## 2 Signal Modeling and CFR Method
### CFR Model Identification with Joint PAPR Clipping  
The CFR model identification algorithm is examined to establish a PAPR reduction for LTE 5-MHz and LTE 10-MHz bandwidth applications, and it is summarized in this section. The development of a platform for LTE applications based on a combination of linearization with CFR from estimation of instantaneous PAPR is able to estimate the maximum power of a sample in an OFDM transmitter symbol divided by the average OFDM power. This condition considerably improves the phase shifts that may exist between subcarriers of a transceiver system. In Figure 2a, it is shown a generalized structure cascade connected using a conventional computation of CFR and the PD model extraction. For this system, the transceiver signal is closed-loop feedback with \(y(n)\) being the PA output, \(x(n)\) as input signal in addition to the CFR stage known in clipping stages that together with the indirect learning approach (ILA) scheme generates a new \(u(n)\) to characterize the amplitude to amplitude (AM-AM) conversion curve of the DUT. Thus, the final signal \(y_{d}(n)\) can be generated from the inverse gain estimate, and correction for this process is crucial for the \(x_{c}(n)\) as shown in Figure 2b. As mentioned before, for LTE applications with a variation of the clipping level, the benefit to remove preliminary unwanted distortion of the system, can help initially to operate the DUT in its linear region. To improve the EVM performance, we reduce the PAPR and the ACPR of the transmitter, so that the developed system consists of the stages of clipping and filtering, peak cancellation, and peak windowing. In this work, the CFR-clipping technique has been exploited to reduce the PAPR values OFDM transmission by minimizing the EVM with a constraint on PAPR for an RF PA operating at 2.40 GHz. Additionally, this involves a very sharp CCDF curve during the PAPR evaluation. The clipping principle is based on detecting peak voltage based on a defined reference related to the linear region of a PA with a signal \(x(n)\) for a power defined by \(P_{ref}\). \[cp(n)= \begin{cases}x(n)\frac{P_{ref}}{|x(n)|}&\text{if }|x(n)|\geq P_{ref}\\ 0&\text{otherwise}\end{cases}  \tag{1}\]  
Figure 2: Block diagram of the closed-loop behavioral modeling process with CFR: (**a**) ILA for linearization with CFR clipping reduction, (**b**) CFR and filter process. The CFR and clipping procedures introduce a filter to compensate the out-of-band component related to \(cp(n)\), the signal can be defined as follows:  
\[x_{c}(n)=x(n)-filter[cp(n)], \tag{2}\]  
CFR and clipping together with a method of linearization can significantly improve the DPD performance required during a hardware implementation. The PAPR can be reduced based on CFR and trimming process under the same structure. The linearization of a transceiver system involving CFR and clipping method can be expressed as:  
\[cp(n) =\gamma_{\alpha}[x(n)], \tag{3}\] \[u(n) =\gamma_{\beta}[x(n)], \tag{4}\]  
where \(x(n)\) can be defined as the input signal, \(cp(n)\) is the CFR function and \(u(n)\) depicts the linearized signal. The clipped signal \(u_{c}(n)\) is expressed as:  
\[u_{c}(n)=u(n)-up(n)=\gamma_{\theta}[u(n)], \tag{5}\]  
where the target to be achieved is defined by \(\theta=\beta-\alpha\). It should be noted that \(\theta\) is represented by a set of parameters of \(\beta\) and \(\alpha\). A variation of the clip and filter approach is the peak cancellation, \(\gamma_{\alpha}\) and \(\gamma_{\beta}\) are a set of coefficients that relate the input signal to the ILA output and the clipped signal; \(z(n)\) is defined by the attenuation associated to the value of the maximum input peak power between the maximum value of the system power multiplied by the amplified signal, \(z(n)\) is used in the coefficient estimation process for the ILA approach. The CFR and linear correction signals are separated, the peaks in the linear signal, measured at the channel filter output, are detected. A band-limited pulse is generated at each peak location.