PA Linearization

A classical closed-loop technique where a portion of the PA output is fed back and compared to the input. The error signal is used to directly correct the input waveform.

• Cartesian Feedback: Demodulates the RF output into I/Q components for baseband comparison, effectively suppressing intermodulation distortion.
• Polar Loop: Compares envelope and phase components separately.
• Limitation: Loop bandwidth must be significantly wider than the signal bandwidth, restricting its use in wideband applications like 5G NR.

An open-loop architecture that extracts the distortion generated by the main PA and injects it, with opposite phase, into the output path via an error amplifier.

• Structure: Uses two loops—a signal cancellation loop to isolate the distortion, and an error cancellation loop to subtract it.
• Advantage: Inherently stable and offers excellent wideband correction.
• Disadvantage: Poor energy efficiency due to the lossy output coupler and the power consumed by the error amplifier, making it less common in modern handsets.

A technique pioneered by Kahn that separates a modulated signal into its envelope and phase components. The phase-modulated, constant-envelope carrier drives a highly efficient saturated PA, while the envelope signal modulates the PA's supply voltage to restore amplitude information.

• Modern Evolution: Closely related to Envelope Tracking (ET).
• Challenge: Precise time-alignment between the envelope and RF paths is critical to avoid severe distortion.

Also known as outphasing. A varying-envelope signal is decomposed into two constant-envelope, phase-modulated signals. These signals drive two highly efficient, identical PAs. A non-isolating power combiner then reconstructs the original amplitude-modulated signal.

• Efficiency: PAs operate at peak efficiency regardless of the output power level.
• Critical Element: The design of the power combiner is paramount to minimize out-of-band emissions and achieve good linearity.

A linearization method applied directly at RF frequencies before the PA. A nonlinear device, such as a diode or a specially biased transistor, generates an expanding gain characteristic to counteract the PA's compression.

• Application: Often used as a supplementary technique to improve the raw linearity of a PA before applying Digital Pre-Distortion (DPD).
• Trade-off: Simpler and lower power than DPD but offers limited correction capability and is less adaptive to changing conditions.

DLA forms a true closed-loop system that directly estimates predistorter coefficients by minimizing the error between the desired ideal input and the actual measured PA output. Unlike ILA, DLA does not assume commutativity.

• Mechanism: Error signal e(n) = x(n) - y(n)/G feeds the coefficient estimator
• Advantage: Robust to measurement noise and strong memory effects
• Challenge: Requires model inversion or iterative optimization at each update
• Algorithms: Often uses Levenberg-Marquardt or Stochastic Gradient Descent for nonlinear optimization

The core mathematical engine driving adaptive DPD. These algorithms solve for the optimal predistorter parameters that minimize a defined cost function, typically the Normalized Mean Squared Error (NMSE) between the ideal and linearized output.

• Least Squares (LS): Batch solution for offline training; optimal for stationary conditions
• Least Mean Squares (LMS): Low-complexity sample-by-sample update; slow convergence
• Recursive Least Squares (RLS): Faster convergence than LMS at higher computational cost
• QR-RLS: Numerically stable RLS variant using QR decomposition to combat ill-conditioning
• Kalman Filtering: Optimal for tracking time-varying coefficients due to thermal drift

Model inversion is the mathematical process of deriving the predistorter transfer function directly from an identified PA behavioral model. This is the critical step in Direct Learning Architectures.

• Analytical Inversion: Closed-form inversion possible for low-order Memory Polynomial Models
• Iterative Inversion: Required for complex models like Volterra Series; uses Newton-type methods
• Indirect Approach: Train a separate inverse model with input/output swapped
• Challenge: Ill-conditioning and overfitting can produce unstable predistorters
• Regularization: Tikhonov regularization stabilizes the inversion by penalizing large coefficient magnitudes

Adaptive filtering provides the self-adjusting signal processing foundation for real-time DPD coefficient tracking. The filter structure defines the predistorter model, while the adaptation algorithm updates its weights.

• Convergence Rate: Speed at which coefficients reach steady-state; critical for tracking rapid PA changes
• Misadjustment: Excess error caused by gradient noise in stochastic updates; trades off with convergence speed
• Coefficient Drift: Gradual deviation from optimal values due to temperature, aging, or numerical instability
• Burst vs. Continuous Training: Updates can occur only during dedicated training slots or continuously sample-by-sample

Quantifying linearization effectiveness requires standardized metrics that capture both in-band signal quality and out-of-band spectral containment.

• Error Vector Magnitude (EVM): Measures in-band distortion; critical for modulation accuracy and demodulation margin
• Adjacent Channel Power Ratio (ACPR): Quantifies spectral regrowth into neighboring channels; the primary regulatory compliance metric
• Normalized Mean Squared Error (NMSE): Time-domain error metric normalized by input power; standard for model training convergence
• Cost Function: The mathematical objective minimized during training, typically a weighted combination of NMSE and spectral constraints