Transient Phase Trajectory

The brief, non-ideal electromagnetic signature emitted when a radio frequency transmitter is initially energized. This period, lasting from nanoseconds to microseconds, contains unique hardware-specific artifacts caused by the chaotic settling of oscillators, amplifiers, and bias networks. Unlike the steady-state signal, the turn-on transient is dominated by non-linear circuit dynamics and component tolerances, making it an exceptionally rich source for physical-layer device identification. The transient phase trajectory during this window directly maps the oscillator's path to frequency lock.

The complete time-domain response of a phase-locked loop as it acquires lock after power-up. This process defines the instantaneous frequency drift and phase discontinuity observed in the transient phase trajectory. Key features include:

• PLL Overshoot: Peak frequency excursion beyond the target lock frequency, indicating the loop filter's damping factor.
• PLL Lock Time: The duration required for synchronization, exposing component tolerances.
• Loop Filter Dynamics: The specific resistor-capacitor values in the loop filter dictate the exponential settling curve, creating a unique, unclonable signature.

A fundamental signal processing operation used to extract the analytic signal from a real-valued transient waveform. By computing the complex-valued representation, the Hilbert transform precisely separates the instantaneous amplitude envelope from the instantaneous phase trajectory. This is a prerequisite for analyzing the transient phase trajectory in the complex plane, as it removes carrier cycle distortion and reveals the underlying baseband dynamics of the transmitter's modulator and oscillator settling behavior.

The non-linear amplitude and phase distortion generated by the power amplifier (PA) when driven through its non-linear region during the rapid ramp-up. As the PA transitions from an off-state to saturation, the AM-AM and AM-PM conversion curves imprint a unique distortion signature on the transient phase trajectory. This behavior is heavily influenced by transient thermal signatures and transient memory effects, where the current transient shape depends on the previous operating state due to charge trapping in semiconductor materials.

A temporary mismatch in gain and phase between the in-phase (I) and quadrature (Q) signal paths during the transient period. While steady-state IQ imbalance is a known fingerprint, the transient variant often differs significantly due to circuit settling. This imbalance causes a distortion in the transient phase trajectory, manifesting as an elliptical rather than circular path in the complex plane. Key contributors include:

• Transient DC Offset: Momentary carrier feedthrough from local oscillator leakage.
• DAC Glitch: Timing skews in the digital-to-analog converter during major code transitions at burst onset.

A higher-order spectral analysis technique that reveals quadratic phase coupling within the transient signal. Unlike the power spectrum, the bispectrum effectively suppresses Gaussian noise and highlights non-linear hardware interactions that are invisible to linear methods. For transient phase trajectory analysis, the bispectrum can detect subtle phase correlations between different frequency components generated by the VCO pulling effect or transient injection locking, providing a robust feature space for deep learning-based emitter identification.