# Wavelet Decomposition Prediction for Digital Predistortion of Wideband Power Amplifiers
## 1 Introduction
To accomplish this, WDP initially employs neural networks (NNs) to model the nonlinear behavior of the PA. Training is halted once the PA's nonlinear model achieves a satisfactory level of accuracy. Subsequently, the parameters of this nonlinear model are copied to an identical model, which is then frozen. This frozen nonlinear model is cascaded with the predistorter, and by linearizing the output of the combined system, the objective of training an effective predistorter is realized [25; 26; 27]. In comparison to the ILA method, WDP offers improved robustness by avoiding reliance on the precise inversion of the PA model. In practical systems, the nonlinear characteristics of the PA can vary over time or with environmental changes, making accurate model inversion challenging and potentially degrading the performance of traditional ILA-based predistortion. In contrast, WDP employs neural networks to directly model the nonlinear behavior of the PA. Once trained, the model parameters are frozen, ensuring stability throughout the predistorter training process and enhancing overall system robustness. Furthermore, compared to the DLA approach, which typically requires inverting the PA output to directly optimize the predistorter parameters, WDP also demonstrates advantages in stability and efficiency. The inversion process in DLA can become numerically unstable or computationally intensive in highly nonlinear systems. By avoiding such complex inverse operations and instead modeling PA nonlinearity through neural networks, WDP improves both system stability and computational efficiency. However, existing WDP-based DPD methods often suffer from limited multi-resolution analysis capabilities and inadequate long-term dependency modeling, which significantly restricts their overall performance. To overcome these challenges, we introduce a novel WDP-based DPD approach that integrates dual-stage recurrent neural networks (RNNs) with wavelet decomposition (WD). The WD enhancement decomposes signals into low-frequency and high-frequency components, allowing the model to learn and distinguish different frequency features of the data more precisely and efficiently. Thisapproach not only retains critical information but also improves the overall signal quality. By leveraging WD, the model gains a deeper understanding of the data's intrinsic structure, enhancing its predictive accuracy and generalization capabilities in real-world applications. Specifically, we use a combination of WD and an update gate RNN (UGRNN) to model the nonlinearity of the PA, and the WD-enhanced framework enhances the model's multi-resolution analysis capability. The UGRNN captures the long-term dependencies of decomposed signal components and introduces a self-attention mechanism to further evaluate the contribution of each component to the model output. In this stage, a normalized mean square error (NMSE) of \(-\)34.96 dB is achieved, which is superior to that of other methods. Subsequently, the UGRNN is replaced with an intersection RNN (IRNN) and cascaded with pretrained and frozen nonlinear models to linearize the output of the combined model and achieve effective DPD processing. Our proposed method provides excellent linearization performance on the open-source dataset 'OpenDPD', achieving adjacent channel power ratio (ACPR) of \(-\)52.71/\(-\)51.93 dBc and error vector magnitude (EVM) of \(-\)48.92 dB. The contributions of this paper are summarized as follows. * We propose a WD-enhanced dual-stage RNN for WDP-based DPD, where the dual-stage RNN captures long-term dependencies in the input while the WD module provides multi-resolution analysis, improving both PA modeling accuracy and DPD effectiveness. * Our approach integrates a dual-stage RNN composed of a UGRNN and an IRNN, both of which extend the vanilla RNN with a lightweight gating mechanism. Specifically, the UGRNN is employed for PA nonlinear modeling, while the IRNN is used in the DPD stage, ensuring that each stage leverages the most suitable RNN variant.