## 1 Introduction  
In modern wireless telecommunications systems, the power amplifier (PA) is a key device in terms of energy consumption. Thus, becomes crucial to provide new techniques to overcome the tradeoff between efficiency and linearity. The PAs are the most critical components in a radio-frequency (RF) transmission system, mostly because they add most short-term and long-term memory effects during a digital information transmission, producing intermodulation products and spectral regrowth in adjacent channels. Memory effects are of two types of short and long term, caused by the biasing circuit or inherent to the active device itself as thermal effects; any low-frequency dispersion effects will manifest as envelope memory affecting the PA performance. Both types can be modeled as a black box based on behavior modeling with memory [1]. To improve the performance in linearity and power efficiency in data waveforms, crest factor reduction (CFR) in conjunction with digital predistortion (DPD) as linearization technique are used [2]. In [3], a novel multi-objective predistortion linearization approach based on a learning procedure constrained algorithm with prescribed linearity levels is able to maximize the RF output power. In the DPD modeling, a CFR technique is usually implemented to apply a correction to reduce significant peaks in the baseband signal. To handle the baseband waveforms, digital multiplexing formats such as orthogonal frequency division multiplexing (OFDM) require an extensive range of data to signals used in wide code division multiple access (W-CDMA), and long-term evolution (LTE), which is the standard used for broadband 5G New Radio (NR) communication networks [4], or as the proposed predistortion algorithm for peak to average power ratio (PAPR) reduction in OFDM transmission, as in [5] without a feedback loop. Due to the demand for high bandwidth efficiency from 20 to 30-MHz [6], and the need for power efficiency, the usage of the DPD techniques offer digital flexibility to linearize the undesired behavior of the PAs. Applications in the 2 GHz band is a current topic, whose techniques are migrating towards 5G NR, applications for 10-MHz LTE bandwidths, so it is essential to develop methodologies that evaluate the error vector magnitude (EVM) and adjacent channel power ratio (ACPR) achieved [7]. An additional work is considered for the evaluation of a system with a memoryless model to reduce the PAPR, thus improving the spectral efficiency based on the signaling technique faster than Nyquist clipping multicarrier [8]. In the same way, a new model for the theoretical calculation of harmonics based on clipping has been developed in order to design loads for positive high-frequency devices to avoid non-linearity effects of second or third order [9]. In [10], an interference-aware iterative clipping and filtering PAPR reduction scheme is developed for multiple-input-multiple-output (MIMO)-OFDM systems. Additionally, in [2], a complete study of existing linearization techniques that shows the aspects to consider into a 5G NR, particularly with W-CDMA and 64-QAM stimulus signals through several methods, such as the feedforward, feedback, and predistortion, is introduced. Additional efforts related to linearization and spectral regulation have been made for LTE and W-CDMA, a cubic spline (CS) has been developed for a DPD system for the outphasing angles and power level correction applied to Class-FPA for a W-CDMA 5-MHz and an LTE 10-MHz [11]. Additionally, a numerically stable digital predistorter for RF PA linearization based on Gegenbauer polynomials has been implemented for PA output under 4-channel W-CDMA and LTE drive signals [12]. An interesting feature to provide real-time prototyping systems for developing new DPD approaches is offered with software-defined radio (SDR), which is a favorable solution to address such problems. SDR is a rapidly developing technology in the telecommunication industry to provide flexible and reconfigurable transceiver architectures.