Training Waveform

The waveform must exhibit a PAPR that matches or exceeds the target communication standard (e.g., 8-12 dB for 5G NR OFDM). A high PAPR is essential to excite the amplifier into its gain compression region, revealing nonlinear characteristics that a constant-envelope signal would miss. Without sufficient peak power, the extracted model will fail to predict spectral regrowth at rated output power.

The stimulus bandwidth must be wider than the intended operational signal to capture the out-of-band distortion products. A rule of thumb is to use a training waveform with 3-5x the modulation bandwidth of the target signal. This ensures the model observes the full adjacent channel leakage and can learn the frequency-dependent memory effects that cause asymmetric spectral regrowth.

The amplitude distribution of the training waveform should approximate a Gaussian or Rayleigh PDF to match modern communication signals. This ensures that the model fitting process weights all power levels proportionally to their real-world occurrence. A uniform PDF would over-emphasize high-power states, biasing the model toward compression behavior and degrading small-signal fidelity.

The waveform must contain sufficient sample-to-sample variation to excite the amplifier's memory effects. Long sequences of constant or repetitive patterns fail to reveal thermal trapping and charge storage dynamics. Pseudo-random sequences with controlled autocorrelation properties ensure the regression matrix is well-conditioned for extracting memory polynomial coefficients.

A well-designed waveform produces a low condition number for the basis function covariance matrix. Ill-conditioning arises when the stimulus lacks spectral diversity, causing basis functions to become highly correlated. This leads to unstable, noise-sensitive coefficient estimates. Techniques like Principal Component Analysis (PCA) can mitigate this, but a properly designed waveform is the first line of defense.

While high PAPR is necessary for model extraction, the waveform should be compatible with Crest Factor Reduction (CFR) algorithms used in the final deployment. The training waveform can be a raw high-PAPR signal, but the extracted model must be validated against CFR-processed variants to ensure the predistorter generalizes to the actual transmitted waveform after signal conditioning.