Turn-On Transient

The detailed shape of the power envelope's rising edge, from the noise floor to the steady-state level. This profile is not an ideal step function; it contains inflection points, overshoot, and non-linearities that directly reflect the specific biasing network and transistor physics of the power amplifier. The rise time (10% to 90% of final value) and its variance across multiple bursts are key metrics.

The trajectory of the instantaneous carrier frequency and phase as the transmitter's synthesis chain stabilizes. Key features include:

• Phase Discontinuity: An abrupt, unintended phase shift during the initial switching of frequency synthesis components.
• Frequency Settling Profile: The path of the carrier frequency as it converges to its nominal value, revealing the PLL loop filter characteristics.
• Instantaneous Frequency Drift: Short-term variation caused by thermal transients and VCO pulling effects.

Broadband spectral noise generated by the rapid switching of the transmitter, causing momentary interference in adjacent channels. The spectral splatter reveals the switching speed and linearity of the hardware. Adjacent channel splatter is a specific, measurable component of this noise, and its power distribution is a unique artifact of the transmitter's output matching network and power amplifier slew rate.

A ringing artifact is a damped sinusoidal oscillation superimposed on the transient envelope, caused by parasitic inductance and capacitance resonating in the transmitter's output matching network. The damped oscillation profile is defined by its resonant frequency and exponential decay time constant, both of which are highly dependent on the precise physical values of reactive components, making it a distinct hardware signature.

The transient signal is inherently non-Gaussian due to deterministic hardware non-linearities. Higher-order statistics like transient kurtosis (peakedness) and transient skewness (asymmetry) quantify this behavior. Transient bispectrum analysis reveals quadratic phase coupling within the signal, effectively suppressing Gaussian noise to isolate the non-linear interactions of the transmitter's power amplifier and modulator.

The high transient current inrush during turn-on causes a momentary transient voltage sag on the regulated supply rail. This sag amplitude-modulates the output signal, revealing the equivalent series resistance of the power supply decoupling network. The resulting transient power supply modulation is a direct, unclonable indicator of the physical power distribution network on the device's printed circuit board.

A unique, unclonable identifier derived from the microscopic hardware impairments observed exclusively during the start-up and shut-down periods of a radio frequency emission. Unlike steady-state signatures, this fingerprint captures the dynamic non-linear response of analog components as they transition from an inert to an active state. The fingerprint is a composite vector of features including overshoot characterization, damped oscillation profiles, and phase discontinuities, making it exceptionally difficult for an adversary to mimic or replay.

The specific amplitude-versus-time profile of a signal burst's leading edge, reflecting the unique charging characteristics of a transmitter's power amplifier and bias circuitry. Key measurable parameters include:

• Rise-time variance: The statistical distribution of the 10% to 90% rise time across multiple bursts.
• Burst leading edge slope: The maximum rate of amplitude change, directly proportional to the power amplifier's slew rate.
• Overshoot characterization: Quantifies the transient amplitude excursion beyond the steady-state level caused by underdamped control loops.

The complete time-domain response of a phase-locked loop (PLL) as it acquires lock to a reference signal after power-up. This period exposes the loop's dynamic characteristics for fingerprinting. The PLL lock time and PLL overshoot—the peak frequency excursion beyond the target—are direct indicators of the loop filter's damping factor and component tolerances. A temporary elevation in the PLL phase noise burst during locking creates a unique noise signature before stabilization.

Broadband spectral noise generated by the rapid switching of the transmitter, causing momentary interference in adjacent channels. This splatter reveals the switching speed and non-linearity of the hardware. Adjacent channel splatter is a key metric for assessing transmitter linearity during burst onset. The transient spectral centroid—the center of mass of the short-time Fourier transform spectrum—indicates whether the transient energy is biased toward higher or lower frequencies, serving as a robust single-value feature.

The dependence of the current transient shape on the previous operating state of the transmitter. This history-dependent signature is caused by:

• Thermal trapping: Charge storage in semiconductor materials from prior transmissions.
• Transient thermal signature: Instantaneous self-heating of the transistor junction during the high-current turn-on event.
• Transient power supply modulation: Momentary fluctuation in supply voltage caused by inrush current, which amplitude-modulates the output and reveals the power distribution network's impedance.

The analytic signal magnitude computed via the Hilbert transform, used to extract the precise amplitude envelope of a transient without the distortion caused by carrier cycles. This mathematical tool is fundamental for transient envelope analysis, enabling the characterization of the attack, decay, sustain, and release profile of a burst. It allows for the clean separation of the transient attack profile and transient decay profile from the modulated carrier, isolating the hardware-specific ramp characteristics.