Glossary

Indirect Learning Architecture (ILA)

A DPD coefficient extraction topology where a post-distorter model is trained on the power amplifier's output and then copied to the predistorter, avoiding the need to assume a specific PA model during identification.

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DPD COEFFICIENT EXTRACTION

What is Indirect Learning Architecture (ILA)?

A DPD training topology that identifies the predistorter by first learning a post-distorter on the power amplifier's output, then copying its parameters to the forward path.

Indirect Learning Architecture (ILA) is a digital predistortion coefficient extraction method where a post-distorter model is trained to linearize the power amplifier's output in a feedback path, and its converged parameters are subsequently copied to the identical predistorter core in the forward transmission path. This topology avoids the need to assume or derive a specific inverse PA model during identification, instead leveraging the fact that if a post-inverse exists, it is mathematically equivalent to the pre-inverse under the nonlinearity order commutation assumption.

The ILA operates in two distinct phases: a training phase where the post-distorter adapts to minimize the error between its output and the original input signal, and a coefficient copying phase where the learned parameters are transferred to the forward predistorter. This architecture is particularly advantageous for FPGA-based DPD implementations because it decouples the training loop from the transmission chain, allowing complex coefficient estimation algorithms like least squares or LMS to run offline or in a slower supervisory processor without impacting the high-speed forward path latency.

Architecture

Key Characteristics of ILA

The Indirect Learning Architecture (ILA) is defined by a unique training topology that decouples coefficient extraction from the forward predistortion path, enabling model identification without assuming a specific PA model structure.

Post-Distorter Identification

The core mechanism of ILA involves training a post-distorter model in the feedback path. This model is placed after the power amplifier (PA) and is trained to minimize the error between its output and the PA's input. The key assumption is that if a post-distorter can linearize the PA's output, its parameters can be directly copied to the predistorter in the forward path. This avoids the need to mathematically invert a complex PA behavioral model.

Model-Agnostic Training

Unlike the Direct Learning Architecture (DLA), ILA does not require an explicit, invertible model of the power amplifier during the coefficient extraction phase. The training algorithm simply finds the parameters for a generic nonlinear filter (e.g., a Memory Polynomial) that best maps the PA's output back to its input. This makes ILA highly flexible and robust when the PA's physical characteristics are not perfectly known or are too complex for closed-form inversion.

Offline and Online Adaptation

ILA supports both offline characterization and online adaptation workflows. In offline mode, a long training sequence is used to extract initial coefficients in a lab setting. For online tracking, the post-distorter can be continuously trained on live traffic using algorithms like Least Mean Squares (LMS) or Recursive Least Squares (RLS). The updated coefficients are then periodically copied to the forward predistorter, enabling the system to track changes due to thermal memory effects and component aging.

Noise Sensitivity in the Feedback Path

A critical design consideration for ILA is its sensitivity to observation receiver noise. The post-distorter is trained on the PA's output signal, which includes any noise introduced by the feedback path's coupler, downconverter, and analog-to-digital converter. This noise can bias the coefficient estimation, leading to a suboptimal predistorter. Mitigation strategies include high-precision time alignment and averaging over multiple training iterations to decorrelate the noise.

PACT Index: Computational Complexity

The computational cost of ILA is dominated by the post-distorter training algorithm. For a Memory Polynomial model, the complexity scales with the polynomial order and memory depth. Key metrics include:

Multiply-Accumulate Operations (MACs): High, driven by matrix inversions in batch Least Squares (LS) estimation.
Adaptation Rate: Slower than DLA for iterative methods, as the post-distorter must first converge before the predistorter is updated.
Hardware Footprint: The training engine, often implemented in embedded ARM cores on a Zynq UltraScale+, requires significant DSP resources for real-time operation.

O(N^3)

LS Estimation Complexity

ARM Core

Typical Training Processor

Assumption of Commutativity

The theoretical foundation of ILA rests on the commutativity assumption of the predistorter and the power amplifier. The architecture assumes that the cascaded order of a nonlinear predistorter and a nonlinear PA can be swapped without changing the overall system output. While this holds perfectly for static, memoryless nonlinearities, it is an approximation for systems with strong memory effects. This assumption can limit the ultimate linearization floor achievable by ILA compared to more complex, direct-inverse architectures.

DPD LEARNING ARCHITECTURE COMPARISON

ILA vs. Direct Learning Architecture (DLA)

Structural and operational comparison of the two primary topologies for extracting digital predistortion coefficients.

Feature	Indirect Learning Architecture (ILA)	Direct Learning Architecture (DLA)
Core Principle	Trains a post-distorter on the PA output, then copies coefficients to the predistorter.	Directly identifies the predistorter by modeling the inverse of the PA using input and output signals.
Optimization Target	Minimizes error between post-distorter output and PA input (indirect criterion).	Minimizes error between desired linear output and actual PA output (direct criterion).
PA Model Requirement
Closed-Loop Stability	Inherently stable; identification loop is open-loop with respect to the forward path.	Requires careful design; the predistorter is inside the estimation loop, risking instability.
Sensitivity to Feedback Noise	Low; noise in the observation path does not directly corrupt the forward predistorter input.	High; feedback noise is directly injected into the coefficient estimation algorithm.
Convergence Speed	Typically slower; requires multiple iterations of post-distorter training and coefficient copying.	Potentially faster; can converge in a single step if the inverse model is well-conditioned.
Hardware Implementation Complexity	Lower; the training engine operates on a copy of the signal path, simplifying pipelining.	Higher; requires tight synchronization between the forward and observation paths for real-time estimation.

INDIRECT LEARNING ARCHITECTURE

Frequently Asked Questions

Clear, technically precise answers to the most common questions about the Indirect Learning Architecture for digital predistortion coefficient extraction.

The Indirect Learning Architecture (ILA) is a DPD coefficient extraction topology where a post-distorter model is trained on the power amplifier's output and then copied to the predistorter, avoiding the need to assume a specific PA model during identification. The architecture operates in two distinct phases: first, the PA output signal is fed into a 'post-distorter' block whose coefficients are estimated by minimizing the error between its output and the original transmitted signal. Once convergence is achieved, these identical coefficients are directly copied to the predistorter block placed before the PA in the forward transmission path. This elegant decoupling means the coefficient extraction process never requires knowledge of the PA's internal nonlinear transfer function—the algorithm simply learns the inverse mapping from output to input. The ILA is particularly advantageous because it transforms the nonlinear inverse modeling problem into a linear-in-parameters estimation task when using polynomial-based predistorter structures, enabling computationally efficient Least Squares (LS) or Recursive Least Squares (RLS) solutions.

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KEY CONCEPTS

Related Terms

Understanding the Indirect Learning Architecture requires familiarity with the core components, algorithms, and hardware interfaces that enable its real-time, adaptive operation.

Direct Learning Architecture (DLA)

The primary alternative to ILA. In a DLA, the predistorter parameters are estimated by directly modeling the inverse of the power amplifier's nonlinear behavior. This requires a pre-assumed PA model, unlike ILA, which identifies the post-distorter first. DLA can be more sensitive to measurement noise in the feedback path.

EXPLORE

Coefficient Extraction & Copy

The defining two-step process of ILA:

Training: A post-distorter model is trained on the PA's output to learn the inverse nonlinearity.
Copy: The converged coefficients are copied directly to the identical predistorter block in the forward transmission path. This architecture avoids the need for a nonlinear optimization loop to find the PA's inverse.

Time Alignment

A critical signal processing prerequisite for ILA. The transmitted reference signal and the observed PA feedback signal must be precisely synchronized in time before model extraction. Even sub-sample misalignments can severely degrade the accuracy of the extracted Volterra kernels or Memory Polynomial coefficients, leading to poor linearization.

Memory Polynomial Model

A widely used behavioral model structure within ILA systems. It captures both the static nonlinearity and the memory effects of a power amplifier by including delayed envelope terms. It is a pruned version of the full Volterra series, offering a practical balance between modeling fidelity and the computational complexity required for real-time coefficient extraction.

FPGA Implementation with HLS

Modern ILA-based DPD systems are often deployed on FPGAs using High-Level Synthesis (HLS). The predistorter core, a complex multiplier applying the inverse nonlinearity, is implemented in the FPGA fabric for low latency. The coefficient extraction algorithm, often involving least-squares estimation, can run on an embedded ARM core in a device like the Zynq UltraScale+.

Real-Time Adaptation

While ILA can be used for offline model extraction, it is often deployed in an adaptive loop. The system continuously captures new PA output data, re-trains the post-distorter model in the background, and updates the predistorter coefficients without interrupting the live transmission. This ensures consistent linearization under dynamic conditions like temperature drift or channel frequency changes.

About the author

Prasad Kumkar

CEO & MD, Inference Systems

Prasad Kumkar is the CEO & MD of Inference Systems and writes about AI systems architecture, LLM infrastructure, model serving, evaluation, and production deployment. Over 5+ years, he has worked across computer vision models, L5 autonomous vehicle systems, and LLM research, with a focus on taking complex AI ideas into real-world engineering systems.

His work and writing cover AI systems, large language models, AI agents, multimodal systems, autonomous systems, inference optimization, RAG, evaluation, and production AI engineering.

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