TRes-DeltaGRU: Energy-Efficient Neural DPD

• TRes-DeltaGRU is a neural digital predistortion algorithm that combines delta-sparse GRU updates with temporal convolutional residuals to linearize RF power amplifiers.
• It employs quantization-aware training and dynamic temporal sparsity to significantly reduce energy consumption while maintaining state-of-the-art ACPR and EVM performance.
• Experimental results show that even with high sparsity (up to 72.5%), TRes-DeltaGRU matches or surpasses previous DPD models in efficiency and linearization quality.

TRes-DeltaGRU is a neural digital predistortion (DPD) algorithm designed for the energy-efficient linearization of radio frequency (RF) power amplifiers (PAs), particularly for wideband signals employing complex modulation formats. Introduced as part of the OpenDPDv2 framework, TRes-DeltaGRU synthesizes temporal residual convolutional processing, a delta-sparse Gated Recurrent Unit (GRU), quantization-aware training, and dynamic temporal sparsity for reduced inference energy, while maintaining or exceeding the linearization performance of state-of-the-art DPD models (Wu et al., 9 Jul 2025).

1. Architectural Structure

TRes-DeltaGRU constructs the DPD mapping $\pi_\mathrm{DPD}$ such that the cascade with a static, pretrained PA model $\pi_\mathrm{PA}$ approximates an ideal linear PA with gain $G$: $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$. The input at time $t$ is a feature vector $\phi_t \in \mathbb{R}^6$ containing the in-phase and quadrature components at $t$ and $t+1$, as well as amplitudes and higher-order magnitudes: $$\phi_t = [I_t, Q_t, I_{t+1}, Q_{t+1}, |x_t|, |x_t|^3]^{\top}$$, where $x_t = I_t + jQ_t$.

The architecture is composed of two parallel paths:

• DeltaGRU Branch: A lightweight recurrent neural structure with a hidden state $\pi_\mathrm{PA}$0 (in experiments). The pre-activation accumulators for the GRU gates are incrementally updated in a delta form, enforcing temporal sparsity. The sequence of gating operations (reset $\pi_\mathrm{PA}$1, update $\pi_\mathrm{PA}$2, candidate $\pi_\mathrm{PA}$3) leads to the hidden state update, followed by a linear projection to produce prediction $\pi_\mathrm{PA}$4.
• Temporal Convolutional Network (TCN) Residual Branch: A two-layer 1D TCN with dilated Conv1D and Hardswish activations processes a local window over $\pi_\mathrm{PA}$5, directly generating a residual output $\pi_\mathrm{PA}$6.

The DPD output is the sum $\pi_\mathrm{PA}$7, computed for each timestep.

2. Delta Update Mechanism and Temporal Sparsity

The delta update principle replaces standard matrix-vector multiplications with delta-thresholded versions. For an input $\pi_\mathrm{PA}$8, the delta is computed as $\pi_\mathrm{PA}$9, with element-wise application of a threshold $G$0:

$G$1

The running reference $G$2 is accordingly updated per element. Input features ($G$3) and hidden states ($G$4) each employ independent thresholds. Computations associated with zeroed deltas (e.g., corresponding weight columns in $G$5) are skipped, yielding a temporal sparsity fraction $G$6 (e.g., 56–72.5%) over long sequences. This mechanism is applicable to both the input and hidden state deltas in the GRU, and directly reduces the number of multiply–accumulate operations (MACs) and memory accesses.

3. Training Loss and Radio-Frequency Metrics

The model is trained end-to-end to minimize the mean squared error (MSE) between the cascade output and the ideal amplified input:

$G$7

Evaluation metrics include:

• Adjacent Channel Power Ratio (ACPR): $G$8 in dBc, quantifying spectral regrowth suppression.
• Error Vector Magnitude (EVM): $G$9 in % or $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$0 in dB, capturing in-band distortion.

These RF metrics are standard for DPD benchmarking.

4. Quantization-Aware Training and Implementation

TRes-DeltaGRU employs quantization-aware training with per-layer learnable scale $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$1 and fixed bit-width $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$2. Quantization is carried out as $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$3, where $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$4, $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$5. The straight-through estimator is used for backpropagation through the quantization step.

Experiments indicate that 12-bit quantization for both weights and activations (“W12A12”) causes less than 1 dB loss in ACPR in the full 996-parameter model. This enables substantial reduction in compute energy without significant linearization cost.

5. Quantitative Performance and Comparison

The algorithm sets a new benchmark in DPD linearization. Key experimental results for FP32 models on the APA_200MHz dataset (TM3.1a, 5×40 MHz 256-QAM, 983 MHz) are summarized as:

Model	#Params	Sparsity (%)	Precision	ACPR (dBc)	EVM (dB)
TRes-DeltaGRU, full	996	0	FP32	–59.4	–42.1
TRes-DeltaGRU (56%)	450	56	FP32	–52.9	–35.7
TRes-DeltaGRU (72.5%)	288	72.5	FP32	–52.0	–37.0
Best prior (DGRU)	1041	0	FP32	–58.4	–39.1

Even with 56% temporal sparsity, the TRes-DeltaGRU–450 matches or exceeds the dense 524-parameter TRes-GRU in ACPR and EVM. The FP32 TRes-DeltaGRU–996 achieves –59.4 dBc ACPR and –42.1 dB EVM, representing new state-of-the-art results for this task (Wu et al., 9 Jul 2025).

6. Dynamic Sparsity and Energy Reduction

The dynamic sparsity mechanism allows computation and memory accesses for inactive features and hidden units to be skipped at runtime. Simulations targeting a single-core ARMv7-A (Gem5, 7 nm node) quantify energy savings:

• INT12 only (full computation, no sparsity): $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$6 lower energy than FP32 for –54.5 dBc ACPR.
• INT12 + 56% delta sparsity (450 params): $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$7 lower inference energy, preserving –50.3 dBc ACPR and –35.2 dB EVM.
• INT12 + 72.5% delta sparsity: $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$8 energy reduction, with ACPR still meeting –45 dBc.

The energy model decomposes total forward-pass energy into $$\hat{y}[n] = \pi_\mathrm{PA}(\pi_\mathrm{DPD}(x[n])) \approx G \cdot x[n]$$9, with each term scaled by the active (non-sparse) fraction $t$0 and the bit-width. Since DPD tasks on wideband RF front ends involve high sample rates, these reductions have significant system-level impact.

7. Integration, OpenDPDv2 Framework, and Availability

TRes-DeltaGRU is integral to the OpenDPDv2 unified framework, which encompasses PA modeling, DPD learning, and joint optimization of energy efficiency and linearization. Code, datasets, and comprehensive documentation are publicly provided at https://github.com/lab-emi/OpenDPD (Wu et al., 9 Jul 2025). This unified approach allows direct comparison, reproducibility, and rapid extension for other RF DPD scenarios.

In summary, TRes-DeltaGRU presents a rigorously engineered neural DPD algorithm achieving state-of-the-art signal quality with aggressive energy reductions, combining delta-sparse GRU updates, lightweight convolutional residuals, quantization-aware training, and explicit energy modeling for embedded RF processing.