Glossary

Direct Learning Architecture (DLA)

A DPD training method that iteratively minimizes the error between the desired linear output and the actual power amplifier output to extract predistorter coefficients.

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DIGITAL PREDISTORTION LEARNING ARCHITECTURES

What is Direct Learning Architecture (DLA)?

A closed-loop parameter identification method for digital predistortion that directly minimizes the error between the desired linear output and the actual power amplifier output.

Direct Learning Architecture (DLA) is a DPD coefficient extraction method that iteratively minimizes the error between the ideal linear output and the actual power amplifier (PA) output. Unlike the Indirect Learning Architecture (ILA), DLA places the predistorter before the PA in the estimation loop, directly solving for the inverse model without assuming commutability.

DLA employs a post-distorter model to identify the PA's inverse characteristic by comparing the attenuated PA output to the original input signal. This approach is inherently more robust to noisy feedback and loop delay estimation errors, making it preferred for strongly nonlinear devices like Doherty amplifiers where the ILA assumption of commutability breaks down.

LEARNING ARCHITECTURE COMPARISON

DLA vs. ILA: Key Differences

Structural and operational comparison between Direct Learning Architecture and Indirect Learning Architecture for adaptive digital predistortion coefficient extraction.

Feature	Direct Learning Architecture (DLA)	Indirect Learning Architecture (ILA)	Notes
Estimation Target	Predistorter coefficients directly	Postdistorter coefficients (inverse model)	ILA copies postdistorter to predistorter
Requires PA Inverse Model			ILA avoids explicit inversion by swapping blocks
Optimization Criterion	Minimizes PA output error directly	Minimizes postdistorter output error	DLA optimizes true linearization objective
Sensitivity to Measurement Noise	Higher	Lower	Noise in feedback path biases DLA gradient
Convergence Speed	Slower (iterative)	Faster (single-shot LS)	ILA uses batch least-squares; DLA requires iterations
Bias Under Noisy Feedback	Unbiased estimate possible	Biased estimate	ILA bias from regressor noise correlation
Compatibility with Neural Network DPD	Native support	Requires model inversion	DLA integrates naturally with gradient-based NN training
Numerical Stability	Requires regularization	Generally stable	DLA Hessian can be ill-conditioned; ridge regression typical

DIRECT LEARNING ARCHITECTURE

Frequently Asked Questions

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

Direct Learning Architecture (DLA) is a closed-loop DPD training method that iteratively minimizes the error between the desired linear output and the actual power amplifier (PA) output to directly extract predistorter coefficients. Unlike the Indirect Learning Architecture (ILA), DLA does not require a post-inverse model identification step. The architecture places the predistorter before the PA, computes the error signal e(n) = y_desired(n) - y_actual(n), and uses this error to update the predistorter parameters via an adaptive algorithm such as least mean squares (LMS) or recursive least squares (RLS). This direct error minimization makes DLA theoretically more robust to measurement noise in the feedback path and avoids the bias introduced when the PA's nonlinear characteristics violate the commutability assumption inherent in ILA approaches.

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DIRECT LEARNING ARCHITECTURE ECOSYSTEM

Related Terms

Understanding DLA requires familiarity with the core algorithms, alternative architectures, and implementation challenges that define adaptive predistortion systems.

Indirect Learning Architecture (ILA)

The primary alternative to DLA that identifies the predistorter by placing it after the power amplifier model in the estimation loop. Unlike DLA, ILA avoids the need to compute an explicit inverse model of the PA, instead using a post-inverse approach. The key trade-off: ILA is computationally simpler but can be sensitive to measurement noise in the feedback path, while DLA directly minimizes the linearization error at the PA output.

Post-Inverse

Estimation Strategy

Noise Sensitive

Primary Limitation

Least Squares (LS) Estimation

The foundational coefficient extraction algorithm used in DLA training loops. At each iteration, DLA formulates a linear regression problem relating the predistorter input to the desired linear output, then solves for coefficients using LS. Key considerations:

Batch LS: processes entire data blocks for offline extraction
Recursive LS (RLS): updates coefficients sample-by-sample for online adaptation
Regularized LS: adds ridge regression penalties to improve numerical stability when the data matrix is ill-conditioned

Loop Delay Estimation

A critical prerequisite for DLA convergence. The time delay between the transmitted reference signal and the observed PA feedback must be accurately measured and aligned. Even sub-sample misalignment can degrade linearization performance by 5-10 dB in ACLR. Common techniques:

Cross-correlation with fractional interpolation
Frequency-domain phase slope estimation
Farrow structure fractional delay filters for precise sub-sample alignment

5-10 dB

ACLR Degradation from Misalignment

Sub-Sample

Required Alignment Precision

Generalized Memory Polynomial (GMP)

A widely-used predistorter model structure often paired with DLA training. GMP extends the standard memory polynomial by including cross-terms between delayed signal samples and their envelope powers, capturing complex memory effects that simpler models miss. DLA extracts GMP coefficients by iteratively minimizing the error between the desired linear output and the actual PA output, making it well-suited for strongly nonlinear devices with significant memory.

Coefficient Interpolation

A technique to reduce DLA calibration overhead across multiple operating conditions. Instead of running full DLA training at every frequency, power level, and temperature, coefficients are extracted at a sparse grid of conditions, then interpolated for uncalibrated states. Methods include:

Linear interpolation in the coefficient space
Nearest-neighbor lookup with adaptive thresholding
Neural network-based coefficient prediction trained on extracted DLA results

Numerical Stability in DLA

DLA coefficient extraction can suffer from ill-conditioned data matrices, especially when the PA exhibits strong nonlinearity or when the training signal has limited dynamic range. Mitigation strategies:

Ridge regression (Tikhonov regularization): adds a penalty term to the LS cost function
Singular value decomposition (SVD): identifies and suppresses unstable modes
Signal conditioning: ensures the training waveform adequately excites all nonlinear orders
Iterative refinement: uses successive DLA iterations with decreasing regularization

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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