# Agnostic Envelope Linearization of Dynamically Supplied Power Amplifiers for Mobile Terminals
## 4 Conclusions  
A new envelope linearization system for ET PAs is presented in this paper. The proposed EOPT linearization approach uses an EGMP behavioral model to optimize the supply envelope in order to meet the linearity requirements at the ET PA output. Despite that the architecture is similar to the ELC approach, since the output of the ETM is not available, the EOPT is agnostic on the ETM behavior. Consequently, a new procedure, based on the reinforcement learning DDPG algorithm, is used to extract the coefficients of the EGMP model. The proposed identification method exploits the SED-GMP ET PA behavioral model to estimate the EGMP coefficients solving a nonlinear least squares problem by means of the LM algorithm.  
The reported experimental results illustrate how the EOPT linearization approach can outperform the conventional GMP-based I-Q DPD linearization (up to 2 dB of ACPR improvement). In addition, the EOPT method can achieve similar linearization performance to the ELC approach (i.e., ACPR close to \(-37\) dBc) with the same number of parameters (84 coefficients) and similar power efficiency (close to 17%). However, the EOPT method is agnostic of the EMT behavior and it does not need monitoring the ETM output, which saves the cost of an extra ADC. Finally, as reported in the experimental results section, the proposed envelope optimization technique can be properly combined with I-Q DPD to improve the ACPR figure by 4 dB.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Linearization** & **\#** & **NMSE** & **ACPR** & **Power** & **Eff.** \\
**Approach** & **Coeffs.** & **(dB)** & **(dBc)** & **(dBm)** & **(\%)** \\ \hline w/o DPD & N/A & \(-24.39\) & \(-28.57\) & \(27.21\) & \(16.58\) \\ GMP & \(128\) & \(-28.39\) & \(-34.79\) & \(27.17\) & \(16.44\) \\ ELC & \(84\) & \(-30.04\) & \(-36.73\) & \(27.26\) & \(17.06\) \\ EOPT & \(84\) & \(-29.27\) & \(-36.93\) & \(27.26\) & \(16.76\) \\ ELC+GMP & \(84\) + \(64\) & \(-33.07\) & \(-40.32\) & \(27.23\) & \(16.36\) \\ EOPT+GMP & \(84\) + \(64\) & \(-32.06\) & \(-38.36\) & \(27.34\) & \(16.76\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: ET PA experimental results with NR-60 MHz OFDM-like signal at band 7.  
supervision, project administration, funding acquisition, P.L.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Huawei Technologies from July 2020 to August 2021; and supported in part by the project PID2020-113832 RB-C21 funded by MCIN/AEI/10.13039/50110001103 and in part by the Government of Catalonia and the European Social Fund under Grant 2021-FI-B-137.  
Not applicable.  
The data presented in this study are available on reasonable request from the corresponding author.  
The authors would like to thank [PERSON] and [PERSON] from HisSilicon for the donation of the ET PA board used in this paper, as well as for their insightful comments and interesting discussions regarding the functioning of the ETM and the key factors influencing the trade-off between linearity and power efficiency in ET PAs.  
The authors declare no conflict of interest.