Wiener Model

The dual counterpart to the Wiener model, consisting of a memoryless nonlinearity followed by a linear time-invariant filter. This structure is particularly effective when the nonlinear distortion precedes the memory effects in the signal chain.

• Block order: Nonlinearity → Linear filter (reverse of Wiener)
• Use case: Models amplifiers where the dominant nonlinearity occurs before frequency-dependent matching networks
• Identification: Often easier to identify than Wiener models using iterative methods
• Relationship: Cascade of Hammerstein and Wiener models forms the more general Wiener-Hammerstein structure

A simplified Volterra series that retains only the diagonal terms of the Volterra kernels, dramatically reducing the number of coefficients while still capturing essential nonlinear memory effects.

• Structure: Sum of polynomial terms with delayed input samples
• Complexity: O(K×M) coefficients for nonlinear order K and memory depth M
• Advantage: Linear-in-parameters, enabling direct least squares estimation
• Limitation: Cannot model cross-terms between different delays, unlike the generalized memory polynomial
• Implementation: Widely used as the baseline DPD model in FPGA implementations due to its computational efficiency

The theoretical foundation for most behavioral models, representing a nonlinear dynamic system as a multi-dimensional convolution of Volterra kernels with input products at various time delays.

• Full model: Captures all nonlinear orders and memory interactions
• Kernel interpretation: First-order kernel = linear impulse response; higher-order kernels = nonlinear interactions
• Practical limitation: Number of coefficients grows exponentially with nonlinear order and memory depth, leading to the curse of dimensionality
• Pruned variants: Memory polynomial, generalized memory polynomial, and dynamic deviation reduction models are all sparse subsets of the full Volterra series

An extension of the memory polynomial that incorporates cross-terms between different time delays and nonlinear orders, significantly improving modeling accuracy for amplifiers with strong memory effects.

• Cross-term structure: Includes products of delayed samples with different delay indices (e.g., x(n)|x(n-1)|²)
• Accuracy gain: Captures lagging envelope effects and long-term memory interactions missed by the standard memory polynomial
• Trade-off: Higher coefficient count than the memory polynomial, but still far fewer than the full Volterra series
• Application: Preferred for wideband signals and GaN amplifiers where memory effects are pronounced

A data-driven approach using artificial neural networks to learn the complex nonlinear mapping and memory dynamics of a power amplifier directly from measured input-output data, without assuming a specific block structure.

• Architectures: Feedforward networks for static nonlinearities; recurrent neural networks (RNNs) and LSTMs for memory effects
• Advantage: Universal approximation capability—can model behaviors that block-structured models may miss
• Training: Requires substantial measured data and careful regularization to avoid overfitting
• Real-time challenge: Higher computational complexity than polynomial models, though pruned and quantized networks are increasingly viable for FPGA deployment

A memory-mapping approach that stores predistortion or amplifier gain values in a table indexed by instantaneous input signal parameters, typically amplitude or power.

• Structure: One-dimensional LUT for memoryless AM-AM/AM-PM correction; multi-dimensional LUTs for memory effects
• Adaptation: Table entries updated using LMS or RLS algorithms during operation
• Efficiency: Extremely fast lookup operation, ideal for high-sample-rate real-time systems
• Limitation: Quantization error from finite table size; memory depth limited by table dimensionality
• Hybrid approach: Often combined with a Wiener or Hammerstein structure where the LUT implements the memoryless nonlinearity block