# Wavelet Decomposition Prediction for Digital Predistortion of Wideband Power Amplifiers
## 1 Introduction  
In modern communication systems, as transmission data rates and spectral efficiency continue to improve, nonlinear distortion has emerged as a critical factor impacting system performance. This distortion primarily originates from nonlinear components such as power amplifiers (PAs), which degrade signal quality, increase bit error rates, and introduce spectral pollution during transmission [1, 2]. Ideally, a PA should exhibit linear behavior, maintaining a constant amplification factor between the input and output signals. However, during high-power operation, PAs inevitably deviate from their linear region, leading to the presence of nonlinear components in the output signal [3]. These nonlinear distortions not only compromise signal integrity but also introduce adjacent channel interference, further degrading overall system performance [4]. A conventional linearization approach is power back-off, which mitigates nonlinearity at the cost of significantly reducing PA efficiency and output power [5, 6]. Consequently, PA design and optimization have long been key research topics in both academia and industry [7, 8, 9, 10, 11, 12]. Among various linearization techniques, digital predistortion (DPD) is widely regarded as the most promising solution due to its flexibility and superior performance [13, 14]. Due to its strong capability in fitting nonlinear characteristics, deep learning has emerged as a powerful tool in DPD research, driven by advancements in its techniques. Deep learning models, particularly neural networks, can effectively capture complex patterns and nonlinear dependencies from large datasets, enabling more precise predistortion. Therefore, in this study, we employ deep learning to model and optimize the DPD process. Direct Learning Architecture (DLA) is a classic implementation method for predistortion techniques, whose core idea is to minimize the error between the PA output andthe expected signal by directly optimizing the parameters of the predistorter. In DLA, the input signal is first processed by a predistorter to generate a predistorted signal, which is then amplified by the PA. Due to the nonlinear nature of PAs, the output signal may introduce distortion. DLA calculates the error signal by comparing the output signal of the PA with the original input signal and directly adjusts the parameters of the predistorter to minimize the error. Although DLA has the advantages of simple structure and easy implementation, its performance is limited by the complexity of inverse operations and model accuracy, especially in highly nonlinear systems, where DLA may face numerical instability and real-time challenges [15; 16; 17; 18; 19; 20]. Different from DLA, Indirect Learning Architecture (ILA) is another classic method for implementing predistortion techniques, whose core idea is to indirectly model the characteristics of a PA and invert its inverse model to achieve predistortion. In ILA, the input signal first passes through the PA to generate an output signal containing nonlinear distortion. The input and output signals of the PA are used to train a forward model that characterizes the nonlinear characteristics of the PA. Subsequently, by inverting the forward model, the inverse model of the PA is obtained and used as a predistorter. Although ILA offers advantages such as model flexibility and indirect optimization, it suffers from several critical drawbacks, including vulnerability to noise due to parameter extraction at the PA output and high dependence on PA model accuracy, which may degrade predistortion performance [21; 22; 23; 24]. Wavelet decomposition prediction (WDP) combines the strengths of both direct and indirect learning approaches, enabling the direct training of predistortion models without requiring model inversion after task completion. This method focuses on training a pre-distortion model within a nonlinear system, offering the advantage of directly computing predistortion coefficients.