Direct Learning Architecture (DLA)

DLA operates by forming a closed feedback loop where the predistorter coefficients are updated based on the error between the power amplifier's output and the desired linear reference signal. Unlike Indirect Learning Architecture (ILA), which assumes commutability of nonlinear blocks, DLA directly minimizes the true linearization error. The error signal is computed as:

e(n) = y_PA(n)/G - x(n)

where y_PA(n) is the PA output, G is the linear gain, and x(n) is the reference input. This direct error formulation eliminates the model mismatch inherent in postdistorter-based approaches.

DLA employs iterative optimization algorithms to update neural network weights in real-time:

• Stochastic Gradient Descent (SGD): Updates coefficients sample-by-sample using the instantaneous gradient of the error surface
• Levenberg-Marquardt Algorithm: Provides faster convergence for batch-mode training by interpolating between Gauss-Newton and gradient descent
• Recursive Least Squares (RLS): Offers rapid convergence for linear-in-parameters predistorter structures

The update rule for a neural DLA predistorter using SGD is:

w(n+1) = w(n) - μ * ∇J(w)

where μ is the learning rate and ∇J(w) is the gradient of the mean squared error cost function with respect to the network weights.

A defining advantage of DLA is its ability to perform online learning during live signal transmission. This enables the predistorter to track:

• Thermal memory effects: PA characteristics drift as the transistor junction temperature changes during operation
• Aging effects: Gradual degradation of PA linearity over months and years of deployment
• Supply voltage variations: Envelope tracking systems that dynamically modulate the drain voltage
• Load impedance changes: Antenna mismatch conditions in mobile handsets

The online training loop continuously minimizes the Adjacent Channel Leakage Ratio (ACLR) and Error Vector Magnitude (EVM) without interrupting service.

For recurrent neural network (RNN) based predistorters within a DLA framework, the gradient of the error with respect to network parameters is computed using Backpropagation Through Time (BPTT). The process involves:

• Unrolling the RNN's temporal operations over a finite sequence length
• Propagating the error signal backward through the unrolled computational graph
• Accumulating gradients across time steps to update shared weights

This is computationally more intensive than standard backpropagation but essential for capturing the long-term memory effects of GaN Doherty power amplifiers in 5G base stations.

Before online adaptation begins, DLA requires an initial predistorter model. This is obtained through offline model extraction:

• A training signal (typically an OFDM waveform with high PAPR) is transmitted through the PA
• The PA input and output are captured synchronously using a vector signal analyzer
• The neural network is trained offline to minimize the linearization error
• The converged weights serve as the initialization point for online adaptation

Proper weight initialization using Xavier or He initialization is critical to ensure stable gradient flow when online training commences.

DLA's closed-loop nature introduces stability considerations not present in open-loop architectures:

• Learning rate sensitivity: An excessively high learning rate μ can cause the predistorter coefficients to oscillate or diverge, potentially damaging the PA
• Loop delay compensation: The feedback path delay must be accurately estimated and compensated to align the reference and feedback signals in time
• Gain normalization: The PA's linear gain G must be precisely estimated to scale the feedback signal correctly before error computation
• Regularization: L2 weight decay or dropout regularization prevents overfitting to specific signal characteristics during online adaptation

These constraints require careful hyperparameter tuning on validation datasets before deployment.