Indirect Learning Architecture

The core mechanism of ILA involves training a post-distorter block placed after the power amplifier. The goal is to find coefficients that make the post-distorter's output match the PA's input. This is formulated as a standard system identification problem, where the PA's input and output are used as the training target and input, respectively. The post-distorter effectively learns the post-inverse of the PA.

• Avoids direct inverse modeling of the PA
• Uses PA input as the training target
• Formulated as a standard system identification problem

Once the post-distorter coefficients are estimated, they are directly copied to the pre-distorter block placed before the PA. This works under the assumption that the pre-inverse and post-inverse of a nonlinear system are identical for the Volterra series and its simplified variants. This copy operation is the defining characteristic that gives the architecture its 'indirect' name.

• Assumes pre-inverse equals post-inverse
• Simple coefficient transfer
• No additional training required for the pre-distorter

Unlike the Direct Learning Architecture (DLA), ILA performs coefficient extraction in an open-loop configuration. The post-distorter is trained offline or during dedicated training slots without being part of a closed feedback loop around the PA. This decoupling simplifies the estimation algorithm and avoids the stability concerns inherent in closed-loop adaptive systems.

• No feedback loop around the PA during training
• Simplifies algorithm stability analysis
• Suitable for offline and batch processing

The primary limitation of ILA is its sensitivity to model mismatch. The assumption that the pre-inverse equals the post-inverse is strictly valid only for exact Volterra models. When using simplified models like the Memory Polynomial, the copied pre-distorter may not perfectly linearize the PA, especially in the presence of strong nonlinearities or measurement noise.

• Performance degrades with simplified models
• Sensitive to measurement noise in training data
• May require iterative refinement for high-linearity targets

ILA commonly employs Least Squares (LS) estimation to extract the post-distorter coefficients. The training data (PA input and output) is arranged into a regression matrix, and the coefficients are solved by minimizing the squared error. This is computationally efficient and provides a closed-form solution, making it ideal for real-time implementation on embedded processors and FPGAs.

• Closed-form solution via matrix inversion
• Computationally efficient for real-time systems
• Can be extended with regularization (e.g., LASSO) for sparse models

In practical systems, ILA is often used as the initial coefficient extraction step, followed by periodic updates. A training sequence is transmitted, the PA output is captured via a feedback receiver, and the post-distorter is identified. The coefficients are then loaded into the pre-distorter. This process can be repeated at regular intervals to track changes in PA behavior due to temperature, aging, or channel frequency changes.

• Used for initial calibration and periodic updates
• Requires a dedicated feedback receiver path
• Tracks slow-varying PA changes effectively

A closed-loop DPD architecture that iteratively updates the pre-distorter coefficients by directly minimizing the error between the desired input and the power amplifier's output. Unlike the indirect method, it does not require a separate post-distorter identification step. The architecture solves for the pre-distorter parameters by minimizing the difference between the PA input and the pre-distorted signal, often using nonlinear optimization techniques. This approach can theoretically achieve better performance but requires the PA model to be invertible and the optimization to be computationally efficient for real-time adaptation.

A mathematical optimization technique used to extract Volterra kernel coefficients by minimizing the sum of the squared errors between the model's predicted output and the measured data. In the context of the Indirect Learning Architecture, least squares is the workhorse algorithm for identifying the post-distorter coefficients. The method assumes a linear relationship between the coefficients and the error, solving a system of normal equations. Its popularity stems from its analytical solution, which guarantees a global minimum for the given model structure, making it a fast and reliable batch processing method for initial coefficient extraction.

Real-time adaptive algorithms that update DPD coefficients continuously during transmission to track changing PA characteristics due to temperature drift, aging, or channel frequency shifts. While the standard Indirect Learning Architecture often operates in batch mode, adaptive variants use recursive least squares (RLS) or least mean squares (LMS) to update the post-distorter copy without interrupting the signal. This creates a seamless, closed-loop tracking system that maintains linearity under dynamic operating conditions.

Offline and online methods for capturing the behavioral model of a power amplifier from input-output measurements. The Indirect Learning Architecture fundamentally relies on a high-fidelity post-distorter model. Extraction techniques include:

• Swept power measurements to capture AM-AM and AM-PM profiles
• Modulated signal excitation with wideband waveforms to excite memory effects
• Time-domain system identification to solve for Volterra or memory polynomial coefficients Accurate model extraction is critical, as any error in the post-distorter model is directly copied to the pre-distorter.

The suite of algorithms responsible for computing the digital predistortion parameters that minimize out-of-band emissions and in-band distortion. In the Indirect Learning Architecture, these algorithms operate on the post-distorter block. Key methods include:

• Least Squares (LS) for batch processing
• Recursive Least Squares (RLS) for adaptive tracking
• Least Mean Squares (LMS) for low-complexity hardware implementation The choice of algorithm balances convergence speed, computational complexity, and numerical stability.

The primary objective of DPD, focused on reducing adjacent channel leakage ratio (ACLR) by canceling the nonlinear distortion products that cause spectral spreading. The Indirect Learning Architecture achieves this by first identifying a post-distorter that suppresses the PA's out-of-band emissions in a virtual loop, then applying that same nonlinear function as a pre-distorter. This effectively pre-distorts the signal with the inverse nonlinearity, ensuring the PA output remains spectrally clean and compliant with regulatory masks.