Power Amplifier Modeling Using Memory Polynomial Models

The memory polynomial model is a classical approach for nonlinear modeling of radio frequency power amplifiers, particularly suitable for amplifier systems exhibiting memory effects. By capturing the nonlinear relationships between current and past input signals, this model accurately characterizes the dynamic behavior of power amplifiers.

The core concept derives from a simplified Volterra series that retains only diagonal terms to reduce computational complexity. Its mathematical expression consists of weighted polynomial combinations of current input signals and their delayed versions, typically involving two key parameters: nonlinearity order and memory depth. The nonlinearity order determines the model's capability to describe nonlinear behavior, while memory depth reflects the system's dependence on historical inputs.

MATLAB implementation generally follows three main steps: First, construct an input vector matrix containing delayed taps using functions like 'toeplitz' for efficient delay line implementation. Second, compute nonlinear terms of different orders and combine them into a feature matrix through element-wise power operations and concatenation. Finally, solve for model coefficients using least squares methods, where the backslash operator (\) or 'pinv' function can efficiently handle the linear system solution. This approach avoids the dimensionality curse associated with direct high-order Volterra series processing while maintaining modeling accuracy.

Engineering applications must address overfitting concerns, where cross-validation techniques can determine optimal model order and memory depth parameters. The model is not only applicable to power amplifier behavioral modeling but also extendable to linearization technologies such as digital predistortion systems, where it serves as basis for inverse modeling algorithms.