Wiener-Hammerstein Cascade

The model sandwiches a static memoryless nonlinearity between two linear time-invariant (LTI) filters. The first LTI block shapes the input signal's spectral content before it hits the nonlinearity, while the second LTI block filters the distorted output. This structure captures frequency-dependent nonlinear effects that simpler two-block models miss.

The Wiener-Hammerstein cascade is a superset of both the Wiener model (LTI filter followed by static nonlinearity) and the Hammerstein model (static nonlinearity followed by LTI filter). If either LTI block is set to an identity operation, the cascade collapses to one of these simpler structures, making it a flexible framework for model selection.

Unlike black-box neural networks, each block maps to a physical phenomenon:

• Input LTI filter: Represents input matching networks and parasitic reactive elements before the active device
• Static nonlinearity: Models the transistor's I-V curve and gain compression
• Output LTI filter: Captures output matching networks, bias tees, and thermal impedance effects

Extracting the three blocks from measured input-output data is non-trivial because the intermediate signals between blocks are unobservable. Common approaches include:

• Iterative optimization: Alternating between estimating the linear and nonlinear blocks
• Best linear approximation (BLA): Using frequency-domain techniques to separate linear dynamics from nonlinear distortion
• Blind identification: Exploiting higher-order statistics to decouple the blocks without access to internal nodes

The dual-filter architecture naturally separates short-term electrical memory (captured by the input LTI filter, related to impedance matching and trapping effects) from long-term thermal memory (captured by the output LTI filter, related to self-heating and bias modulation). This separation improves modeling accuracy for GaN and GaAs power amplifiers where both memory types are significant.

Computing the inverse of a Wiener-Hammerstein model for digital predistortion is more complex than for simpler structures. The inverse of a Wiener-Hammerstein cascade is itself a Hammerstein-Wiener cascade (nonlinearity sandwiched between two LTI filters, but in reverse order). This requires careful numerical inversion of each block, often using iterative learning control or indirect learning architectures.

A two-block model where a static memoryless nonlinearity is immediately followed by a linear time-invariant (LTI) dynamic filter. This structure is effective for modeling power amplifiers where the nonlinear distortion generation physically precedes the memory effects, such as those caused by bias network or thermal impedance matching circuits at the output. The model's simplicity makes it computationally efficient for digital predistortion implementation.

A two-block model consisting of a linear time-invariant (LTI) dynamic filter followed by a static memoryless nonlinearity. This topology accurately represents power amplifiers where the input signal undergoes linear filtering and dispersion before encountering the primary nonlinear gain compression. It is the structural inverse of the Hammerstein model and is particularly useful for modeling frequency-dependent AM/AM and AM/PM characteristics.

An advanced architecture that deploys multiple Hammerstein branches operating in parallel. Each branch contains a unique static nonlinearity followed by a dedicated linear filter. This parallel structure allows the model to capture complex nonlinear dynamics that a single-branch model cannot, such as the interaction between short-term semiconductor trapping effects and long-term thermal memory. The output is the sum of all branch contributions.

A widely adopted behavioral model that uses a polynomial with tapped delay lines to capture both nonlinear distortion and memory effects. It can be viewed as a simplified Volterra series that retains only the diagonal kernels. The MP model serves as a practical baseline for digital predistortion, offering a direct trade-off between linearization accuracy and computational complexity through its two key parameters: nonlinear order and memory depth.

An enhanced MP model that introduces cross-terms between the signal and its lagging or leading envelope samples. These cross-terms capture complex memory effects, such as those caused by low-frequency impedance interactions in the bias network, that the standard MP model misses. The GMP achieves superior modeling accuracy for wideband signals and Doherty amplifiers at the cost of increased coefficient count and computational load.

A complexity reduction technique that systematically removes insignificant kernels from a full Volterra series model. By applying a significance metric, such as the kernel's contribution to the mean squared error, the most critical distortion terms are retained while negligible ones are discarded. This results in a sparse, computationally efficient model that preserves the essential nonlinear dynamics without the prohibitive complexity of the full Volterra series.