# Wavelet Decomposition Prediction for Digital Predistortion of Wideband Power Amplifiers
## 3 The Proposed WDP Architecture
\begin{table}
\begin{tabular}{c c c c} \hline
**DPD Methods** & **NMSE (dB)** & **SIM-ACPR (dBc, L/R)** & **SIM-EVM (dB)** \\ \hline RVTDCNN [32] & \(-31.26\pm 0.15\) & \(-44.49\pm 0.95/-44.10\pm 0.83\) & \(-33.88\pm 0.14\) \\ VDLSTM [31] & \(-31.73\pm 0.11\) & \(-45.92\pm 0.23/-45.37\pm 0.79\) & \(-34.44\pm 0.15\) \\ Feature\(+\)GRU [27] & \(-40.92\pm 3.96\) & \(-49.34\pm 0.52/-47.11\pm 0.82\) & \(-43.78\pm 3.92\) \\ DGRU [27] & \(-39.62\pm 3.55\) & \(-49.14\pm 0.64/-46.06\pm 0.89\) & \(-42.43\pm 3.54\) \\ IRNN [30] & \(-34.76\pm 1.81\) & \(-47.85\pm 1.12/-46.81\pm 0.99\) & \(-35.84\pm 1.97\) \\
**WDP (Ours)** & \(\mathbf{-45.51\pm 0.65}\) & \(\mathbf{-52.71\pm 0.78/-51.93\pm 0.61}\) & \(\mathbf{-48.92\pm 0.83}\) \\ \hline \end{tabular}
\end{table} 
Table 3: DPD performance comparison of various methods. ### Visual Interpretation

PA nonlinear distortion can impact adjacent channels. To test this, we used a 200 MHz OFDM signal, which makes linearization more difficult. As illustrated in Figure 5, the signal without DPD processing significantly affected adjacent channels; however, after DPD processing, this issue was substantially improved. Among the methods tested, WDP showed the greatest improvement in the spectrum. Despite the high degree of PA nonlinear distortion, the results shown in Figure 6 for amplitude modulation (AM) and AM-phase modulation (PM) with and without DPD demonstrate that WDP excelled at linearizing distorted signals in the 200 MHz OFDM signal, effectively mitigating PA nonlinearity and significantly reducing memory effects. Furthermore, Figure 7 presents the loss curves of various models on the validation set. It is evident that WDP not only converged the fastest but also achieved the lowest loss value, whereas other DPD methods showed slower convergence and higher loss values throughout the training process. All methods were trained on the same dataset, ensuring a fair comparison. The results highlight that the integration of wavelet decomposition and RNNs enabled WDP to more effectively capture the nonlinear features of signals, contributing to its superior fitting performance. Figure 5: Linearization performance of PA using various methods. Figure 6: PA characteristics with and without WDP. ## 5 Conclusions

In this paper, we employed the WDP approach for nonlinear PA and DPD modeling. Unlike direct and indirect learning methods, this approach enabled the direct training of the DPD model, offering the advantage of directly calculating the predistortion coefficient, leading to more accurate parameter estimation. We applied WD to DPD tasks for the first time and demonstrated its effectiveness. The performance of the WDP was validated through experimental testing, achieving an NMSE of \(-45.51\) dB, an ACPR of \(-52.71/-51.93\) dBc, and an EVM of \(-48.92\) dB. The results indicate that WDP effectively handled the PA's nonlinear distortion and phase shift, delivering excellent linearization performance. In future work, we plan to evaluate our method under high-noise and -distortion conditions in real RF environments, seeking collaborative opportunities and necessary experimental equipment for further validation. Additionally, we aim to systematically analyze the impact of different hyperparameter settings and minimum sample size requirements to enhance the generalizability and robustness of our approach. Methodology, S.P. ; validation, S.P. ; formal analysis, S.P. ; investigation, S.P. ; resources, J.Y. ; writing--original draft preparation, S.P. ; writing--review and editing, S.P. ; visualization, S.P. ; supervision, J.Y. ; funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the Science and Technology Project of Jiangsu Provincial Administration for Market Regulation in 2023 grant number KJ2023053. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest.