy, the distribution and directionality of individual error vectors across the constellation reveals the specific impairment signature.

Quantitative descriptors of the shape of a constellation point distribution used as robust features for machine learning-based fingerprinting. These include:

• Variance: The spread of points around the ideal locus
• Skewness: Asymmetry of the point distribution
• Kurtosis: The 'tailedness' of the distribution, sensitive to outlier impairments These moments provide a compact, rotation-invariant feature set for neural network classifiers.

Constellation Distortion Stability is the degree to which a transmitter's impairment signature remains constant under fixed environmental conditions—a critical requirement for reliable fingerprinting. Conversely, Constellation Distortion Drift describes the slow temporal variation of the signature due to temperature change and component aging. Robust systems employ adaptive tracking algorithms to compensate for this drift without requiring full re-enrollment.