Blind DPD Adaptation

Leverages the constant envelope property of phase-modulated signals to drive coefficient adaptation. The algorithm penalizes amplitude variations in the PA output, forcing the combined predistorter-PA cascade toward a constant envelope response.

• Cost function: Minimizes deviation from constant modulus
• Best suited for: QPSK, GMSK, and other constant-envelope modulations
• Limitation: Performance degrades with high peak-to-average power ratio (PAPR) signals like OFDM

Exploits the fact that communication signals exhibit known higher-order cumulant signatures that nonlinear distortion alters. The adaptation engine minimizes the difference between the observed and expected cumulant values at the PA output.

• Key metric: Fourth-order cumulant (kurtosis) matching
• Advantage: Works with non-constant modulus modulations (16-QAM, 64-QAM)
• Computational cost: Higher than CMA due to sample cumulant estimation

Assumes the undistorted transmitted spectrum possesses a known symmetry property that nonlinear amplification destroys. The DPD coefficients are updated to restore this spectral symmetry at the PA output.

• Principle: Nonlinearity introduces spectral asymmetry; correction restores it
• Feedback requirement: Only power spectrum estimation, no phase recovery needed
• Application: Effective for wideband signals where out-of-band emissions must be minimized

Treats the demodulated and re-modulated symbol decisions as a reference signal for coefficient updates. The receiver chain provides implicit feedback by comparing transmitted and received constellations after symbol detection.

• Mechanism: Slicer errors drive LMS or RLS coefficient updates
• Risk: Decision errors at low SNR can cause adaptation divergence
• Mitigation: Incorporate confidence weighting based on soft-decision metrics

Exploits the fact that the undistorted transmitted signal and the nonlinear distortion products are statistically independent. The adaptation algorithm minimizes the mutual information between the input signal and the error residual.

• Foundation: Blind source separation theory applied to DPD
• Implementation: Minimizes cross-cumulants between input and error signals
• Robustness: Insensitive to modulation format changes and signal bandwidth

Blind algorithms exhibit slower convergence than pilot-based methods due to the stochastic nature of the adaptation signal. Convergence time depends on signal statistics and algorithm step size.

• Typical convergence: 10^4 to 10^6 samples for steady-state
• Step-size tradeoff: Larger steps accelerate convergence but increase misadjustment noise
• Tracking capability: Adequate for thermal drift; may lag rapid beam-switching in massive MIMO

The dominant architectural framework for blind DPD adaptation. In ILA, the predistorter training is performed in a post-distorter configuration where the PA input and output are swapped to identify the inverse model.

• Key advantage: Avoids the need for a PA forward model, directly estimating the predistorter coefficients.
• Blind compatibility: The post-distorter can be trained on the actual transmitted waveform without requiring a dedicated training sequence.
• Convergence: Typically converges to the optimal least-squares solution under stationary conditions.

The core online optimization algorithm that enables coefficient tracking without batch processing. Blind DPD systems use SGD variants to iteratively update predistorter parameters sample-by-sample.

• LMS and NLMS: Normalized least mean squares algorithms provide computationally efficient, real-time coefficient updates.
• Momentum and Adam: Advanced optimizers accelerate convergence when the PA nonlinearity changes due to thermal or beamforming effects.
• Step-size trade-off: A smaller step size reduces steady-state misadjustment but slows tracking of dynamic impedance changes.

A classic blind equalization algorithm adapted for DPD that exploits the constant envelope property of certain communication signals. CMA minimizes the deviation of the PA output amplitude from a constant value.

• No reference required: Operates purely on the statistical property that the transmitted waveform has a known constant modulus.
• Application: Particularly effective for linearizing PAs in systems using phase-shift keying or other constant-envelope modulations.
• Limitation: Performance degrades for signals with high peak-to-average power ratios like OFDM.

Blind techniques that exploit cumulants and polyspectra of the transmitted signal to identify the nonlinear system. These methods leverage the fact that Gaussian noise has zero higher-order cumulants.

• Fourth-order cumulants: Can separate the linear and nonlinear components of the received signal without pilot symbols.
• Polyspectral inversion: The nonlinear system is identified by solving for the Volterra kernels in the higher-order spectral domain.
• Robustness: Inherently immune to Gaussian measurement noise, making them suitable for over-the-air feedback scenarios.

An alternative to ILA where the predistorter coefficients are updated by directly minimizing the error between the desired linear output and the actual PA output. DLA requires a PA forward model for gradient computation.

• Model dependency: Blind DLA implementations must simultaneously estimate the PA model and the predistorter, increasing complexity.
• Advantage: Can theoretically achieve better performance than ILA when the PA characteristic is accurately known.
• Two-step blind approach: First identify the PA model blindly, then compute the predistorter as the inverse of the identified model.

A family of online system identification algorithms that update model parameters by minimizing the prediction error between the observed and predicted PA output. These methods form the statistical foundation for many blind DPD schemes.

• Recursive Least Squares (RLS): Offers faster convergence than LMS at the cost of higher computational complexity.
• Kalman filter formulation: Treats the DPD coefficients as a state vector to be estimated, enabling optimal tracking of time-varying PA nonlinearity.
• Forgetting factor: A tunable parameter that controls the algorithm's memory, balancing steady-state accuracy against tracking agility.