# Agnostic Envelope Linearization of Dynamically Supplied Power Amplifiers for Mobile Terminals
## 3 Experimental Setup and Linearization Results
### Experimental Results with the NR-60 MHz Test Signal  
This subsection shows the experimental results of applying the proposed agnostic digital linearization approach for ET PAs when operated with a 60 MHz 5G-NR QPSK modulated signal at band 7. Every data batch consists of 0.5 ms of transmitted signal, which contains 1 slot in a 30 kHz subcarrier spacing (SCS) subframe. Considering a baseband clock of 614.4 MHz (corresponding to an observation and predistortion bandwidth at baseband around 300 MHz), the number of data samples for every batch is 307,200. The maximum number of epochs per iteration for the nonlinear least squares coefficient adaptation was set to 17; this way it was possible to observe the stability of the proposed linearization method. In order to provide a fair comparison between the ELC approach in [19] (that requires measuring the supply envelope at the ETM output) with the EOPT approach proposed in this paper, the same input data with the same input power were used for testing. Figure 9 shows the evolution of key performance indicators such as power efficiency, NMSE, or ACPR over several training iterations of the EOPT when considering different test cases. These test cases include ELC, GMP-based I-Q DPD and EOPT linearization with and without exploration, and different learning rate values (i.e., \(\gamma\) in (12) and (19)) for the EOPT training process. The supply envelope used is the SR reduction shaping with steps \(\mathbb{N}=30\) and offset percentage \(OP=20\%\). The power efficiency can be well maintained (i.e., the efficiency is kept or improved), with ELC, GMP-based I-Q DPD or EOPT linearization with \(\gamma=0.4\), and exploration. The power efficiency with EOPT, but without the envelope exploration process, experienced significant variations along the training iterations. When considering EOPT with the exploration process and a high learning rate, e.g., \(\gamma=0.6\) or \(\gamma=0.9\), the efficiency had a smaller variation but finally converged to a lower value compared to the initial power efficiency value. Regarding the linearity performance (in terms of NMSE and ACPR), only the EOPT without the envelope exploration process fails to improve the overall linearity. With the ELC approach, the linearity requirement of \(-36\) dBc of ACPR is met with only two iterations of the ELC adaptation. The GMP-based I-Q DPD can improve the linearity after two training iterations, but after that it does not improve further, and the targeted ACPR cannot be met (e.g., the results in Figure 9 show up to the fourth iteration of the GMP-based I-Q DPD to evidence its limitations). Figure 8: Simplified block diagram and picture of the ET PA linearization test bench. The labels are as follows: (1) ET PA EVB: HiSilicon’s ET PA evaluation board including ETM and RF ET PA; (2) USB-MIP: FTTI USB to MIPI bridge; (3) Diff-Amp: Differential amplifier TH54508 RGT from Texas Instruments; (4) Pre-PA: RF pre-amplifier ZHL-42 from Minicircuits; (5) DSO: Digital oscilloscope RTP084 from Rohde and Schwarz; (6) AWG: Arbitrary waveform generator M8190A from Keysight. Figures 10 and 11 show the AM-AM characteristics of the ET PA and the ETM with and without ELC and EOPT linearization, respectively. The baseband AM-AM plots are similar to each other since both linearization approaches reached the same level of linearity at the end. The AM-AM characteristic at the ETM relating the generated envelope and the difference between the ETM output and generated envelopes, evidences the difference between the ELC and the EOPT linearization approaches. In both cases, the normalized \(Env_{gen}\) starts taking values from 0.2 because the OP configuration of the SR envelope is set to 20%. With the ELC linearization approach, the RF leakage is treated as the error to be canceled by using the EGMP model. Consequently, the AM-AM plot after ELC linearization shows the linearization efforts to achieve a constant flat gain.