Direct Learning Architecture (DLA)

Unlike the Indirect Learning Architecture (ILA), DLA operates in a true closed-loop configuration. The cost function is formulated directly on the error between the desired input signal and the measured PA output. This means the predistorter coefficients are optimized to minimize the actual nonlinear distortion observed at the amplifier's output, rather than relying on a postdistorter copy. The optimization problem is typically solved using iterative gradient-based methods like Stochastic Gradient Descent (SGD) or Levenberg-Marquardt to navigate the potentially non-convex error surface.

A core mathematical challenge of DLA is the need for model inversion. The predistorter must represent the exact inverse of the power amplifier's nonlinear transfer function. During training, the algorithm effectively solves for this inverse by backpropagating the error through a known or estimated PA model. This requires a robust behavioral model of the PA, such as a Memory Polynomial or Generalized Memory Polynomial, to be integrated into the training loop. Numerical stability during this inversion is critical and often addressed with Tikhonov Regularization or QR-RLS decomposition.

The performance of a DLA system is intrinsically linked to the fidelity of the power amplifier behavioral model used in the coefficient estimation path. Any mismatch between the model and the physical PA—due to thermal memory effects, aging, or manufacturing variance—directly degrades linearization. This contrasts with ILA, which implicitly identifies the inverse. To mitigate this, DLA implementations often incorporate online training algorithms that continuously update both the PA model and the predistorter coefficients using sample-by-sample or block update strategies.

When properly trained with an accurate PA model, DLA theoretically achieves a lower Normalized Mean Squared Error (NMSE) than ILA. This is because ILA's coefficient copying step introduces a systematic bias in the presence of measurement noise. DLA's direct minimization of the output error avoids this bias, leading to superior Adjacent Channel Power Ratio (ACPR) and Error Vector Magnitude (EVM). This makes DLA the preferred architecture for applications demanding the highest spectral purity, such as wideband 5G signals and massive MIMO arrays.

The direct error formulation in DLA often results in a non-convex optimization problem, requiring more sophisticated and computationally intensive solvers compared to the linear least-squares approach common in ILA. Algorithms like Recursive Least Squares (RLS) or Kalman filtering are frequently employed to track time-varying coefficients, but they demand significant FPGA resources. The need to run a full PA model in the adaptation loop also increases the computational burden, creating a trade-off between linearization accuracy and hardware cost.

DLA exhibits inherent robustness to observation path noise. Since the adaptation algorithm directly minimizes the measured error signal, uncorrelated noise in the feedback path does not bias the coefficient estimate; it only increases the misadjustment or steady-state variance. This is a key advantage over ILA, where noise in the postdistorter training data directly corrupts the extracted coefficients. Techniques like burst training can further isolate the system from transient noise sources during critical coefficient updates.

The primary alternative to DLA. ILA trains a postdistorter placed after the power amplifier to replicate the inverse transfer function, then copies its coefficients to the predistorter. Unlike DLA, ILA avoids the need for PA model inversion but assumes the postdistorter-to-predistorter copy is mathematically valid, which can introduce bias when measurement noise is present in the feedback path.

The algorithmic core of any DLA implementation. This process determines optimal predistorter parameters by minimizing a cost function—typically the error between the desired linear input and the actual PA output. Methods include:

• Least Squares Estimation for batch processing
• Stochastic Gradient Descent (SGD) for sample-by-sample updates
• Recursive Least Squares (RLS) for fast convergence
• Kalman Filtering for tracking time-varying coefficients

A direct learning technique unique to DLA where the power amplifier behavioral model is mathematically inverted to derive the predistorter transfer function. This approach requires the PA model to be invertible and numerically well-conditioned. When the model's condition number is high, techniques like Tikhonov Regularization or Levenberg-Marquardt optimization stabilize the inversion process.

DLA operates in a closed-loop topology, continuously updating coefficients based on real-time feedback from the transmit observation path. This contrasts with open-loop DPD, where coefficients are applied statically without feedback. Closed-loop operation enables:

• Thermal drift compensation as the PA heats up
• Aging effect mitigation over component lifetime
• Frequency-dependent adaptation across carrier bandwidth

DLA effectiveness is quantified using three standard metrics:

• Normalized Mean Squared Error (NMSE): Measures the error between ideal and linearized output normalized by input power
• Error Vector Magnitude (EVM): Quantifies in-band distortion quality as the magnitude of the error vector relative to the ideal reference
• Adjacent Channel Power Ratio (ACPR): The critical regulatory metric measuring spectral regrowth into adjacent channels caused by PA nonlinearity

A failure mode in adaptive DPD systems where predistorter coefficients gradually deviate from optimal values. Causes include:

• Thermal memory effects altering PA characteristics
• Numerical instability from ill-conditioned matrices
• Component aging shifting the nonlinear transfer function DLA's closed-loop nature inherently counters drift through continuous re-estimation, unlike open-loop architectures.