Least Squares (LS) Estimation

An adaptive filtering algorithm that recursively updates predistorter coefficients by minimizing a weighted linear least squares cost function. Unlike the batch LS method, RLS processes data sample-by-sample, making it suitable for tracking time-varying power amplifier characteristics.

• Convergence: Offers an order of magnitude faster convergence than LMS-based methods
• Complexity: Computationally heavier than LMS (O(N²) vs O(N)) but lighter than full batch LS inversion
• Forgetting Factor: A critical parameter (λ, typically 0.95–0.999) that weights recent data more heavily to track amplifier drift
• Application: Ideal for online, closed-loop DPD adaptation where PA behavior changes with temperature or aging

A matrix factorization method that decomposes the observation matrix A into an orthogonal matrix Q and an upper triangular matrix R (A = QR). This approach solves the least squares problem with superior numerical stability compared to direct normal equations.

• Stability: Avoids squaring the condition number, making it robust for ill-conditioned basis function matrices
• Implementation: Typically computed using Householder reflections, Givens rotations, or Modified Gram-Schmidt
• Use Case: Preferred for offline coefficient extraction in memory polynomial models where numerical precision is critical
• Variant: Recursive QRD-RLS combines QR decomposition with recursive updates for adaptive tracking

A regularized form of least squares estimation that adds an L2 penalty term (λ||w||²) to the cost function. This technique prevents overfitting and improves the robustness of extracted DPD coefficients, especially when the basis function matrix is ill-conditioned.

• Cost Function: Minimizes ||y - Aw||² + λ||w||², where λ is the regularization parameter
• Effect: Shrinks coefficient magnitudes toward zero, reducing sensitivity to measurement noise
• Parameter Selection: λ is typically chosen via cross-validation or the L-curve method
• Benefit: Essential for high-order memory polynomial models where basis functions become highly correlated

A greedy sparse approximation algorithm that iteratively selects the most correlated basis function from a dictionary to build a compact predistorter model. OMP provides an alternative to full LS estimation when model complexity must be minimized.

• Process: Starts with an empty model, iteratively adds the basis function most correlated with the current residual
• Stopping Criterion: Terminates when residual power drops below a threshold or a maximum number of terms is reached
• Sparsity: Produces models with far fewer coefficients than full LS, reducing FPGA resource usage
• Application: Used in Volterra kernel pruning to identify only the most significant distortion terms