Thermal-Induced Memory Polynomial

Extends the standard memory polynomial by appending a dedicated thermal sub-model. The baseband output is expressed as the sum of conventional high-pass memory terms and a separate low-pass filtered envelope term. This decomposition explicitly separates short-term electrical memory (nanoseconds to microseconds) from long-term thermal memory (milliseconds to seconds), preventing the model from conflating physically distinct distortion mechanisms.

The thermal contribution is modeled by applying a low-pass filter to the squared magnitude of the input envelope. This filter approximates the thermal impedance of the device, capturing the frequency-dependent attenuation of temperature fluctuations. Key characteristics:

• Cutoff frequency typically in the 1 Hz to 100 kHz range
• Filter order corresponds to the number of thermal time constants
• Implements a Foster or Cauer thermal model equivalent in the digital domain

The filtered envelope signal feeds a nonlinear basis function set, typically a polynomial expansion, to generate the thermal correction terms. This captures how junction temperature variations nonlinearly modulate AM-AM and AM-PM characteristics. The thermal sub-model operates on the envelope power history rather than the instantaneous RF carrier, reflecting the physical reality that self-heating is proportional to average dissipated power.

Coefficients are extracted using least-squares estimation on measured input-output data. The procedure requires:

• Two-tone or multitone excitation with varying tone spacing to excite thermal dynamics
• Pulsed-RF measurements to isolate thermal transients from electrical memory
• Segmented extraction: conventional memory polynomial terms extracted first, then thermal sub-model fitted to the residual error
• Cross-validation across ambient temperature and duty cycle conditions ensures robustness

The thermal-induced memory polynomial introduces additional computational overhead compared to a standard memory polynomial. Key considerations:

• Filter implementation: IIR structures preferred for low cutoff frequencies to minimize tap count
• Coefficient storage: Thermal LUT dimensions increase with envelope history depth
• Update rate: Thermal coefficients require slower adaptation rates (Hz vs. kHz) due to the long time constants
• FPGA resource: Dedicated DSP slices for the low-pass filter chain and additional polynomial evaluators

A defining capability of this model is correcting thermal-induced spectral asymmetry—an imbalance between upper and lower intermodulation sidebands that memoryless or short-memory models cannot address. The low-pass envelope filtering introduces a dispersive phase response that mirrors the physical thermal lag, enabling the predistorter to generate anti-phase asymmetry that cancels the amplifier's thermally induced AM-PM distortion across the full modulation bandwidth.