Spectral Regrowth

The fundamental mechanism driving spectral regrowth is the amplitude-dependent transfer function of the power amplifier. As the input signal envelope fluctuates, the amplifier's gain compresses (AM-AM distortion) and its phase shift varies (AM-PM distortion). This non-constant envelope behavior generates intermodulation products that spread energy into adjacent channels. The specific shape of the AM-AM compression curve and AM-PM conversion coefficient is unique to each amplifier's semiconductor physics, making the resulting regrowth spectrum a hardware-specific fingerprint.

Spectral regrowth is dominated by third-order intermodulation products (IM3) generated when the amplifier's cubic non-linearity term mixes spectral components of the modulated signal. These products appear as spectral shoulders immediately adjacent to the main channel. Key characteristics include:

• IM3 power relative to the carrier is a direct function of the amplifier's third-order intercept point (IP3)
• The asymmetry between upper and lower regrowth shoulders reveals memory effects
• Higher-order products (IM5, IM7) contribute to far-out spectral spreading
• The precise IM3 shoulder shape varies between nominally identical amplifiers due to semiconductor doping variations

Real power amplifiers exhibit memory effects where the current output depends on previous input states due to:

• Thermal time constants: Die temperature changes modulate gain on microsecond scales
• Bias circuit impedance: Low-frequency envelope components modulate the transistor's operating point
• Trapping effects: Charge capture and release in semiconductor defects alters gain dynamically

These effects produce asymmetric spectral regrowth where the upper and lower sidebands differ in shape and power. This asymmetry pattern is highly device-specific, reflecting the unique thermal impedance and bias network parasitics of each physical amplifier.

ACLR is the primary regulatory metric quantifying spectral regrowth severity, defined as the ratio of transmitted power within the assigned channel to power leaking into adjacent channels. For device fingerprinting, ACLR provides a coarse but stable identifier:

• Typical values range from -30 dBc to -50 dBc depending on amplifier linearity and back-off
• ACLR varies measurably between individual units of the same model due to process variation
• The frequency dependence of ACLR across multiple offset channels creates a multi-dimensional signature
• ACLR changes predictably with temperature and supply voltage, enabling environmental compensation

The spectral regrowth pattern is not static—it depends on the probability density function (PDF) of the transmitted signal's instantaneous power. Higher peak-to-average power ratio (PAPR) signals drive the amplifier deeper into compression, producing more severe regrowth. This creates a signal-dependent signature where:

• Different modulation formats (QPSK vs. 256-QAM) produce distinct regrowth shapes from the same amplifier
• The complementary cumulative distribution function (CCDF) of the signal interacts with the amplifier's transfer curve
• Fingerprinting systems must either control for modulation or learn modulation-invariant features

Modern transmitters employ digital pre-distortion (DPD) to linearize the power amplifier and suppress spectral regrowth. However, DPD cancellation is never perfect, leaving a residual regrowth signature that reveals the amplifier's underlying non-linearity. This residual is particularly valuable for fingerprinting because:

• The imperfect cancellation reflects the specific mismatch between the DPD model and the physical amplifier
• DPD coefficients themselves, when observable, encode a compressed representation of the amplifier's distortion
• The residual regrowth pattern changes subtly with DPD adaptation cycles, providing temporal dynamics for identification

The root cause of spectral regrowth. When a transmitter's final amplification stage operates near its 1 dB compression point, the non-linear transfer function generates intermodulation products that spill into adjacent channels. The specific shape of this distortion curve—characterized by AM-AM and AM-PM conversion—varies between individual amplifiers due to semiconductor process variations.

The regulatory metric that quantifies spectral regrowth. ACLR measures the ratio of transmitted power within the assigned channel to power leaking into offset channels. While standards like 3GPP mandate minimum ACLR values, the precise leakage level varies per device due to amplifier manufacturing tolerances, making it a useful feature for physical-layer authentication.

The dependence of a power amplifier's current output on previous input states due to thermal time constants, bias circuit capacitance, and trapping effects in semiconductor materials. This history-dependent behavior creates a dynamic distortion pattern that varies with signal envelope frequency. Memory effects make spectral regrowth asymmetric and uniquely characteristic of each amplifier's physical construction.

The primary mitigation technique for spectral regrowth. DPD applies an inverse non-linear function to the baseband signal before the power amplifier, canceling out the amplifier's distortion. The DPD coefficients themselves become a unique signature—the correction required to linearize one amplifier differs from another, effectively encoding the hardware's impairment profile in the coefficient set.

The mechanism producing spectral regrowth. When multiple frequency components pass through a non-linear device, they mix to generate sum and difference products. For a modulated signal, this creates a continuum of intermodulation products that manifests as spectral spreading. The relative amplitudes of these products are determined by the amplifier's specific non-linearity coefficients.

The semiconductor physics foundation underlying why spectral regrowth patterns are device-unique. PVT variation causes transistor threshold voltages, transconductance, and parasitic capacitances to differ between integrated circuits. These microscopic differences alter the amplifier's transfer function, making the spectral regrowth profile a silicon biometric that cannot be cloned even with identical designs.