In this paper, we present an adaptive modeling and linearization algorithm using the weighted memory polynomial model (W-MPM) implemented in a chain involving the indirect learning approach (ILA) as a linearization technique. The main aim of this paper is to offer an alternative to correcting the undesirable effect of spectral regrowth based on modeling and linearization stages, where the 1-dB compression point (P1dB) of a nonlinear device caused by memory effects within a short time is considered. The obtained accuracy is tested for a highly nonlinear behavior power amplifier (PA) properly measured using a field-programmable gate array (FPGA) system. The adaptive modeling stage shows, for the two PAs under test, performances with accuracies of −32.72 dB normalized mean square error (NMSE) using the memory polynomial model (MPM) compared with −38.03 dB NMSE using the W-MPM for the (i) 10 W gallium nitride (GaN) high-electron-mobility transistor (HEMT) radio frequency power amplifier (RF-PA) and of −44.34 dB NMSE based on the MPM and −44.90 dB NMSE using the W-MPM for (ii) a ZHL-42W+ at 2000 MHz. The modeling stage and algorithm are suitably implemented in an FPGA testbed. Furthermore, the methodology for measuring the RF-PA under test is discussed. The whole algorithm is able to adapt both stages due to the flexibility of the W-MPM model. The results prove that the W-MPM requires less coefficients compared with a static model. The error vector magnitude (EVM) is estimated for both the static and adaptive schemes, obtaining a considerable reduction in the transmitter chain. The development of an adaptive stage such as the W-MPM is ideal for digital predistortion (DPD) systems where the devices under test vary their electrical characteristics due to use or aging degradation.