Direct Learning Architecture (DLA)

DLA operates by directly minimizing the error signal—the instantaneous difference between the desired linear output and the observed PA output captured by the feedback receiver. This closed-loop structure continuously monitors the PA's nonlinear behavior and adapts the predistorter coefficients in real-time. The architecture requires precise time alignment between the reference and feedback signals, often employing fractional delay filters to achieve sub-sample synchronization. Unlike open-loop methods, DLA inherently compensates for loop delay and feedback path impairments, making it robust to component aging, temperature drift, and manufacturing variances.

A defining characteristic of DLA is its reliance on an identified power amplifier behavioral model to compute the error gradient. During adaptation, the algorithm backpropagates the error through this PA model to determine how predistorter coefficients should be updated. This process, known as model extraction, requires accurate system identification of the PA's nonlinear dynamics. Common modeling approaches include:

• Memory polynomial models for capturing nonlinearity with memory effects
• Generalized memory polynomial structures for cross-term modeling
• Neural network-based models for highly complex distortion patterns The accuracy of the PA model directly impacts convergence rate and steady-state linearization performance.

DLA employs iterative optimization algorithms to update predistorter coefficients by minimizing a defined cost function. The architecture supports multiple adaptation strategies:

• Least Mean Squares (LMS): Simple stochastic gradient descent with low computational overhead, suitable for resource-constrained implementations
• Normalized LMS (NLMS): Improves convergence stability by normalizing step size by input signal power
• Recursive Least Squares (RLS): Offers faster convergence using a forgetting factor to track time-varying PA characteristics, at higher computational cost
• Stochastic Gradient Descent (SGD): Forms the backbone of online learning, updating parameters using gradients computed on instantaneous or mini-batch error samples The learning rate hyperparameter balances rapid convergence against steady-state misadjustment.

DLA implementations must address ill-conditioning of the correlation matrix formed by basis function autocorrelations. When the condition number is high, coefficient estimation becomes highly sensitive to small perturbations, leading to unstable or divergent behavior. Mitigation techniques include:

• QR decomposition for solving least-squares problems with superior numerical stability
• Regularization parameters added to the correlation matrix diagonal to prevent overfitting
• Coefficient freeze mechanisms that halt adaptation during low-input or unreliable feedback conditions These considerations are critical for FPGA-based DPD implementation using fixed-point arithmetic, where finite-precision effects can degrade numerical stability.

DLA supports background calibration, where DPD coefficients are updated transparently during normal data transmission without interrupting the communication link. This continuous training mode eliminates the need for dedicated training sequences or service interruptions. The architecture tracks:

• Thermal memory effects from PA self-heating during operation
• Long-term drift due to component aging and environmental changes
• Dynamic operating point shifts caused by varying signal PAPR Background calibration ensures consistent ACLR and EVM performance throughout the operational lifetime, a critical requirement for 5G base stations and mission-critical communication systems.

The predistorter in DLA is constructed from a set of basis functions—predefined nonlinear transformations applied to the input signal. These functions form the building blocks of the DPD model and directly influence linearization bandwidth and complexity. Common basis function sets include:

• Memory polynomial terms: Capturing nonlinearity with temporal memory effects
• Volterra series kernels: General framework for nonlinear systems with memory
• Orthogonal basis functions: Improving numerical conditioning of the estimation problem
• Augmented basis sets: Including cross-terms for multi-band DPD architectures and Doherty amplifier optimization The selection of basis functions represents a fundamental trade-off between modeling accuracy and computational complexity.

The primary alternative to DLA. ILA estimates predistorter coefficients by placing a copy of the predistorter in the feedback path, bypassing the need for explicit PA model identification. While simpler, ILA is theoretically suboptimal in the presence of significant measurement noise because it minimizes the post-distorter error rather than the true PA output error. DLA directly targets the amplifier's nonlinear output, offering superior performance when an accurate PA model is available.

The critical prerequisite for DLA operation. This process estimates the parameters of a behavioral model—such as a memory polynomial or neural network—from measured PA input-output data. The extracted model serves as the differentiable forward path required to compute the error gradient for predistorter adaptation. Accuracy here directly determines DLA performance; a poor model yields incorrect gradients and suboptimal linearization.

The mathematical objective that DLA seeks to minimize, typically the mean squared error between the desired linear output and the actual PA output. The cost function quantifies the aggregate distortion and drives the gradient computation. Common formulations include:

• Instantaneous squared error for LMS-based updates
• Weighted least squares for frequency-selective emphasis
• Regularized cost functions to prevent coefficient drift

The instantaneous difference between the desired linear signal and the observed PA output captured by the feedback receiver. This signal is the fundamental driving force of the adaptation loop. Accurate error computation requires precise time alignment and gain/phase normalization between the reference and feedback paths. Any misalignment introduces bias that degrades linearization performance.

A dedicated observation chain that down-converts and digitizes a coupled sample of the PA output. This component provides the ground truth for error computation in DLA. Key requirements include:

• Sufficient bandwidth to capture out-of-band distortion products
• High dynamic range to observe both the main signal and spectral regrowth
• Low noise floor to avoid contaminating the error gradient
• Calibrated linearity to avoid introducing its own distortion

The speed at which the DLA adaptation loop approaches the optimal coefficient set. This metric is governed by the learning rate, the conditioning of the basis function correlation matrix, and the algorithm choice (e.g., LMS vs. RLS). Faster convergence enables tracking of time-varying PA behavior due to thermal drift or changing operating conditions, but may sacrifice steady-state accuracy if not properly tuned.