Generalized Memory Polynomial (GMP)

The direct predecessor to the GMP, the Memory Polynomial captures nonlinearity and memory effects using only diagonal Volterra kernels. It represents the PA output as a sum of polynomial functions of the current and delayed input samples.

• Structure: Uses only aligned envelope-dependent terms
• Complexity: Significantly fewer coefficients than GMP
• Limitation: Cannot model complex memory interactions like lagging/leading envelope effects
• Application: Baseline model for real-time DPD where computational simplicity is critical

An enriched variant that augments the standard memory polynomial with lagging and leading envelope cross-terms. This structure explicitly captures the interaction between a signal sample at one time instant and the envelope of the signal at a different time instant.

• Key innovation: Adds terms like x(n-m) * |x(n-m-k)|^p to the basis set
• Benefit: Models strong nonlinear memory effects with fewer coefficients than a full Volterra series
• Trade-off: Higher computational load than MP but better accuracy for wideband signals
• Use case: Preferred when GMP complexity is too high but MP accuracy is insufficient

A block-structured neural network that cascades a static nonlinearity followed by a linear time-invariant filter, augmented with parallel branches for cross-terms. This architecture directly mimics the physical signal flow in a power amplifier.

• Topology: Nonlinear block → Linear dynamic block
• Neural implementation: Static nonlinearity can be a shallow MLP; dynamics handled by FIR filters
• Augmentation: Extra branches model complex memory interactions similar to GMP cross-terms
• Advantage: Physically interpretable structure that simplifies coefficient extraction

The most general polynomial-based framework for modeling nonlinear dynamic systems with memory. The Volterra series represents the PA output as a sum of multidimensional convolution integrals, but its exponential coefficient growth makes it impractical for real-time DPD.

• Full model: Includes all diagonal and off-diagonal kernel terms
• Pruning: GMP and MP are sparse subsets of the full Volterra series
• Complexity: O(M^K) coefficients where M is memory depth and K is nonlinearity order
• Role: Serves as the theoretical gold standard from which simplified models like GMP are derived

A feedforward neural network that processes real-valued I/Q components through tapped delay lines to model PA memory effects. Unlike the GMP's fixed polynomial basis functions, the RVTDNN learns its own nonlinear basis functions from data.

• Input: Separate I and Q streams with multiple delayed taps
• Architecture: Fully connected hidden layers with nonlinear activations
• Comparison to GMP: More flexible basis functions but requires gradient-based training
• Hardware: Can be implemented on FPGAs with fixed-point quantization for real-time inference

A neural network architecture that operates directly on complex-valued I/Q baseband signals using complex weights and complex activation functions. This preserves the phase relationships that are critical for accurate PA behavioral modeling.

• Weights: Complex-valued parameters with real and imaginary parts
• Activation: Functions like complex tanh or split ReLU applied separately to magnitude and phase
• Advantage over GMP: Learns both AM/AM and AM/PM distortions jointly without decomposition
• Training: Requires Wirtinger calculus for backpropagation through complex operations