Direct Learning Architecture (DLA)

DLA operates by forming a direct error signal between the desired linear output and the actual PA output. This error is used to update the predistorter coefficients through iterative optimization, typically using stochastic gradient descent or Levenberg-Marquardt algorithms. Unlike indirect methods, there is no intermediate PA model identification step.

• Error signal: e(n) = y_desired(n) - y_pa(n)
• Directly minimizes NMSE and EVM
• Requires a feedback observation path with sufficient linearity and bandwidth

In DLA, the predistorter is placed before the PA, but its parameters are identified by observing the signal after the PA. This creates a non-trivial optimization problem because the predistorter coefficients appear non-linearly in the error function. The system must backpropagate through the unknown PA transfer function.

• Requires an analytically differentiable PA model or a real-time approximation
• Often uses a two-step approach: forward PA modeling followed by iterative inverse identification
• More computationally intensive than ILA but achieves superior linearization

DLA excels at tracking time-varying PA behavior caused by temperature drift, aging, and antenna load mismatch. The direct error formulation allows the adaptation algorithm to respond immediately to changes in the PA's non-linear characteristics without waiting for a separate model identification cycle.

• Supports sample-by-sample or block-based coefficient updates
• Effective for envelope tracking PAs where supply voltage modulation changes the distortion profile dynamically
• Convergence rate depends on the condition number of the Hessian matrix in the optimization

Modern DLA systems increasingly use neural networks as the predistorter function, where the network weights are updated directly from the PA output error. Architectures include:

• Real-Valued Time-Delay Neural Networks (RVTDNN) with tapped delay lines for memory effects
• Augmented Real-Valued Time-Delay Neural Networks (ARVTDNN) with envelope-dependent terms
• Recurrent Neural Networks (RNN) for long-term memory dependencies
• Convolutional Neural Networks (CNN) for spectral feature extraction

Training uses backpropagation through time with the PA in the loop, requiring a differentiable PA surrogate model.

DLA's direct error formulation can suffer from local minima and instability if the initial predistorter parameters are far from the optimal solution. Mitigation strategies include:

• Pre-training the predistorter using ILA before switching to DLA for fine-tuning
• Regularization terms in the cost function to penalize large coefficient jumps
• Learning rate scheduling with warm restarts to escape local minima
• Gradient clipping to prevent divergence during transient conditions

The Bussgang theorem provides theoretical guarantees for convergence when the PA non-linearity is memoryless and the input signal is Gaussian.

While ILA swaps the PA input and output to estimate the post-distorter and then copies it to the predistorter, DLA directly optimizes the predistorter in place. Key trade-offs:

• DLA advantage: Superior performance when measurement noise is present in the feedback path
• DLA advantage: No copy error from post-distorter to predistorter
• ILA advantage: Lower computational complexity per iteration
• ILA advantage: Simpler implementation without needing a differentiable PA model

DLA typically achieves 1-3 dB better ACLR than ILA in practical deployments with noisy feedback receivers.

The iterative process by which DLA updates predistorter parameters in real time. Adaptation algorithms—such as Least Mean Squares (LMS), Recursive Least Squares (RLS), or gradient-based optimizers—minimize the error signal between the desired linear output and the actual PA output. DLA's closed-loop nature allows it to track thermal drift, aging effects, and load mismatch without interrupting transmission.

DLA directly identifies the inverse transfer function of the power amplifier. This is mathematically challenging because the PA's compression region makes the inverse ill-conditioned. Neural network-based DLA architectures—such as Real-Valued Time-Delay Neural Networks (RVTDNN)—excel here by learning complex, non-monotonic inverse mappings that polynomial models struggle to represent.

DLA is inherently suited for online adaptation because it operates during live transmission. The error signal is continuously observed at the PA output, and coefficients are updated sample-by-sample or frame-by-frame. This contrasts with offline training methods that require dedicated training sequences and cannot respond to dynamic environmental changes such as antenna VSWR variations.

The primary optimization target in DLA. EVM quantifies the deviation of transmitted constellation points from their ideal positions, capturing both AM-AM and AM-PM distortion. DLA directly minimizes EVM by reducing the error between the predistorter input and the PA output, making it a more direct optimization criterion than the indirect post-distorter error used in ILA.

A widely used behavioral model structure often employed as the predistorter basis function within DLA. GMP extends the memory polynomial with cross-terms between the signal and its lagging or leading envelope values, capturing complex memory effects. When combined with DLA's direct error minimization, GMP-based predistorters achieve excellent linearization for Doherty amplifiers and other high-efficiency PA architectures.