Behavioral Cloning

The core principle is learning a direct function f(x) that maps desired linear output to predistorted input. Unlike Direct Learning Architecture (DLA) which requires closed-loop adaptation, behavioral cloning trains on a pre-computed dataset of (ideal input, predistorted output) pairs. The network learns to replicate the behavior of a high-fidelity reference predistorter—often a Generalized Memory Polynomial (GMP) or Volterra series model—in a single supervised training phase.

Training data is generated by an offline, computationally intensive reference predistorter. This 'teacher' model—typically a high-order Memory Polynomial (MP) or iterative DLA solution—processes a representative signal dataset to produce ideal predistorted waveforms. The neural network student then learns to approximate this mapping, effectively distilling the teacher's knowledge into a more efficient, hardware-friendly architecture suitable for real-time FPGA-Based DPD Implementation.

Behavioral cloning is architecture-agnostic, accommodating various neural network topologies:

• Real-Valued Time-Delay Neural Network (RVTDNN) for I/Q component processing with tapped delay lines
• Complex-Valued Neural Network (CVNN) for direct complex baseband handling
• Cascade Forward Neural Network for improved gradient flow
• Augmented Wiener or Augmented Hammerstein structured networks The choice depends on the PA's memory depth and nonlinearity characteristics.

The primary limitation is distributional shift—the cloned policy may encounter signal conditions not represented in the teacher's training distribution. When deployed on signals with different Peak-to-Average Power Ratio (PAPR) characteristics or bandwidths, performance degrades. Mitigation strategies include Data Augmentation (phase rotation, amplitude scaling) and Dropout Regularization to prevent overfitting to the teacher's specific output distribution rather than learning the true underlying PA inverse.

Once trained, the cloned neural network executes a fixed forward pass with deterministic Inference Latency—typically orders of magnitude faster than the iterative coefficient solvers used in online Indirect Learning Architecture (ILA). This makes behavioral cloning ideal for Model Quantization and Neural Network Pruning prior to deployment on resource-constrained FPGA fabric. The static computational graph enables precise worst-case execution time analysis for real-time wideband systems.

Behavioral cloning serves as a foundation for Transfer Learning across power amplifiers. A network cloned from a reference PA model can be fine-tuned on a smaller dataset from a target PA, dramatically reducing measurement requirements. This teacher-student paradigm also enables Model Extraction from high-fidelity simulations, where a computationally expensive Volterra series model trained in simulation is distilled into a lightweight neural network for physical deployment.

A closed-loop training topology where the predistorter network is placed before the power amplifier (PA). The network's weights are updated in real-time by minimizing the error between the PA's actual output and the desired linear reference signal. This architecture directly optimizes for the system-level linearization goal, inherently compensating for any model mismatch, but requires the PA to be in the loop during training.

An open-loop identification method that avoids placing the PA in the training loop. A postdistorter network is first trained to model the inverse of the PA's nonlinearity, using the PA's output as its input and the desired signal as the target. The converged weights are then copied to the predistorter, assuming the nonlinear blocks are commutable. This is the most common architecture for offline behavioral cloning.

A foundational feedforward network for behavioral cloning that processes the I and Q components of a signal as separate real-valued inputs. Tapped delay lines (TDLs) on these components explicitly model the PA's memory effects. This architecture is highly compatible with standard deep learning frameworks and hardware, making it a practical baseline for predistorter design.

A network architecture that directly processes complex baseband I/Q signals using complex-valued weights and activation functions. By preserving the phase relationship between I and Q components natively, CVNNs can represent nonlinearities with fewer parameters than their real-valued counterparts. Training requires specialized complex backpropagation algorithms.

The critical ability of a cloned predistorter to maintain linearization performance on signals and conditions not seen during training. A network that merely memorizes the training signal's specific characteristics will fail on a different modulation scheme or bandwidth. Techniques like data augmentation and dropout regularization are essential to force the network to learn the true underlying PA physics.

An adaptive paradigm where the predistorter's coefficients are continuously updated during live signal transmission. This allows the behavioral clone to track time-varying PA characteristics caused by temperature drift, component aging, or channel switching. It transforms a static, offline-trained model into a dynamic system that maintains optimal linearization over its operational lifetime.