I/Q Constellation Centroid

The constellation centroid is the arithmetic mean of the I and Q coordinate values for all measured points belonging to a specific symbol. In an ideal, impairment-free transmitter, this centroid coincides exactly with the ideal symbol locus. In practice, DC offset and carrier leakage displace the centroid, while I/Q imbalance causes symbol-dependent centroid shifts. The vector from the ideal point to the measured centroid is a direct measurement of the static impairment for that symbol.

A global DC offset in the I or Q baseband path shifts the entire constellation, moving the origin point and all symbol centroids by an identical vector. This is distinct from I/Q gain imbalance, which scales centroids along one axis. The centroid of the constellation's origin-point cluster (when a zero-amplitude symbol is transmitted) directly reveals the combined DC offset of the I and Q channels, making it a primary diagnostic feature for local oscillator leakage in zero-IF architectures.

The set of centroid offset vectors for all symbols in a modulation scheme constitutes a distortion profile unique to each transmitter. Key properties for fingerprinting include:

• Uniqueness: Manufacturing variances in DACs and mixers create distinct, repeatable offset patterns.
• Stability: Under fixed temperature and voltage, centroid positions remain highly consistent over short intervals.
• Symbol Dependency: The offset magnitude often varies per symbol due to non-linearities, enriching the feature space.
• Modulation Agnosticism: Centroid analysis applies to QPSK, 16-QAM, 64-QAM, and higher-order schemes.

Accurate centroid estimation requires sufficient samples to average out additive white Gaussian noise (AWGN) and phase noise, which create the symmetric constellation cloud around the centroid. Techniques include:

• Time-domain averaging: Accumulating I/Q samples over multiple symbol periods.
• Decision-directed estimation: Using demodulated symbol decisions to group points before calculating the mean.
• Blind estimation: Computing centroids without prior knowledge of transmitted symbols, useful for non-cooperative emitter identification.
• Statistical moment analysis: Using higher-order moments to separate centroid offset from noise variance.

The centroid defines the location of a symbol cluster, while the constellation cloud defines its spread. These are orthogonal features:

• Centroid offset is caused by deterministic hardware impairments (DC offset, I/Q imbalance).
• Cloud dispersion is caused by stochastic processes (thermal noise, phase noise, inter-symbol interference).
• A transmitter can have a large centroid offset but a tight cloud (clean but miscalibrated), or a small offset but a diffuse cloud (noisy but well-balanced).
• Both are exploited independently in I/Q constellation morphology analysis for multi-dimensional fingerprinting.

Centroid positions drift slowly with temperature, voltage variation, and component aging. This I/Q constellation distortion drift poses a challenge for long-term authentication. Mitigation strategies include:

• Periodic re-enrollment: Updating the reference centroid map during known quiescent periods.
• Adaptive tracking: Using Kalman filters or exponential moving averages to follow slow centroid migration.
• Temperature-indexed profiles: Storing centroid maps at multiple temperature points and interpolating.
• Relative centroid analysis: Using the vector relationships between symbol centroids, which are often more stable than absolute positions.