Online Learning

Unlike offline training, online learning processes each incoming sample or batch in a streaming fashion, updating the predistorter weights incrementally. The system minimizes the error between the desired linear output and the actual PA output in real time, allowing the DPD to track slow-varying impairments such as thermal memory effects and bias circuit drift. This is typically implemented using stochastic gradient descent variants with small, constant learning rates to ensure stability during live operation.

The core mechanism relies on a feedback observation receiver that digitizes a coupled sample of the PA output. This signal is compared against the ideal reference to generate an error vector in the complex baseband domain. The error is backpropagated through the neural network to adjust the predistorter coefficients. This Direct Learning Architecture (DLA) continuously minimizes the Normalized Mean Squared Error (NMSE) between the transmitted and intended waveforms, compensating for both AM/AM and AM/PM distortions.

Power amplifiers exhibit time-varying nonlinear behavior due to several physical phenomena:

• Thermal memory effects: Die temperature changes alter transistor gain and phase characteristics over milliseconds to seconds.
• Aging effects: Semiconductor degradation over months shifts the optimal bias point and linearity profile.
• Load impedance variation: Antenna mismatch due to environmental changes alters the PA's output reflection coefficient. Online learning continuously re-estimates the inverse PA transfer function to maintain spectral mask compliance under all conditions.

To prevent the model from becoming biased by old, irrelevant data, online learning algorithms incorporate a forgetting factor (λ) or exponential weighting. Recent samples are given higher importance in the loss function, enabling the neural network to gracefully discard outdated PA characteristics. This is critical during rapid environmental shifts, such as a transmit power change or carrier frequency hop, where the historical error surface no longer represents the current nonlinearity.

Real-time online learning imposes strict latency budgets. For a 100 MHz 5G NR signal, the predistorter must process samples at 491.52 Msps or higher. The coefficient update path must operate in parallel without blocking the inference pipeline. Implementation strategies include:

• Pipelined gradient computation on FPGA fabric.
• Mini-batch updates accumulated over short intervals.
• Reduced-precision training using 16-bit or 8-bit floating-point arithmetic. The update rate is typically orders of magnitude slower than the sample rate, allowing complex gradient calculations to span multiple clock cycles.

A critical design consideration is preventing the adaptive loop from diverging or oscillating. Techniques include:

• Gradient clipping to bound the magnitude of weight updates.
• Leakage factors that slowly decay weights toward zero, preventing unbounded growth.
• Learning rate scheduling that reduces the step size as the error floor is approached.
• Regularization terms (L2 weight decay) in the online loss function. These mechanisms ensure the Adjacent Channel Leakage Ratio (ACLR) monotonically improves and stabilizes without introducing transient spectral regrowth during adaptation.

A closed-loop adaptive topology where the predistorter coefficients are updated by directly minimizing the error between the power amplifier's output and the desired linear reference signal.

• Operates on the actual transmitted signal, not an assumed model
• Requires a feedback observation receiver to capture PA output
• Naturally compensates for time-varying PA drift due to temperature and aging
• Eliminates the commutability assumption required by indirect methods

An open-loop identification method where a postdistorter neural network is first trained on the PA's output signal, then copied to the predistorter position.

• Assumes the nonlinear blocks are commutable (swap order without effect)
• Training occurs offline on captured data before deployment
• Simpler to implement but less adaptive to real-time PA variations
• Often used as an initial model before transitioning to online DLA fine-tuning

An adaptive filtering algorithm that recursively updates predistorter coefficients by minimizing a weighted least-squares cost function with exponential forgetting.

• Fast convergence compared to gradient-based methods like LMS
• Forgetting factor λ controls the memory of past data (typical range: 0.95–0.999)
• Computational complexity of O(N²) where N is the number of coefficients
• Well-suited for tracking slowly varying PA characteristics in real-time

A lightweight online training method where neural network weights are updated sample-by-sample or in small mini-batches using the instantaneous error gradient.

• Low latency update suitable for high-bandwidth signals
• Learning rate scheduling is critical to balance stability and tracking speed
• Can be combined with momentum to smooth updates in noisy gradient estimates
• Often implemented directly on FPGA fabric for real-time coefficient adaptation

A practical technique where predistorter coefficients are updated during idle periods or low-traffic slots, then frozen during active transmission to maintain stability.

• Prevents transient distortion during coefficient switching
• Look-up table (LUT) entries can be interpolated between update cycles
• Critical for maintaining ACLR compliance during live traffic
• Enables scheduled model updates aligned with network timing

The ability of an online-trained predistorter to maintain linearization performance when the signal statistics change—such as bandwidth, power level, or modulation scheme.

• Catastrophic forgetting can occur if the model overfits to recent data
• Elastic weight consolidation (EWC) preserves critical parameters from earlier training
• Regularization techniques prevent the model from chasing noise in the feedback path
• Validation on held-out signal types ensures robust generalization