## 4 Modeling and Linearization Stage Setup
### Indirect Learning Approach for the Proposal Modeling Stage
In addition to this, a model derived from the general Volterra Series such as the MPM is described; the W-MPM is proposed as an adaptive modeling technique in a comparison process where the fundamental basis of the dynamic weighting selection proposal is considered as a modeling stage for estimation of the distortion curves. In this case, the P1 dB compression point of the device is identified by programming and represents the point at which there is a gain level of 79.43% in relation to the expected results based on its linear area of the device. The dynamic factor is automatically calculated and established as the \(X_{th}\) value. Furthermore, the model is analyzed in two stages, dynamic and static parts, and is able to update the coefficient in case of wide variation in the amplification process due to the memory effects in short time. An adaptive and static modeling technique is used to estimate the highly nonlinear behavior of the PA NXP 10 W at 2.34 GHz. In this case, the precise modeling stage is crucial, which can be used for a linearization technique; in this paper, we have shown the IIA technique that was compatible with modeling stage based on MPM and W-MPM. The adaptive modeling stage reaches for the NXP semiconductor of 10 W GaN HEMT RF-PA an accuracy of \(-\)32.72 dB NMSE using the MPM compared with \(-\)38.03 dB for the dynamical modeling stage based on the extraction algorithm. Additionally, it compared the highly nonlinear behavior of the device ZHL-42W+ at 2000 MHz 32.24 dBm, where an NMSE accuracy of the modeling stage of \(-\)44.34 dB was reached for the MPM, while for the W-MPM adaptive algorithm, it is around \(-\)44.90 dB. In addition to this, the used hardware resources on the Cyclone V development card show a usage of 340 adaptive logic modules for the W-MPM compared with the 378 used resources for the MPM (see Table 3). The transmission chain involves two channels designed for handling sampled data with resolution \(2^{n}\) of the input signal with respect to the outputs. It is shown a voltage offset block stage for adjustment linked to the DACs. In the simulation stage, the coefficients of the modeling stages are calculated through the LSE method for the MPM and W-MPM, The even terms are used in both conversion curves estimation since they give the best precision based on NMSE error. An attenuator was designed for the voltage unbalance of the input signal and the maximum peak voltage of the amplified signal. The most important contribution of this work lies in the proposal of a W-MPM model and IIA scheme for highly nonlinear models and data dispersion in the same way a whole dynamic weighting selection system is developed where the change in amplitude can be monitored. The W-MPM yields a considerably lower number of coefficients compared to the MPM; the related P1 dB parameter that involves 7 coefficients plus one per nonlinear stage in total generates 42 coefficients for the device under test. In the static part, since it does not consider memory, the design is implemented with a W-MPM with nonlinearity of 13 and memory effect of zero, which gives a total of 55 coefficients. In relation to the MPM, to obtain relatively the same result based on the metric NMSE, a total of 67 coefficients are  
Figure 6: Linearization based on IIA based on W-MPM for the device ZHL-42W+ at 2000 MHz 32.24 dBm RF-PA. (**a**) AM/AM modeling and linearization stage and (**b**) AM/PM modeling and linearization stage. involved and a system of nonlinearity order 11 and high memory with level 6 is required. The EVM reduction is estimated for the developed static and dynamic modeling stages; both linearization process are compared. As we can see, the achieved EVM reduction is considerably better after the linearization stage. The improved EVM is shown in Table 6.