## 4 Experimental Results
### Determining the Digital Predistorter Model  
For the predistorter, a behavioral model is used in the first instance. In this case, the ILA technique is used to correct the residual spectral regrowth, this correction is validated for a mathematical model, and the power reduction in the sidebands is evaluated, in addition to the EVM performance. For the residual ACPR spectral regrowth after CFR, a modeling and linearization stage based on the polynomial model with memory for the purpose of the AM-AM curve of the device is developed. The derived modeling procedure generates the amplitude relationship for a modulation scheme under test, in this work are performed for quadrature phase-shift keying (QPSK), and LTE digital multiplexing under 64-QAM modulation. \[y(n)=\sum_{k=1}^{K}\sum_{m=0}^{M-1}=d_{k,m}y_{d}(n-m)|y_{d}(n-m)|^{k}. \tag{14}\]  
Based on the peak gain of the system, the \(y_{d}(n)\) is determined, which is expressed by the following Equation (15):  
Figure 11: CCDF of OFDM signal; (**a**) CFR iterative factor for LTE 5-MHz waveform and (**b**) LTE 10-MHz waveform. Figure 10: Gain for the normalized input and output signal vs. memoryless AM–AM characteristic. \[y_{d}(n)=y(n)/G(n), \tag{15}\]  
where \(G(n)\) is based on the maximum values of \(x(y)\) and \(y(n)\), as expressed in Equation (16). \[G(n)=y(n)\max|x(n)|/\max|y(n)|, \tag{16}\]  
As mentioned before in a first approach the CFR uses the baseband LTE signal to reduce the clipping in the signal, thus improving the PAPR. However, the residual spectral regrowth can be also mitigated by applying DPD. The Volterra series variation provides an approximation on nonlinear effects of the short-term memory effects of a DUT under test and the linear time-invariant (LTI) stage. In this sense, a structure derived from the Volterra Series is chosen as the memory polynomial model (MPM) to introduce in a single-stage the static and non-linear functions to represent the AM-AM recorder [26; 27]. In this case, by taking into account only the diagonal kernels, the MPM makes an adequate approximation of the model. The structure used by the MPM is representative of the Equation (17):  
\[y(n)=\sum_{k=1}^{K}\sum_{m=0}^{M}=a_{m,k}x(n-m)|x(n-m)|^{k-1}, \tag{17}\]  
where, \(a_{m,k}\) represents the coefficients related to the static and dynamic part of the model, \(x(n)\) the sampled and discretized input signal, \(y(n)\) the output signal, \(M\) the short-term memory level of the system, and \(K\) the order of the polynomial to represent the static part. The coefficients to determine the behavior DUT are determined by the least-squares method (LSM). The MPM stages divided into two sections are represented by the Figure 12. DPD uses digital processing and is established in the FPGA domain, the high-frequency signal that operates in the 2 GHz band for the down-conversion of the development card and is established as input \(y(n)\) of the DPD system. Subsequently, a CFR stage will be implemented based on a three-level cut stage for PAPR reduction. The system is implemented for a ZX60-5916 MA-S+ with a typical gain \(\approx\) 17.33 bias with 5 V for commercial LTE applications and QPSK testing. Considering the closed-loop behavioral modeling process that was shown in Figure 2, it provides the general diagram of the indirect learning architecture (ILA) for the amplifier  
Figure 12: Block diagram for the polynomial model with memory. as DUT. In this procedure, we estimated the \(x(n)\) signal introduced before/after the CFR stage. In this case, based on Equation (2), an \(x_{c}(n)\) is obtained, this is the block where the peak cancellation and the peak window are performed, the resulting signal \(x_{c}(n)\) is introduced in an iterative procedure to the ILA linearization block to obtain a \(u(n)\) that will be introduced to the DUT. Therefore, the actual input signal \(x(n)\) can be swept to an input stimulus to obtain the output signal \(y(n)\).