Coefficient Drift

Power amplifier junction temperature directly modulates transistor gain and phase characteristics. As the PA heats up during operation, the optimal predistorter coefficients shift. GaN and GaAs devices exhibit distinct thermal time constants—fast electrical memory effects (nanoseconds) and slow thermal trapping effects (milliseconds to seconds). Without continuous adaptation, a DPD trained at cold-start will undercompensate as the amplifier reaches thermal equilibrium, causing spectral regrowth and degraded ACPR.

Over months and years, semiconductor hot carrier injection, gate oxide breakdown, and electromigration alter transistor behavior. These physical changes shift the PA's AM-AM and AM-PM characteristics. A predistorter trained during factory calibration will gradually mismatch the aged amplifier. Bias voltage drift in the gate supply and capacitor dielectric aging further compound the problem. Long-term drift necessitates periodic recalibration or continuous online adaptation.

Adaptive algorithms like RLS and LMS can suffer from coefficient drift due to finite-precision arithmetic. In fixed-point FPGA implementations, quantization errors accumulate during recursive updates. Ill-conditioned covariance matrices with high condition numbers amplify rounding errors, causing coefficients to wander even when the PA characteristic is static. Techniques like QR-RLS and Tikhonov regularization stabilize the solution by improving numerical conditioning.

Fluctuations in the PA's drain bias voltage directly alter its gain compression point and nonlinear transfer function. In envelope tracking systems, the dynamic supply modulation intentionally varies voltage, but unintended ripple or load transients cause unpredictable coefficient shifts. Battery-powered devices experience voltage sag during discharge, while automotive and aerospace systems face wide input voltage ranges. DPD coefficients optimized at nominal voltage become suboptimal under these variations.

Antenna VSWR changes due to environmental factors—proximity to objects, moisture, or physical damage—alter the impedance seen by the PA output. This modifies the load-pull contours and shifts the optimal predistorter coefficients. In mobile handsets, the antenna impedance varies with grip position and case material. Mismatch-induced drift is particularly severe in massive MIMO arrays where mutual coupling between elements creates dynamic impedance interactions.

A primary physical cause of coefficient drift. As the power amplifier heats up during operation, its nonlinear transfer function changes dynamically. This is distinct from electrical memory effects; thermal time constants are much slower (milliseconds to seconds).

• Self-heating: Bias point shifts due to dissipated power.
• Environmental changes: Ambient temperature swings alter the quiescent operating point.
• GaN/GaAs sensitivity: Wide-bandgap semiconductors exhibit strong thermal dependencies that must be tracked by the predistorter.

A computational source of drift where the coefficient estimation algorithm fails to converge to a stable solution. This often occurs in fixed-point hardware implementations.

• Ill-conditioning: A high condition number in the data covariance matrix amplifies rounding errors.
• QR-RLS mitigation: Using QR decomposition-based Recursive Least Squares prevents the divergence seen in standard RLS.
• Tikhonov Regularization: Adds a penalty term to the cost function to stabilize the matrix inversion process.

Long-term physical changes in the power amplifier hardware that permanently alter its nonlinear characteristics, requiring the adaptive filtering system to track a moving target.

• Gate oxide trapping: Charge accumulation in the transistor gate region shifts the threshold voltage.
• Drain lag: Slow transient responses caused by deep-level traps in the semiconductor.
• Bias network drift: Passive component values (capacitors, resistors) changing over years of operation.

The primary architectural defense against coefficient drift. A closed-loop DPD system continuously monitors the transmit observation path to compute the error between the desired signal and the actual PA output.

• Sample-by-sample update: Corrects drift instantly but demands high computational throughput.
• Block update: Processes batches of samples to reduce noise in the cost function gradient.
• Burst training: Updates coefficients only during specific idle periods to save power.

In a Direct Learning Architecture (DLA), drift occurs if the model inversion process becomes inaccurate. The predistorter is derived by mathematically inverting the PA model, which is highly sensitive to estimation errors.

• Levenberg-Marquardt: A robust optimization algorithm that prevents divergence during the inversion of ill-conditioned models.
• Indirect Learning (ILA): Avoids explicit inversion by training a postdistorter and copying its coefficients, often proving more stable against drift in volatile conditions.