###### Abstract  
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 (P1 dB) 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. FPGA; memory effects; nonlinear modeling; power amplifiers; W-MPM +
Footnote †: journal: Applied Sciences
t trends in the linearization of power amplifiers (PAs) [3; 4; 5]. Additionally, bandwidth requirements in conventional radio frequency (RF) paths for multi-band transmission systems involve high nonlinearities and memory effects added by the device under test [4]. In recent years, the cutting-edge development to provide innovative integrated circuits (ICs) integrated along with foundry/technology selection through complementary metal-oxide semiconductor CMOS, gallium arsenide (GaAs), and GaN PA designs have demonstrated an improvement in performance, cost reduction, and digital functionality. Therefore, optimal solutions are conducted to guarantee 5G wireless communications systems with antenna array design integration such as those for massive multiple input/multiple output (MIMO) realizations [2]. It is well-known that the radio frequency power amplifier (RF-PA) performance can often dominate the overall transmitter (TX) behavior, such as the power-added efficiency (PAE), which impacts the power and heat dissipation for the TX chain. The focal point of the RF-PAs is to boost the signal level in order to reach in the receiver chain a signal with suitable power levels to allow for the detection and demodulation process. However, it is the device in the transmission chain that adds most of the nonlinearities and short-term memory effects, which generate the undesirable effect of spectral regrowth and second- and third-order intermodulation (IMD3) products. As it is well known, single-band RF-PAs generate intermodulation, which increases the interference to neighboring channels and the transmission quality [5]. Therefore, special techniques and proposals for corrections during a wireless transmission are required in order to avoid penalties by the telecommunications regulatory entities in each country. To achieve this objective, linearization adaptive techniques and schemes consider the electrical factor of the chain to properly correct short-term memory effects [6]. Models derived from the Volterra Series estimation have been proven to have appropriate accuracy in modeling stages for nonlinear systems.