Neural Network Model

The foundational neural network architecture for static nonlinearity modeling. An MLP with one or more hidden layers maps instantaneous input envelope samples to output complex gain using nonlinear activation functions (tanh, ReLU) at hidden nodes.

• Captures AM-AM and AM-PM distortion without memory
• Training uses backpropagation with Levenberg-Marquardt or Adam optimizers
• Input features: I/Q components or envelope magnitude and phase
• Serves as the memoryless nonlinearity block in Wiener-Hammerstein cascade structures

Limitation: Cannot model memory effects without explicit tapped-delay input augmentation.

Extends the MLP by incorporating tapped-delay lines at the input, feeding the network a window of past and present signal samples. This explicit temporal context enables learning of short-term memory effects caused by bias circuit impedance and matching network dynamics.

• Memory depth controlled by number of taps and tap spacing
• Learns a direct mapping from input history to instantaneous output
• Effective for narrowband to moderate bandwidth signals
• Computationally efficient compared to recurrent architectures

Key tradeoff: Fixed memory depth; cannot adaptively retain information over variable time scales.

A TDNN variant that processes real-valued I and Q components separately rather than complex-valued inputs. The network receives in-phase and quadrature samples as distinct input features, with separate output neurons predicting I and Q output components.

• Avoids complex-valued backpropagation complexities
• Naturally handles I/Q imbalance by learning asymmetric I and Q paths
• Input vector: [I(n), I(n-1), ..., Q(n), Q(n-1), ...]
• Widely adopted in DPD literature for its simplicity and effectiveness

Advantage: Standard real-valued optimization toolkits apply directly without modification.

A recurrent neural network architecture employing gated memory cells to selectively retain or forget information over extended sequences. LSTMs excel at capturing long-term thermal and trapping memory effects that span hundreds of samples.

• Forget gate, input gate, and output gate control information flow
• Cell state maintains a gradient highway, mitigating vanishing gradients
• Models self-heating and bias circuit relaxation dynamics
• Particularly effective for GaN HEMT amplifiers with significant charge trapping

Training consideration: Requires Backpropagation Through Time (BPTT); more computationally intensive than TDNN.

A simplified recurrent architecture that merges the LSTM's forget and input gates into a single update gate, reducing parameter count while preserving long-term memory capability. GRUs offer comparable modeling accuracy to LSTMs for PA behavioral modeling with faster training convergence.

• Update gate controls retention of previous hidden state
• Reset gate determines how much past information to discard
• No separate cell state; hidden state serves both roles
• Preferred for real-time adaptive DPD where training speed matters

Empirical finding: GRUs often match LSTM NMSE performance on standard PA benchmarks with 25-30% fewer parameters.

Applies 1D convolutional filters across the temporal dimension of I/Q input sequences to automatically learn local temporal features before feeding them to dense layers. CNNs capture envelope-dependent memory patterns through hierarchical feature extraction.

• Convolutional kernels learn short-term temporal correlations
• Pooling layers reduce dimensionality and provide translation invariance
• Can be combined with LSTM/GRU in hybrid architectures
• Effective for wideband signals where spectral memory patterns vary with frequency

Architecture: Typically 2-3 conv layers followed by 1-2 dense layers for final regression.

The dependence of a power amplifier's current output on past input values due to thermal, electrical, or trapping phenomena. This causes frequency-dependent distortion that static models cannot capture.

• Thermal memory: Slow temperature changes affecting gain over milliseconds
• Electrical memory: Bias network impedance variations at the envelope frequency
• Trapping effects: Charge capture/release in semiconductor materials

Neural networks excel here because recurrent architectures like LSTM naturally model these long-range temporal dependencies without requiring explicit kernel formulations.

A comprehensive mathematical framework using multi-dimensional convolution kernels to model nonlinear dynamic systems with memory. It serves as the theoretical foundation for many behavioral models.

• Represents the system as a sum of increasing-order functionals
• Truncated Volterra models are used in practice due to exponential complexity growth
• Neural networks can be viewed as universal approximators that implicitly learn Volterra-like mappings

When comparing neural network models to Volterra-based approaches, the key tradeoff is model flexibility vs. coefficient interpretability.

An extension of the memory polynomial model that incorporates cross-terms between different time delays and nonlinear orders. This improves modeling accuracy for amplifiers exhibiting strong memory effects.

• Adds lagging and leading envelope terms to the standard memory polynomial
• Captures complex interactions between current and past signal samples
• Often used as a baseline benchmark when evaluating neural network model performance

Neural network models typically outperform GMP on wideband signals where the memory depth and nonlinear order interactions become too complex for polynomial structures.

A recurrent neural network architecture specifically designed to model long-range temporal dependencies in power amplifier behavior. LSTM cells contain gating mechanisms that control information flow.

• Forget gate: Decides what past information to discard
• Input gate: Determines what new information to store
• Output gate: Controls what information to pass forward

LSTM-based PA models effectively capture long-term memory effects spanning hundreds of samples, making them ideal for GaN amplifiers with significant trapping-induced memory.

A metric quantifying the average power of the error signal normalized by the power of the reference signal. NMSE is the primary figure of merit for assessing behavioral model fidelity.

• Expressed in decibels (dB): typical targets are -35 dB to -45 dB
• Calculated across the full signal bandwidth
• Does not specifically weight out-of-band performance

For DPD applications, NMSE should be complemented with ACPR and ACEPR measurements to ensure the model accurately predicts spectral regrowth behavior.

A modeling failure where the extracted model memorizes training data noise instead of learning the underlying system dynamics. This results in excellent training performance but poor generalization to new signals.

• Symptoms: Low training NMSE but high validation NMSE
• Causes: Too many parameters relative to training data diversity
• Mitigation: Regularization, dropout, early stopping, and cross-validation

Neural network models with millions of parameters are particularly susceptible. Cross-validation using multiple signal types (LTE, 5G NR, WCDMA) is essential to verify generalization.