Real-Valued Time-Delay Neural Network (RVTDNN)

The RVTDNN separates the complex baseband signal into its in-phase (I) and quadrature (Q) components before processing. Each component is treated as an independent real-valued input stream, allowing the network to learn asymmetric nonlinear distortions that affect I and Q paths differently.

• Eliminates the need for complex-valued backpropagation
• Captures IQ imbalance and modulator impairments naturally
• Doubles input dimensionality compared to complex-valued networks

A finite impulse response (FIR) filter structure feeds time-delayed copies of the I and Q inputs into the network. Each tap captures the signal envelope at a previous time step, enabling the model to represent memory effects caused by thermal dynamics, bias circuit reactance, and trapping phenomena.

• Typical depth: 3–10 delay taps per input branch
• Delay spacing matched to the signal bandwidth and sampling rate
• Models both short-term (electrical) and long-term (thermal) memory

The delayed I/Q samples feed into one or more fully connected hidden layers with nonlinear activation functions. These layers learn the complex mapping between the input signal history and the required predistortion correction.

• Common activations: tanh, sigmoid, or ReLU variants
• Typical architecture: 2–3 hidden layers with 10–30 neurons each
• Output layer produces predistorted I and Q components for reconstruction

By operating entirely in the real domain, the RVTDNN leverages standard real-valued backpropagation and gradient descent optimizers without modification. This avoids the mathematical complexity of Wirtinger calculus required for complex-valued neural networks.

• Compatible with standard deep learning frameworks (TensorFlow, PyTorch)
• Supports Levenberg-Marquardt, Adam, and L-BFGS optimizers
• Enables straightforward hardware implementation on FPGAs and DSPs

The Augmented Real-Valued Time-Delay Neural Network extends the standard architecture by adding envelope-dependent terms as supplementary inputs. These terms—computed as the instantaneous power |x(n)|² or magnitude |x(n)|—provide explicit nonlinearity information that improves modeling of strongly nonlinear devices like Doherty PAs and GaN amplifiers.

• Reduces hidden layer size requirements for equivalent accuracy
• Improves NMSE by 2–5 dB over standard RVTDNN in saturation regions
• Adds minimal computational overhead compared to the base architecture

The RVTDNN can be configured with either a single combined output layer that jointly produces I and Q predistorted values, or dual independent output branches that separately generate each component. The dual-output variant provides greater flexibility for correcting cross-talk between I and Q paths.

• Single-output: shared hidden representation, fewer parameters
• Dual-output: independent I/Q correction paths, higher modeling capacity
• Selection depends on observed AM-PM distortion asymmetry

An enhanced architecture that extends the standard RVTDNN by feeding envelope-dependent terms (|x(n)|, |x(n)|², etc.) as additional inputs alongside the I/Q components and their delayed taps. This explicit injection of even-order nonlinear terms improves modeling accuracy for strongly nonlinear devices like GaN PAs operating near saturation. The augmentation reduces the hidden layer complexity required to learn amplitude-dependent distortion patterns.

A training methodology where the predistorter is identified by placing a copy of the DPD model after the PA in the estimation loop. The post-distorter is trained to produce the original input signal, and its coefficients are then copied to the pre-distorter. ILA avoids the need to compute an explicit inverse model of the PA, making it computationally attractive for RVTDNN training. However, it assumes the PA is invertible and can be sensitive to measurement noise in the feedback path.

An iterative training approach that directly minimizes the error between the desired linear output and the actual PA output to extract predistorter coefficients. Unlike ILA, DLA explicitly models the PA characteristic and uses gradient-based optimization to update the RVTDNN weights. This method is more robust to measurement noise and does not require the PA to be strictly invertible, but demands an accurate PA behavioral model within the training loop.

A Volterra-based model that serves as a classical baseline against which RVTDNN performance is measured. GMP includes cross-terms between delayed signal samples and their envelope powers to capture complex memory effects. While GMP provides linear-in-parameters estimation (enabling direct least-squares solutions), RVTDNNs often outperform GMP on strongly nonlinear devices due to the neural network's universal approximation capabilities and ability to learn higher-order interactions implicitly.

A technique to derive RVTDNN weights for uncalibrated operating conditions (e.g., different frequencies, temperatures, or power levels) by interpolating between known coefficient sets. This reduces the calibration overhead in production systems where exhaustive training at every operating point is impractical. Interpolation can be linear, polynomial, or neural network-based, and is critical for deploying RVTDNN-based DPD in dynamic environments like 5G NR where conditions change rapidly.

The robustness of the RVTDNN training algorithm against ill-conditioned matrices that arise from highly correlated input features (e.g., closely spaced delay taps). Techniques like ridge regression (L2 regularization) and Levenberg-Marquardt optimization improve stability during weight estimation. Poor numerical conditioning can lead to coefficient divergence in adaptive systems, making stability analysis a critical step in deploying RVTDNN-based DPD in real-time hardware.