Long Short-Term Memory DPD (LSTM-DPD)

Unlike memory polynomials limited by finite tap lengths, LSTM-DPD captures long-range memory effects spanning hundreds of samples. The gated recurrent architecture—comprising forget, input, and output gates—selectively retains or discards information over extended sequences. This enables accurate modeling of thermal memory effects and trapping phenomena in GaN amplifiers that evolve over microsecond timescales, significantly outperforming Generalized Memory Polynomial (GMP) models for wideband signals with deep memory.

LSTM-DPD eliminates manual basis function selection required by Volterra series models. The recurrent layers automatically learn hierarchical temporal features directly from complex baseband I/Q waveforms:

• Lower layers: Capture instantaneous AM-AM and AM-PM distortion patterns
• Deeper layers: Model envelope-dependent memory effects and cross-term interactions
• Output layer: Synthesizes the inverse nonlinear characteristic for predistortion

This data-driven approach adapts to amplifier-specific nonlinear signatures without domain-specific kernel engineering.

The LSTM cell maintains an internal hidden state and cell state that propagate across time steps during inference. This stateful processing provides a natural mechanism for modeling the dynamic nonlinear behavior of power amplifiers without requiring explicit tapped delay lines. At each sample, the network processes the current I/Q input alongside the carried-forward state, producing a predistorted output that compensates for distortion shaped by the entire signal history—critical for wideband 5G NR signals with high PAPR.

Traditional DPD architectures often cascade separate blocks for static nonlinearity correction (e.g., LUT-based) and memory effect compensation (e.g., FIR filters). LSTM-DPD unifies both functions within a single recurrent architecture. The gating mechanisms inherently disentangle instantaneous distortion from history-dependent effects, enabling joint optimization during training. This unified approach reduces overall model complexity while improving ACLR suppression and EVM performance compared to cascaded architectures.

LSTM-DPD models trained on diverse stimulus signals generalize robustly across varying average power levels, carrier frequencies, and signal bandwidths. The recurrent architecture's ability to encode context in its hidden state allows a single trained model to linearize across a range of output back-off (OBO) levels without requiring coefficient interpolation or multi-dimensional LUTs. This reduces calibration overhead in massive MIMO and beamforming systems where per-element, per-beam retraining is impractical.

LSTM-DPD training employs Truncated Backpropagation Through Time (TBPTT) to manage the computational complexity of unrolling long sequences. The training process:

• Unrolls the recurrent network over a fixed window (e.g., 100-200 samples)
• Computes gradients through the unrolled computational graph
• Updates weights to minimize the error between desired linear output and PA output
• Carries forward the final hidden state to the next training segment

This approach balances gradient accuracy with memory constraints during offline model extraction.

Slowly varying changes in power amplifier gain and phase caused by self-heating and substrate temperature fluctuations dependent on signal history. LSTM-DPD architectures are uniquely suited to model these effects because their gated recurrent units can maintain state over thousands of time steps, capturing the long thermal time constants that conventional memory polynomial models miss. This is critical for GaN-based amplifiers where thermal trapping creates complex, history-dependent distortion patterns.

Slow charge capture and release phenomena in semiconductor materials like GaN that cause long-term memory effects and dynamic nonlinear behavior. Unlike short-term electrical memory, trapping effects manifest over extended symbol sequences, making them difficult to model with finite impulse response structures. LSTM-DPD cells maintain an internal cell state that can accumulate and decay information over arbitrary durations, providing a natural inductive bias for modeling these semiconductor physics phenomena without explicit physical equations.

An extended Volterra-based model incorporating cross-terms between delayed signal samples and their envelope powers to capture complex memory effects. While GMP provides a strong baseline for DPD, its memory depth is limited by the number of explicitly programmed taps. LSTM-DPD offers a complementary approach by learning implicit memory representations through recurrent connections, often achieving comparable or superior linearization with fewer parameters when long-range dependencies dominate the distortion characteristic.

A DPD training method that identifies the predistorter by placing it after the power amplifier model in the estimation loop, avoiding the need for an inverse model. When combined with LSTM-DPD, the ILA framework enables offline training of the recurrent network using captured input-output data. The LSTM model learns to approximate the post-distorter, which is then copied to the predistorter path. This approach decouples training from real-time constraints, allowing gradient-based optimization through backpropagation through time (BPTT).

A DPD training method that iteratively minimizes the error between the desired linear output and the actual power amplifier output to extract predistorter coefficients. For LSTM-DPD, DLA presents unique challenges because the recurrent network must be trained through the nonlinear PA transfer function. This requires gradient approximation techniques or model-based backpropagation through the amplifier characteristic. DLA-trained LSTM predistorters can adapt to changing operating conditions without requiring a separate model extraction step.

A feedforward neural network DPD architecture processing in-phase and quadrature components separately with tapped delay lines to model memory effects. LSTM-DPD represents an evolution beyond RVTDNN by replacing fixed-length delay taps with recurrent connections that can theoretically model infinite impulse response behavior. While RVTDNN requires explicit selection of memory depth, LSTM cells learn to retain or forget information adaptively, making them more parameter-efficient for signals with widely varying memory requirements.