Constellation Diagram Analysis

Occurs when the in-phase (I) and quadrature (Q) branches of the modulator exhibit unequal amplification. This stretches the constellation into a rectangular shape rather than a perfect square.

• Visual signature: Constellation points elongate along one axis
• Measurement: Amplitude ratio between I and Q rails, typically expressed in dB
• Origin: Resistor tolerance mismatches in differential amplifiers and mixer stages
• Stability: Highly stable over temperature, making it an excellent long-term fingerprint

A 0.5 dB gain imbalance creates a measurable aspect ratio change that persists across modulation schemes.

When the I and Q local oscillator signals are not exactly 90 degrees apart, the constellation shears diagonally. This non-orthogonality causes cross-talk between the I and Q channels.

• Visual signature: Constellation appears skewed or rhomboid
• Measurement: Phase deviation from ideal 90° quadrature, in degrees
• Origin: Phase splitter inaccuracies in the local oscillator distribution network
• Impact: Increases symbol error rate by pulling decision boundaries

Even a 2-degree quadrature error produces visible skewing in high-order QAM constellations like 256-QAM.

A constant DC bias added to the baseband signal causes the entire constellation to shift away from the origin. This manifests as carrier feedthrough—an unmodulated tone at the center frequency.

• Visual signature: Entire constellation displaced from origin
• Measurement: Offset magnitude relative to average symbol amplitude, in dBc
• Origin: Local oscillator leakage through mixer ports and PCB trace coupling
• Fingerprint value: The vector direction and magnitude of the offset is device-unique

DC offset creates a deterministic error vector that is independent of the transmitted data sequence.

Random fluctuations in the local oscillator phase cause the constellation points to rotate about the origin with a Gaussian angular distribution. This creates crescent-shaped or smeared clusters.

• Visual signature: Arc-shaped spreading of constellation points, especially at outer rings
• Measurement: Single-sideband phase noise in dBc/Hz at specific offsets (1 kHz, 10 kHz, 100 kHz)
• Origin: Oscillator phase-locked loop dynamics and VCO tuning sensitivity
• Uniqueness: The phase noise profile is a function of the physical crystal and PLL components

Phase noise is particularly visible in higher-order modulations where the angular separation between symbols is small.

When a power amplifier operates near saturation, the outer constellation points compress inward while inner points remain relatively unaffected. This creates a non-uniform clustering pattern.

• Visual signature: Outer symbols pulled toward origin, creating a 'pinched' appearance
• Measurement: AM/AM (amplitude-to-amplitude) and AM/PM (amplitude-to-phase) conversion curves
• Origin: Transistor non-linearity in the amplifier's gain region
• Device specificity: Each amplifier has unique compression characteristics due to semiconductor doping variations

The 1 dB compression point and the shape of the non-linear transition region form a distinctive hardware signature.

A relative time delay between the I and Q signal paths causes frequency-dependent constellation distortion. The error increases with baseband bandwidth, creating a frequency-selective impairment.

• Visual signature: Constellation points spread into diagonal ellipses, worsening at band edges
• Measurement: Relative delay in picoseconds or as a fraction of the symbol period
• Origin: Trace length mismatches on PCB and group delay differences in analog filters
• Detection: Most visible in wideband signals where the phase error accumulates across frequency

Timing skew creates a unique spectral signature that can be extracted through frequency-domain analysis of the error vector magnitude.

A hardware impairment where the in-phase (I) and quadrature (Q) branches of a modulator exhibit unequal gain or non-orthogonal phase. This creates a measurable distortion in the constellation diagram, manifesting as an elliptical stretching and skewing of the ideal square grid. The specific gain mismatch and phase error values are unique to each transmitter's analog components, serving as a robust, unclonable physical-layer identifier.

A constant voltage bias added to the baseband signal caused by local oscillator leakage or mixer port isolation. In the constellation diagram, this shifts the entire symbol cluster away from the origin. The magnitude and phase of this offset create a unique signature, often visible as a distinct spectral tone at the carrier frequency, which is highly stable over time and temperature.

The random fluctuation in the phase of a transmitter's local oscillator causes spectral spreading and constellation point rotation. In a constellation diagram, phase noise appears as an angular smearing of symbol points along a circular arc. The power spectral density profile of this phase noise is a unique, unclonable fingerprint derived from the oscillator's physical crystal and phase-locked loop circuitry.

A metric measuring the deviation of actual transmitted symbols from their ideal constellation points. The statistical distribution of this error vector—not just its magnitude—serves as a device fingerprint. Key characteristics include:

• Mean EVM: Indicates systematic impairments like I/Q imbalance
• EVM variance: Reveals random noise processes
• EVM distribution shape: Captures amplifier non-linearity patterns unique to each device

Distortion introduced by a power amplifier operating near its saturation point, characterized by AM/AM (amplitude-to-amplitude) and AM/PM (amplitude-to-phase) conversion curves. In the constellation diagram, this causes outer symbols to compress inward and rotate relative to inner symbols, creating a distinctive warping pattern. Each amplifier's unique semiconductor doping variations produce a repeatable, device-specific distortion signature.

The extraction of device-specific features directly from the demodulated symbol sequence, focusing on errors in the ideal symbol constellation caused by hardware impairments. Unlike raw waveform analysis, this approach operates on the recovered symbols, analyzing:

• Symbol deviation vectors from ideal constellation points
• Phase trajectory between consecutive symbols
• Cluster variance around each constellation point This method is computationally efficient and directly compatible with existing receiver architectures.