Coefficient Interpolation

Traditional DPD requires exhaustive characterization across every combination of frequency, power, and temperature. Coefficient interpolation collapses this measurement space by extracting coefficients at a limited set of anchor points and deriving intermediate values mathematically.

• Reduces factory calibration time from hours to minutes
• Enables field adaptation without full retraining
• Critical for massive MIMO arrays where per-element calibration is impractical

Coefficients are interpolated across multiple operating dimensions simultaneously. Common domains include:

• Carrier frequency: Coefficients shift with center frequency changes
• Average input power: Nonlinearity severity varies with drive level
• Temperature: Thermal memory effects alter optimal predistorter shape
• Beam-steering angle: In phased arrays, active impedance mismatch changes per-element behavior

Multivariate interpolation techniques like thin-plate splines or radial basis functions handle these coupled dependencies.

The choice of interpolation method balances accuracy against computational complexity:

• Linear interpolation: Simple, low-latency, but may miss nonlinear coefficient trajectories
• Polynomial interpolation: Higher accuracy for smooth coefficient surfaces, risks Runge phenomenon at boundaries
• Spline interpolation: Piecewise polynomial fits that maintain continuity at anchor points
• Neural network interpolation: A small auxiliary network learns the mapping from operating conditions to coefficient vectors, capturing complex nonlinear relationships

For GaN power amplifiers with strong thermal memory, nonlinear methods often outperform linear approaches.

DPD coefficients are complex-valued (I/Q), requiring interpolation that preserves both magnitude and phase relationships. Direct interpolation on real and imaginary parts separately can introduce phase discontinuities.

• Magnitude-phase decomposition: Interpolate magnitude and unwrapped phase independently
• Complex spline interpolation: Operates directly in the complex plane
• Riemannian manifold methods: Treat coefficients as points on a complex hypersphere for geometrically consistent interpolation

Proper handling prevents spectral regrowth artifacts that would otherwise defeat the purpose of linearization.

In operational environments, operating conditions drift continuously. Adaptive interpolation updates the coefficient surface online as new measurements become available:

• Recursive least squares (RLS) updates the interpolation function incrementally
• Kalman filtering tracks time-varying coefficient trajectories with uncertainty estimates
• Gaussian process regression provides both interpolated coefficients and confidence bounds

This enables closed-loop DPD that tracks amplifier aging, temperature fluctuations, and load variations without interrupting transmission.

The quality of interpolation depends critically on where anchor points are placed in the operating space. Optimal selection minimizes the maximum interpolation error:

• Uniform gridding: Simple but inefficient for nonlinear coefficient surfaces
• Curvature-aware sampling: Places more anchors where coefficient surfaces change rapidly
• Sequential experimental design: Iteratively adds anchors at points of maximum predicted uncertainty
• Mutual information maximization: Selects anchors that provide the most information about unmeasured regions

For mmWave beamforming arrays, anchor points must also account for beam-angle-dependent impedance variations.