Augmented Wiener Model

Reverses the physical Hammerstein model by placing a linear dynamic block before a static nonlinearity. This architecture models the PA's frequency-dependent behavior followed by its amplitude distortion, making it mathematically well-suited for predistorter identification. The linear filter captures memory effects, while the subsequent nonlinearity handles AM/AM and AM/PM conversion.

Extends the standard Wiener model with lagging and leading envelope cross-terms that capture complex memory interactions. These parallel branches multiply delayed versions of the signal envelope with the current sample, modeling phenomena like:

• Thermal memory effects from substrate heating
• Trapping effects in GaN HEMT devices
• Bias circuit modulation at envelope frequencies This augmentation dramatically improves normalized mean squared error (NMSE) by 3-5 dB over the standard Wiener model.

The linear dynamic block is implemented as a finite impulse response (FIR) filter with trainable coefficients, while the static nonlinearity uses a complex-valued neural network or a spline-based activation function. This hybrid approach combines the interpretability of linear systems theory with the universal approximation capability of neural networks. The entire structure is differentiable, enabling end-to-end training via backpropagation.

Compared to a full Volterra series or Generalized Memory Polynomial (GMP) model, the Augmented Wiener structure achieves comparable linearization performance with 30-50% fewer coefficients. This parameter efficiency is critical for:

• FPGA implementation with limited DSP slices
• Real-time adaptation with constrained update rates
• Reduced overfitting risk on limited training data The structured decomposition separates memory depth from nonlinearity order, avoiding the combinatorial explosion of Volterra kernels.

Integrates naturally with the Direct Learning Architecture (DLA) for closed-loop predistorter training. The model's output is compared to the desired linear reference, and the error signal propagates through the differentiable Wiener cascade to update all parameters simultaneously. This avoids the commutability assumption required by Indirect Learning Architectures, which can introduce systematic errors when the PA's nonlinearity is strong.

Excels at linearizing wideband signals (100+ MHz instantaneous bandwidth) for 5G NR and satellite communications. The cross-term branches capture the frequency-dependent memory effects that become dominant at wide bandwidths, where traditional memory polynomial models struggle. Typical results show ACLR improvement exceeding 20 dB and EVM reduction below 1% for 256-QAM signals after Augmented Wiener DPD application.

The dual architecture to the Augmented Wiener Model, placing a static nonlinearity before a linear dynamic block. While the Wiener model excels at predistorter design, the Hammerstein structure is often preferred for forward PA behavioral modeling. Augmented variants add parallel branches with cross-terms to capture complex memory effects that simple cascade models miss.

• Reverses the Wiener cascade order
• Natural fit for PA forward modeling
• Augmented branches capture envelope memory
• Often used in Direct Learning Architecture loops

An enriched memory polynomial structure that introduces lagging and leading envelope cross-terms to the standard diagonal kernel formulation. These cross-terms explicitly model the interaction between a signal sample at time n and the envelope of samples at times n±q, capturing the nonlinear memory effects that simple memory polynomials miss.

• Extends GMP with additional cross-term orders
• Models envelope-dependent memory interactions
• Provides basis functions for neural network layers
• Improves ACLR by 2-3 dB over standard MP

A signal preprocessing technique that separates the complex I/Q baseband signal into magnitude and phase or in-phase and quadrature components before feeding them into separate real-valued neural network paths. This decomposition allows the Augmented Wiener Model's static nonlinearity block to operate on real-valued envelope terms while preserving phase information through parallel branches.

• Splits complex signals for real-valued networks
• Enables separate AM/AM and AM/PM modeling
• Reduces network complexity vs. complex-valued approaches
• Compatible with RVTDNN architectures

A deep network design pattern where layers learn the difference between the target and the input via skip connections. In Augmented Wiener predistorters, residual blocks simplify optimization by allowing the network to learn only the nonlinear distortion correction rather than the full signal transformation. This enables much deeper architectures without vanishing gradient problems.

• Skip connections bypass one or more layers
• Network learns residual correction: y = F(x) + x
• Enables 20+ layer predistorter networks
• Improves training stability for wideband signals

An open-loop predistorter identification method where a postdistorter is first trained on the PA's output, then copied to the predistorter position. This assumes commutability of the nonlinear blocks—a valid assumption for the Augmented Wiener Model's cascade structure. ILA avoids the real-time feedback loop required by Direct Learning Architectures.

• Trains postdistorter on PA output data
• Copies trained weights to predistorter
• Assumes cascade commutability holds
• Simpler implementation than closed-loop DLA

An adaptive training paradigm where Augmented Wiener Model coefficients are continuously updated during live signal transmission. This tracks time-varying PA characteristics caused by temperature drift, device aging, and carrier frequency changes. Online algorithms use recursive least squares or stochastic gradient descent with forgetting factors to prioritize recent data.

• Continuous coefficient updates during transmission
• Tracks thermal and aging effects in real-time
• Uses forgetting factors to weight recent samples
• Critical for base station deployments with 24/7 operation