Direct Learning Architecture

DLA operates by forming a feedback loop around the entire transmission chain. The architecture computes the error signal as the difference between the reference input and the attenuated PA output. An adaptive algorithm then iteratively adjusts the predistorter coefficients to drive this error to zero. This direct minimization of the linearized output error distinguishes DLA from indirect learning architectures that train on the pre-inverse.

Because the predistorter and power amplifier are cascaded nonlinear systems, the error surface is generally non-convex with respect to the predistorter parameters. DLA must employ iterative optimization techniques to navigate this surface. Common approaches include:

• Newton-Raphson methods for rapid local convergence
• Stochastic gradient descent for sample-by-sample adaptation
• Levenberg-Marquardt for robust parameter updates This nonlinear optimization requirement makes DLA computationally more intensive than indirect methods but yields superior linearization performance.

A practical DLA implementation often begins with an initial identification stage. During this phase, a post-distorter model is trained using the PA input and output data to obtain a coarse estimate of the inverse amplifier characteristic. This initial model is then copied to the predistorter to provide a starting point for the closed-loop adaptation. This two-stage approach prevents the DLA from diverging during the initial convergence period and accelerates the overall adaptation time.

The DLA adaptation engine continuously monitors the residual distortion at the PA output. Key components of the update path include:

• Observation receiver: Captures the attenuated PA output with high linearity
• Time alignment: Aligns reference and feedback signals to sub-sample accuracy
• Error computation: Subtracts the aligned reference from the feedback
• Coefficient solver: Executes the optimization algorithm to compute updated predistorter parameters This continuous tracking capability allows DLA to compensate for thermal drift, aging effects, and dynamic load changes during live operation.

DLA stability depends critically on the loop gain and adaptation step size. If the step size is too large, the system may oscillate or diverge. If too small, convergence becomes unacceptably slow. Practical implementations employ variable step-size algorithms such as Normalized Least Mean Squares (NLMS) that scale the update by the inverse of the input signal power. Additionally, leakage factors are often introduced to prevent coefficient drift in low-excitation conditions, ensuring robust operation across varying signal statistics.

While both DLA and Indirect Learning Architecture (ILA) aim to linearize the PA, they differ fundamentally in their optimization targets:

• ILA: Minimizes the error between the predistorter output and the post-distorter output, assuming the post-inverse equals the pre-inverse
• DLA: Minimizes the error between the reference signal and the actual PA output directly DLA avoids the copy error inherent in ILA where the post-distorter is assumed to be identical to the predistorter. This makes DLA more accurate, especially when measurement noise is present in the feedback path, but at the cost of higher computational complexity.

The primary alternative to DLA. ILA trains a post-distorter model on the PA output and copies it to the predistorter, avoiding direct inverse modeling. Key differences:

• Does not require the ideal reference signal in the training loop
• Assumes the post-distorter and predistorter are interchangeable
• More sensitive to measurement noise in the feedback path
• Simpler to implement but less robust than DLA for strong nonlinearities

A stochastic gradient descent algorithm frequently used for iterative coefficient updates within DLA. LMS adapts predistorter weights sample-by-sample to minimize instantaneous squared error. Characteristics:

• Extremely low computational complexity per iteration
• Slow convergence for correlated input signals
• Step size controls the stability-convergence tradeoff
• Often replaced by NLMS in practical DLA implementations for improved stability

An adaptive filtering algorithm offering faster convergence than LMS at higher computational cost. In DLA contexts, RLS updates coefficients by minimizing a weighted least-squares criterion recursively:

• Converges an order of magnitude faster than LMS
• Incorporates a forgetting factor to track time-varying PA behavior
• Computational complexity of O(N²) versus O(N) for LMS
• Preferred when rapid adaptation to changing amplifier characteristics is critical

The residual nonlinear distortion that DLA explicitly minimizes. Calculated as the difference between the ideal linear output and the actual PA output after predistortion. This error signal:

• Drives the coefficient adaptation loop in DLA
• Directly correlates with Adjacent Channel Leakage Ratio (ACLR) improvement
• Must be captured through a linear feedback receiver with sufficient dynamic range
• Convergence of this error to zero indicates successful linearization

A critical pre-processing step for DLA implementation. The propagation delay through the transmit chain, PA, and observation receiver must be precisely measured to align reference and feedback signals. Requirements:

• Sub-sample accuracy for wideband signals
• Typically estimated via cross-correlation techniques
• Misalignment causes coefficient divergence and spectral regrowth
• Must be re-estimated if hardware configuration changes

A complementary system identification approach that constructs a mathematical replica of the PA by mapping input signals to measured outputs. While DLA directly optimizes the predistorter, forward modeling:

• Provides an accurate PA behavioral model for simulation
• Can be used to validate DLA performance offline
• Serves as the foundation for indirect learning architectures
• Often employs the same basis functions (memory polynomials, Volterra series) as DLA predistorters