The choice of the compression region for operation near saturation, thus avoiding the back-off driving of a power amplifier (PA), poses a transcendental challenge in terms of the search for a tradeoff between efficiency and linearity. This fact combined with addressing design issues and solutions in PAs adapted to the 5G mobile requirements, together with using new digital modulations for mobile applications and the high demand for applications, services, and mobile devices, becomes even more critical. Thus, to meet user capacity requirements, higher data rates, and additional bandwidth that exceeds 1 GBit/s for mobile access are required to reach this arrangement [
1]. It will be extremely challenging to achieve those aggressive 5G performance metrics all at once, and thus, the 5G revolution is expected to occur in stages [
2]. In contrast, base stations capable of dealing with multi-band signals have gained widespread popularity, which leads to new research trends in the linearlization 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. Alternative techniques such as Wiener, Hammerstein, and serial or parallel configurations consider the nonlinear (NL) and linear time invariant (LTI) stages as a suitable strategy in the modeling of nonlinear devices [
7,
8]. Additionally, memory polynomial model (MPM) and the generalized memory polynomial (GMP) model are related works that make important approximations in this area. A novel output generalized memory polynomial (OGMP) behavioral model based on the previous output signal for linearization of PA was proposed in [
9]. Conventional MP or GMP models use polynomials of the previous input signal to characterize memory effects [
8]. The behavioral models for PAs devices driven with single and multiband signals have been designed to mimic the nonlinear regimes and to provide a useful approximation of its nonlinear response under several stimuli. Additionally, it is proposed to model a digital predistorter generalized parallel two-box (GPTB) based on hybrid memory polynomial since it consists of a hybrid memory polynomial and a memoryless nonlinear function [
10].
Regarding this nonlinear aspect, special efforts are needed to investigate the effects of nonlinear distortion produced by RF-PAs, which include amplitude distortion, phase distortion [
11], and the spread of signal constellations based on the quasi-memoryless Saleh model when passed through the additive white gaussian noise (AWGN) channel. This model was chosen because it involves the amplitude-to-amplitude (AM/AM) and amplitude-to-phase (AM/PM) conversion curves [
12]. Additionally, the need to establish methodologies for transmitting and modeling data primarily with digital multiplexing such as long-term evolution (LTE) and wideband code division multiple access (WCDMA) are of current interest [
13], even implementing a two-chain amplifying structure in parallel for the
GHz band [
14]. However, some linearization techniques for RF-PAs have low performance and limited adaptability regarging data variations due to short-term memory effects [
15]. The 1-dB compression point (P1dB) is one of the main electrical characteristics that represents the change between the linear and compression sections of any RF-PA device. The P1dB makes a comparative performance in the linear region and the saturation zone of the nonlinear device [
16,
17]. In this work, the weighted memory polynomial model (W-MPM) is proposed as an adaptive technique that takes into account the electrical variation of a nonlinear device under test corrected by a indirect learning approach (ILA) linearization scheme [
18]. The variations in time of a device as RF-PA are generated by the impedances and parasitic capacitances within the device; unfortunately, during the amplification process, the devices are brought to the saturation zone, and it is precisely in this region where it behaves as highly nonlinear. A device in this region produces not only in-band distortion but also spectral regrowth. The amplification process after the P1dB generates a low efficiency of the used power; this condition is increased in high frequencies. The state-of-the-art reports different linearization methods that can be developed in the simulation stage prior to implementation; one of them is related to fixed data, where the best correlation data is sought in the output of the system, techniques such as look-up table (LUT) based ones [
19]. Other methods based on the data variation are indirect learning approach (ILA) or direct learning approach (DLA). In the ILA stage, a post-distortion is used, where the device’s output measurements are taken as the post-distortion input and the input measurements are taken as the post-distortion output. Then, the post-distorter is estimated based on the least square error (LSE) method, and the result is placed before the RF-PA. Unlike DLA, it is required to define an RF-PA model then, and finally, the total linearization is just the inverse result of this model [
18,
20,
21]. Some linearization works related to compensation of nonlinear systems use a compensation model to update the coefficients of a system, such as nonlinear applications of the global system for mobile communication (GSM) [
22]; in addition, models derived from Volterra Series such as MPM to compensate for the characteristics of the short-wave PA are presented, where IMD3 to overcome the nonlinear behavior are reduced [
23]. Additionally, a two-step approach was developed for DLA as linearization technique based on convolutional neural network [
24]. It should be noted that, in the works developed, they do not use an electrical parameter that can vary to adjust the modeling stage or to compensate the system. Therefore, to address the aggressive multi-carrier LTE-A and WCDMA modulation schemes, it is still an important challenge to fulfill the power, efficiency, and linearity requirements in new architectures of RF-PAs [
25]. The main aim of this paper is to offer an adaptive alternative to correct the undesirable effect of spectral regrowth, based on modeling and linearization stages, where the P1dB of a nonlinear device caused by the memory effects in short time is considered, the obtained results are tested into a development board, the error vector magnitude (EVM) is evaluated, and the developed adaptive linearization scheme is able to adapt to the nonlinear behavior under analysis. The novelty presented in this work is the integration of an adaptive modeling stage for RF-PA linearization for applications in the 2.5 GHz band for highly nonlinear devices related to telecommunications and for worldwide interoperability for microwave transmissions access (WiMax) and long-term evolution (LTE), where the modeling stage considers the P1dB as a metric for updating coefficients.
The remainder of this paper is organized as follows. In
Section 2, the modeling description involving the MPM, W-MPM, and ILA linearization methods are depicted.
Section 3 describes the experimental setup used to perform the measurements of the RF-PA under test in addition to the simulation system implementation based on the DSP builder tool prior to implementing it on the FPGA development board.
Section 4 shows the obtained results and precision of the highly nonlinear device under test, the modeling accuracy, and the linearization result. Finally, in
Section 5, a discussion and the main conclusions obtained are presented.