Augmented Real-Valued Time-Delay Neural Network (ARVTDNN)

The defining architectural enhancement of the ARVTDNN is the explicit inclusion of instantaneous envelope magnitude |x(n)| and its powers as additional input features alongside the I/Q components. This provides the network with direct knowledge of the signal's amplitude trajectory, allowing it to learn AM-AM distortion and AM-PM conversion patterns more efficiently than a standard RVTDNN, which must infer envelope information implicitly from I/Q samples.

ARVTDNN excels at capturing the behavior of power amplifiers operating in deep compression near saturation, where nonlinearities are severe. By feeding |x(n)|, |x(n)|², and higher-order envelope terms directly into the hidden layers, the network can separate static nonlinearity from dynamic memory effects. This makes it particularly effective for GaN Doherty amplifiers and envelope tracking systems where conventional memory polynomials struggle with convergence.

Like the base RVTDNN, the ARVTDNN employs tapped delay lines on both the I/Q inputs and the envelope-dependent terms to capture memory effects spanning multiple sample periods. The memory depth is configurable:

• Short-term memory: 3-5 taps for instantaneous thermal effects
• Long-term memory: 10+ taps for trapping effects and bias modulation
• Cross-memory: Interactions between delayed I/Q and delayed envelope terms

Compared to fully complex-valued neural networks or Volterra series with equivalent modeling accuracy, the ARVTDNN offers reduced parameter count and faster convergence. The real-valued architecture avoids complex backpropagation, while the explicit envelope terms reduce the nonlinear order required in hidden layer activation functions. This translates to lower FPGA resource utilization when deployed in real-time DPD systems.

The ARVTDNN can be viewed as a neural generalization of the Generalized Memory Polynomial (GMP). Where GMP uses fixed polynomial basis functions with cross-terms between signal and envelope delays, the ARVTDNN learns optimal basis functions through training. This provides superior modeling fidelity for amplifiers exhibiting non-polynomial nonlinearities, such as those with sharp saturation knees or kink effects in GaN HEMT devices.

At millimeter-wave frequencies, power amplifiers exhibit stronger nonlinearities, wider bandwidths, and more pronounced memory effects than at sub-6 GHz. The ARVTDNN's envelope augmentation is particularly valuable in mmWave DPD because beamforming arrays introduce active impedance mismatch that varies with signal envelope, creating complex nonlinear behaviors that purely I/Q-based networks cannot adequately resolve.

The core augmentation in ARVTDNN. In addition to delayed I/Q samples, the network receives explicit envelope-dependent terms as supplementary inputs. These are typically functions of the instantaneous input magnitude, such as:

• |x(n)|: Instantaneous envelope amplitude
• |x(n)|²: Instantaneous input power
• |x(n)|³: Higher-order envelope terms The envelope terms provide direct information about the signal's instantaneous power level, allowing the network to more easily learn the AM-AM and AM-PM distortion characteristics without needing to infer them solely from I/Q interactions.

The most common training framework for deploying ARVTDNN-based predistorters. In ILA, the predistorter is trained by placing an identical copy after the power amplifier in the estimation path. The post-distorter is trained to produce the original input signal, and its converged coefficients are then copied to the pre-distorter. This avoids the need to compute an inverse model of the PA directly. For ARVTDNN, the ILA structure works well because the augmented envelope inputs provide sufficient information for the network to learn the inverse characteristic, even for strongly nonlinear devices with significant memory effects.

An alternative neural network approach that competes with ARVTDNN architectures. CNN-DPD uses 1D convolutional layers to automatically learn hierarchical temporal features from complex baseband I/Q waveforms. Unlike ARVTDNN's explicit tapped delay lines and envelope terms, CNNs learn feature extraction implicitly through learned convolutional kernels. CNN-DPD can achieve excellent linearization performance but may require more computational resources. ARVTDNN offers a more interpretable structure with its explicit envelope augmentation, which can be advantageous for hardware implementation and debugging.

A recurrent neural network approach designed to capture long-range temporal dependencies in power amplifier behavior. LSTM cells contain gating mechanisms that allow the network to selectively remember or forget information over extended sequences. This is particularly relevant for modeling thermal memory effects and trapping effects in GaN amplifiers, which can span hundreds of microseconds. ARVTDNN, with its finite tapped delay lines, has a fixed memory depth. LSTM-DPD can theoretically model longer memory, but at the cost of increased training complexity and more challenging real-time implementation on FPGAs.