Offline Training

Unlike online methods that process samples sequentially, offline training operates on the entire captured dataset at once. The algorithm has access to all input-output pairs simultaneously, enabling globally optimal solutions through batch linear algebra techniques.

• Processes full capture buffers in a single computation cycle
• Enables use of SVD and QR decomposition for numerical stability
• Eliminates convergence transients present in iterative methods
• Typical dataset sizes: 10,000 to 100,000 sample pairs

The dominant mathematical framework for offline coefficient extraction is the least squares (LS) method. The algorithm minimizes the sum of squared errors between the desired linear output and the actual predistorted signal.

• Solves the Normal Equation: w = (X^H X)^-1 X^H y
• Produces the Wiener-optimal solution for stationary data
• Computationally dominated by matrix inversion: O(N^3) complexity
• Can incorporate regularization parameters to prevent ill-conditioning

When the input correlation matrix becomes ill-conditioned—common with narrowband or highly correlated signals—direct matrix inversion fails. Offline training employs robust factorization methods to maintain accuracy.

• QR decomposition with Givens rotations avoids explicit matrix inversion
• Singular Value Decomposition (SVD) handles rank-deficient matrices
• Condition number monitoring detects ill-conditioning before computation
• Tikhonov regularization adds a diagonal loading term for stability

Offline training follows a structured capture-then-compute pipeline. The process begins with stimulus signal generation and ends with validated coefficient vectors ready for hardware deployment.

• Step 1: Generate a spectrally rich stimulus signal covering the target bandwidth
• Step 2: Capture synchronized PA input-output data via vector signal analyzer
• Step 3: Time-align and normalize captured waveforms
• Step 4: Construct the regression matrix from the model basis functions
• Step 5: Solve for coefficients using LS, QR-RLS, or SVD methods

The fundamental limitation of offline training is its reliance on time-invariance. Coefficients computed from a single capture session cannot adapt to changing conditions without retraining.

• Assumes amplifier behavior remains constant between training sessions
• Vulnerable to thermal drift, aging, and supply voltage variations
• Requires periodic recalibration cycles in slowly varying environments
• Contrasts with online training which tracks changes sample-by-sample

With access to finite training data, offline methods risk fitting measurement noise rather than true amplifier dynamics. Regularization and validation strategies are essential for generalization.

• Early stopping in iterative batch solvers prevents noise fitting
• Cross-validation on held-out data segments verifies generalization
• Model order selection balances bias-variance tradeoff
• Minimum description length criteria guide parsimonious model selection