## 4 Modeling and Linearization Stage Setup
### Indirect Learning Approach for the Proposal Modeling Stage
\begin{table}
\begin{tabular}{c c c} \hline
**Description** & **W-MPM Resource Utilization** & **MPM Resource Utilization** \\ \hline Logic Utilization (ALMs) & 340/56,480 (\(<\)1\%) & 378/56,480 (\(<\)1\%) \\ Total Registers & 771 & 751 \\ Total Pins I/O & 40/480 (8\%) & 40/480 (8\%) \\ Total block memory bits & 43,008/7,024,0640 (\(<\)1) & 43,008/7,024,0640 (\(<\)1) \\ Total PILs & 1/7 (14\%) & 1/7 (14\%) \\ \hline \end{tabular}
\end{table} 
Table 3: Hardware resources occupation in Cyclone V 5 CEFAF31I7 FPGA device with comparison for the W-MPM and MPM models. Figures 3 and 4 show the linearization performance based on MPM and W-MPM, respectively; in both cases, the amplitude and phase distortion were properly linearized. The results obtained from the adaptive W-MPM algorithm minimized the required resources and coefficients compared with the MPM. These models and the learning code were implemented in FPGA development board Cyclone V, and it was achieved by reducing the amount of coefficients and by improving the accuracy compared with reported works in the literature. The accuracy obtained was \(-32.72\) dB NMSE using the MPM compared with \(-38.03\) dB NMSE for adaptive W-MPM. Figures 5 and 6 show the developed models that replicate effectively the highly nonlinear device under analysis. For both devices, it was estimated the EVM after the linearization algorithm and the distortion between the receiver and transmitter chain were reduced. In this case, it was improved by \(13.07\%\) and by \(15.48\%\) for the EVM for the NXP 10 W at 2.34 GHz using the static MPM and dynamic W-MPM, respectively. For the ZHL-42W+ device operating at 2000 MHz with an output power of around \(32.24\) dBm, it was improved by \(24.1\%\) and \(24.22\%\), while the EVM is in the same conditions before and after the proposed linearization algorithm. Table 5 summarizes the performance comparison with a study of the involved works in the state-of-the-art comparing mainly the RF-PA linearity order required to properly address the behavior under a complexity analysis. Using the aforementioned simplification the analysis assumes the required coefficient number of the modeling stages and yields a feasible accuracy. Additionally, it is depicted as the technology of the RF-PA under experimentation. In Figure 7 is depicted the development board Cyclone V and acquisition card. Since the contribution of this paper is to offer an adaptive linearization scheme, in this case, the baseband components with the up conversion cards are not required to frequency shift from IF to baseband or even to use physical attenuators to attenuate the signal power levels. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Complexity Metric** & **W-MPM** & **MPM** \\ \hline Number of distinct operators & 7 & 7 \\ Number of distinct operands & 7 & 7 \\ Total number of operators & 9 & 11 \\ Total number of operands & 7 & 7 \\ Program vocabulary & 14 & 14 \\ Program length: & 16 & 18 \\ Calculated estimated program length & 39.30 & 39.30 \\ Volume & 60.92 & 68.53 \\ Difficulty & 3.50 & 3.50 \\ Effort & 213.21 & 239.86 \\ Time required to program (s) & 11.85 & 13.33 \\ Number of delivered bugs & 0.07 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Halstead complexity analysis for W-MPM and MPM. Figure 4: Linearization based on ILA based on W-MPM for the device NXP 10 W at 2.34 GHz. (**a**) AM/AM modeling and linearization stage and (**b**) AM/PM modeling and linearization stage. Figure 5: Linearization based on ILA based on 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. Figure 3: Linearization based on ILA based on MPM for the device NXP 10 W at 2.34 GHz. (**a**) AM/AM modeling and linearization stage and (**b**) AM/PM modeling and linearization stage. Table 5 summarizes a comparison of the proposed work as a dynamical modeling stage compared with other related works.