## 1 Introduction
### Related Work  
Several pieces of literature have proposed a machine learning algorithm for the mitigation of the PAPR [4, 11, 12, 13]. Before this study, we will discuss the nonlinearity reduction technique, which resulted in PAs. The first one is a PA with memoryless nonlinearity; the most common method used in this nonlinear PA model is the solid-state power amplifier (SSPA), soft limiter (SL), and traveling wave tube (TWT). For nonlinearity reduction, another PA model with memory nonlinearity is used, which is described in the literature [14, 15, 16, 17, 18]. The digital predistortion (DPD) algorithm is used in current telecommunication networks for the mitigation of PAPRs. A tremendous amount of research has been presented about the DPD. It deforms the signal before it goes to the PA in a way that the nonlinearity is reversed. It solves the problem of information loss due to nonlinear amplification in the PA. Hence, it is regarded as an adaptive and iterative process, which means the signal input and time will change its coefficients of DPD filters [19]. Thus, taking the inverse function of the PA input and output characteristics, an ideal predistorter can be formed. A large back-off is needed to resolve the nonlinearity problem; in other words, PBO (peak back-off) [20]. It is the difference in the power (dB) between the max desired output and the power of PA saturation. This makes a forceful operation by making the PA linear because the input passes through the nonlinear region of its characteristics and then the input power of the signal is reduced. When the value of the PBO is higher, it results in a higher BER and less efficiency. Among all linearization methods, the DPD is the only choice selected by the industry. The DPD algorithm is briefly explained in [21, 22]. In [7], the authors evaluated the performance of OFDM modulated symbols in a frequency-selective fading channel. The authors utilized a traveling wave tube (TWT) model of the PA in the article [23]. To reduce the nonlinearity, the authors presented novel research in the literature [24]--the signal constellation based on active constellation extension (ACE) built with a neural network termed time-frequency neural network (TFNN) is estimated. In this method, the time and frequency domain are considered simultaneously. The clipping technique is used to reduce the magnitude in the time domain. Furthermore, for the frequency domain, the constellation movement is restricted to only a few reasonable values. This model separates the real and complex parts of the symbols. The two neural networks are formed as \(\mathit{Model}_{Rail}^{TNN}\) and \(\mathit{Model}_{Imaginary}^{TNN}\). The authors used the maximum likelihood method to detect the distorted symbols at the receiver. The autoencoder scheme for the reduction of the PAPR in the literature [25] uses the autoencoder of deep learning termed PRNet. The PRNet method performs well in both PAPR and BER at the cost of computational complexity. The deep neural network-based OFDM receiver has been proposed in the literature [26; 27] for UWA communication. The authors used a single neural network to implement aggregate signal processing. This method was tested by using a ray-tracing toolbox with a sound speed profile (SSP) measured in a real sea experiment. In the research [28], the authors adopted adaptive modulation for reducing the filter concatenation effect for optical OFDM communication. The transmission performance was improved by up to 60%. Four types of optical filters, including fiber Bragg grating (FBG), wavelength-selective switch (WSS), thin film, and Chebyshev, were used to evaluate system's performance. The power loading (PL), bit loading, and bit-and-power (BPL) loading algorithms were introduced in the literature [29] by over 1000 statistically constructed worst-case multimode fiber (MMF) links without incorporating inline optical amplification. The authors proposed compressed sensing (CS) in [30; 31; 32] for mitigation of clipping noise in UWA communication.