Cross-Validation

The dataset is partitioned into k equal-sized folds. The model is trained on k-1 folds and validated on the remaining fold, rotating through all folds. The final performance metric is the average across all k iterations. For PA modeling, k=5 or k=10 is typical, ensuring every measured data point contributes to both training and validation. This method provides a robust estimate of model generalization with reduced variance compared to a single train-test split.

The simplest validation approach: split data into a training set (typically 70-80%) and an independent test set (20-30%). The model is trained exclusively on the training partition and evaluated once on the held-out test data. While computationally efficient, performance estimates can exhibit high variance depending on the specific random split. For PA behavioral modeling, this method is suitable for large datasets where a single split adequately represents the signal distribution.

A variant of k-fold that preserves the class distribution or signal characteristic proportions in each fold. For PA modeling, stratification ensures each fold contains representative samples across input power levels, avoiding folds dominated by low-power or saturation-region data. This is critical when modeling amplifiers with distinct behavioral regimes—linear, compression, and saturation zones must all be represented in training and validation folds to prevent biased performance estimates.

An extreme case of k-fold where k equals the number of samples. The model trains on all data points except one, validates on the excluded point, and repeats for every sample. LOOCV provides an almost unbiased estimate of generalization error but is computationally prohibitive for large PA datasets. It is most useful for very small measurement campaigns where maximizing training data per iteration is essential, though the high variance of individual estimates requires careful interpretation.

Designed for temporally ordered data, this method respects the sequential nature of PA measurements. Training uses only past data points to predict future behavior, preventing information leakage from future samples. The validation window rolls forward through time. This is essential for evaluating memory effect models where temporal dependencies exist—standard random shuffling would destroy the sequential structure and produce overly optimistic generalization estimates.

Ensures that all samples from the same logical group—such as measurements from a single amplifier unit, temperature condition, or signal type—remain together in either training or validation. This prevents data leakage where highly correlated samples artificially inflate performance. In PA modeling, grouping by device under test or measurement session tests whether the model generalizes to unseen hardware units rather than merely interpolating within known device characteristics.

A modeling failure where the extracted model memorizes training data noise instead of learning underlying amplifier dynamics. In PA behavioral modeling, an overfit model will accurately reproduce the training signal but fail to predict distortion for new modulation schemes or power levels. Key indicators:

• Low training NMSE but high validation NMSE
• Excessive coefficient magnitudes in memory polynomial models
• Poor generalization to different signal statistics

A technique that adds a penalty term to the least squares cost function during model extraction to constrain coefficient magnitudes. Common forms in DPD coefficient estimation:

• L2 (Ridge): Penalizes squared coefficient magnitude, shrinking all coefficients
• L1 (Lasso): Promotes coefficient sparsity by driving unnecessary terms to zero
• Elastic Net: Combines L1 and L2 penalties for correlated predictor handling Regularization directly improves numerical stability when the data matrix has high condition number.

A metric quantifying the average power of the error signal normalized by the power of the reference signal. NMSE is the primary fidelity metric for PA behavioral models and is typically reported separately for:

• Training set: Measures fitting quality
• Validation set: Measures generalization ability A large gap between training and validation NMSE is the definitive signal of overfitting. Typical targets for wideband DPD models are below -35 dB NMSE.

The process of determining behavioral model parameters by fitting its structure to measured input-output data from a physical power amplifier. Cross-validation is critical during extraction to:

• Select the appropriate model complexity (e.g., nonlinear order and memory depth)
• Compare competing architectures (GMP vs. Volterra vs. neural network)
• Validate performance across different signal types (LTE, 5G NR, multi-carrier) Proper extraction requires representative datasets spanning the amplifier's operating range.

A property where a significant number of model coefficients are zero or near-zero, enabling complexity reduction through pruning. Cross-validation guides sparsity decisions by revealing which terms genuinely contribute to prediction accuracy versus which merely fit noise. Benefits in DPD implementation:

• Reduced FPGA multiplier usage
• Lower power consumption in real-time predistortion
• Faster coefficient update cycles Pruning without cross-validation risks removing terms that are critical for specific signal conditions.

A model validation metric that measures the prediction error power specifically in adjacent channels. While NMSE assesses overall in-band fidelity, ACEPR evaluates how well the behavioral model predicts spectral regrowth—the most critical distortion for regulatory compliance. Cross-validation with ACEPR ensures the model generalizes to:

• Different carrier configurations
• Varying signal bandwidths
• Multiple adjacent channel offsets Poor ACEPR on validation data indicates the model has not captured the true nonlinear memory dynamics.