Power Amplifier Non-Linearity

Amplitude-to-Amplitude distortion describes the non-linear relationship between input signal amplitude and output signal amplitude. As the PA approaches saturation, gain compression occurs—incremental input increases yield diminishing output increases.

• Gain Compression: Output amplitude plateaus, distorting the signal envelope
• 1 dB Compression Point (P1dB): The input power where gain drops by 1 dB from ideal linearity
• Saturation Power (Psat): Maximum output power achievable, regardless of input increase

This compression curve is unique per device due to semiconductor process variations.

Amplitude-to-Phase conversion is the unintended phase shift introduced to the output signal as a function of instantaneous input amplitude. Unlike AM/AM, this distortion affects the signal's angular component.

• Phase Shift vs. Input Power: Higher input levels induce greater phase rotation
• Memory Effects: Phase distortion depends on signal history, not just instantaneous amplitude
• Constellation Warping: Causes rotation and spreading of symbol points in modulation schemes like QAM

AM/PM is particularly valuable for fingerprinting because it captures reactive parasitic elements unique to each amplifier's physical layout.

Memory effects occur when the PA's output depends not only on the current input sample but also on previous samples. These thermal and electrical memory phenomena create a distinctive temporal signature.

• Thermal Memory: Die temperature changes modulate gain over microsecond timescales
• Electrical Memory: Bias network impedance variations and capacitor charge states introduce envelope-frequency-dependent distortion
• Long-Term Memory: Slowly varying effects from substrate heating across multiple transmission bursts

Memory effects make the distortion pattern signal-dependent and history-aware, greatly increasing the uniqueness and complexity of the RF fingerprint.

Spectral regrowth is the broadening of a transmitted signal's bandwidth caused by PA non-linearity. Energy spills into adjacent channels, creating a distinctive out-of-band emission profile.

• Adjacent Channel Power Ratio (ACPR): Quantifies the power leakage into neighboring frequency bands
• Shoulder Asymmetry: Upper and lower spectral regrowth shoulders often differ due to memory effects
• Intermodulation Products: Non-linearity generates sum and difference frequency components

The specific shape and asymmetry of spectral regrowth shoulders provide a rich, device-specific fingerprint observable even with simple spectrum analysis.

Intermodulation distortion (IMD) arises when multiple frequency components pass through a non-linear PA, generating new frequencies at sums and differences of the originals and their harmonics.

• Third-Order Intercept Point (IP3): A figure of merit extrapolating the input power where third-order IMD products would equal the fundamental tones
• Odd-Order Dominance: Odd-order products (3rd, 5th) fall near the original signal band and are hardest to filter
• IMD Asymmetry: Upper and lower IMD sidebands often exhibit amplitude imbalance due to memory effects

IMD products carry a unique spectral signature reflecting the specific polynomial transfer function of each amplifier.

The Volterra series provides a mathematical framework to model PA non-linearity with memory as a sum of multi-dimensional convolution integrals. It captures the complete behavioral signature.

• Kernel Extraction: Each Volterra kernel represents a specific order of non-linearity and memory depth
• Pruned Models: Simplified Volterra structures (e.g., memory polynomial, generalized memory polynomial) reduce complexity while retaining fingerprinting fidelity
• Coefficient Uniqueness: Extracted kernel coefficients form a compact, device-specific feature vector

Volterra-derived coefficient vectors serve as highly discriminative inputs for SEI classifiers, directly encoding the physical distortion mechanism.