Vector Decomposition

The complex baseband signal is separated into its magnitude (envelope) and phase components. The magnitude captures the instantaneous power level driving the PA's nonlinearity, while the phase preserves the angular information.

• AM/AM distortion: Magnitude errors corrected by the magnitude path
• AM/PM distortion: Phase rotation errors corrected by the phase path
• Enables independent modeling of amplitude and phase nonlinearities
• Commonly used with polar transmitter architectures

The complex signal is decomposed into its I (in-phase) and Q (quadrature) components, representing the real and imaginary parts of the baseband waveform. This is the most common decomposition for Cartesian transmitter architectures.

• Preserves the full vector nature of the signal
• Compatible with standard real-valued neural network layers
• Each branch processes one dimension of the complex envelope
• Enables tapped delay lines on each path for memory effect modeling

Vector decomposition enables the use of tapped delay lines on each real-valued signal path, allowing the neural network to model the PA's memory effects without complex-valued temporal operations.

• Each decomposed component receives a history of past samples
• The network learns short-term and long-term memory dependencies
• Eliminates the need for Backpropagation Through Time (BPTT) in feedforward architectures
• Memory depth is a tunable hyperparameter balancing complexity and accuracy

By decomposing the complex I/Q signal, standard real-valued neural network architectures like the RVTDNN can be applied directly to the predistortion problem without requiring complex-valued weights or activation functions.

• Leverages mature deep learning frameworks (TensorFlow, PyTorch)
• Avoids challenges of complex backpropagation and non-holomorphic activation functions
• Enables use of standard regularization: dropout, batch normalization
• Simplifies hardware implementation on FPGAs with fixed-point arithmetic

The decomposed magnitude component is used to generate envelope-dependent polynomial basis functions that capture the PA's nonlinear behavior as a function of instantaneous input power.

• Magnitude raised to odd powers: |x|, |x|³, |x|⁵, ...
• These basis terms are multiplied with delayed I/Q samples
• Forms the foundation of memory polynomial and GMP models
• Provides a structured input representation that accelerates neural network convergence

After the neural network processes the decomposed components, the predistorted outputs must be recombined into a single complex baseband signal for digital-to-analog conversion and RF upconversion.

• I/Q recombination: I_pred + jQ_pred
• Magnitude-phase recombination: |x|_pred * exp(j * φ_pred)
• Phase continuity must be preserved to avoid spectral regrowth
• Reconstruction error directly impacts Adjacent Channel Leakage Ratio (ACLR)

A neural architecture that directly processes complex I/Q signals without decomposition, using complex weights and activation functions. Unlike vector decomposition approaches that split signals into real-valued paths, CVNNs preserve phase orthogonality natively.

• Uses Wirtinger calculus for backpropagation
• Avoids information loss from magnitude/phase decoupling
• Often compared against RVTDNNs for linearization fidelity

A feedforward network that processes decomposed I and Q components through tapped delay lines to model PA memory effects. Vector decomposition is a prerequisite for this architecture, as it converts the complex baseband signal into two real-valued input streams.

• Each branch captures temporal dependencies independently
• Outputs are recombined to form the predistorted complex envelope
• Foundation for most hardware-implementable DPD solutions

A block-structured neural model that places a linear dynamic filter before a static nonlinearity. When combined with vector decomposition, the I and Q components pass through separate filter branches enriched with cross-terms to capture quadrature imbalance.

• Models AM/AM and AM/PM distortion jointly
• Augmented structure handles strong memory effects
• Often used as a baseline for comparing neural DPD performance

The process of correcting gain mismatch and phase offset between the I and Q branches of a modulator. Vector decomposition exposes these impairments as separate error signals, enabling neural networks to learn joint predistortion and imbalance correction.

• Critical for direct-conversion transmitter architectures
• Reduces unwanted image sideband emissions
• Often integrated into the same neural DPD pipeline

A simplified Volterra model using only diagonal kernel terms to represent nonlinearity with memory. When implemented as a neural network basis function, the MP structure operates on decomposed I/Q signals, with each polynomial term acting as a fixed input transformation before trainable weights.

• Computationally efficient for FPGA implementation
• Serves as the nonlinear basis for augmented neural architectures
• Limited in modeling strong cross-term memory effects

The artificial expansion of PA measurement datasets through transformations applied to decomposed signal components. Phase rotation and amplitude scaling of I/Q vectors create diverse training examples that improve neural network generalization.

• Prevents overfitting to specific signal constellations
• Simulates varying operating conditions without additional measurements
• Applied independently to magnitude and phase branches in decomposed architectures