Principal Component Analysis (PCA) for DPD

PCA transforms the original, highly correlated polynomial basis function matrix into a set of orthogonal principal components. This eliminates multicollinearity, which is the primary cause of ill-conditioned data matrices in memory polynomial models. The resulting components are uncorrelated, ensuring that each captures unique variance in the PA's nonlinear behavior without redundancy.

Each principal component is associated with an eigenvalue that quantifies the amount of variance it captures from the original basis function set. PCA ranks components in descending order of their eigenvalues, allowing engineers to identify which distortion mechanisms are statistically dominant. This provides a clear, quantitative criterion for model truncation:

• The first few components typically capture >99% of the nonlinear behavior
• Low-variance components often represent noise or measurement artifacts

By projecting the basis function matrix onto its principal components, PCA dramatically reduces the condition number of the data matrix used in coefficient estimation. A lower condition number means:

• Least squares (LS) and recursive least squares (RLS) algorithms converge faster
• The solution is less sensitive to quantization noise in fixed-point FPGA implementations
• Matrix inversion during QR decomposition (QRD) becomes numerically stable

PCA enables systematic model order reduction by retaining only the top k principal components that cumulatively explain a target percentage of variance (e.g., 99.9%). This directly reduces the number of coefficients the predistorter must compute in real time. For a GMP model with hundreds of cross-terms, PCA can often reduce the active coefficient count by 50-80% with negligible degradation in adjacent channel power ratio (ACPR).

Low-variance principal components frequently model noise and measurement artifacts rather than true PA nonlinear dynamics. By discarding these components, PCA acts as an implicit regularization mechanism, similar to ridge regression but with a discrete cutoff. This prevents the predistorter from fitting to training data idiosyncrasies, ensuring robust linearization performance when the signal statistics or environmental conditions shift.

In online training architectures, the PCA transformation matrix can be computed once during an initial calibration phase and then held fixed. Subsequent coefficient updates operate in the reduced-dimensional principal component space, requiring fewer multiply-accumulate operations per iteration. This is critical for FPGA-based DPD implementations where update latency must remain below the coherence time of the PA's thermal memory effects.