## 3 The Algorithm  
Once the ECM-368 standard and the PAPR problem has been briefly described, in this section, a solution is devised. In the literature, there are many proposal for PAPR reduction in OFDM-based signals, as explained at the introduction. Among them, the ACE algorithm is one of the best options to obtain a signal with arbitrarily low PAPR with the adequate number of iterations (usually high). The ACE method modifies and expands the constellation points within an allowable region without affecting the demodulation slicer, and thus, it does not need side information. As it is described in [10], the ACE-AGP is an iterative algorithm. In the following, the algorithm will be summarized. Every constellation point is moved within the allowable region away from its initial position in an iterative procedure. As example, for QPSK and 16-QAM cases, in Figure 3, the allowable regions are depicted (shadowed). We first clip the signal peaks in the time-domain signal and observe what happens in the frequency-domain. If points moved into an allowable region, the algorithm keeps them, if not, they are restored to their previous positions and the time-domain signal is evaluated again. Mathematically, it can be summarized as follows:  
1. Use \(IFFT\) to obtain \(x\) from the modulated signal \(X\). Reset the number of iterations \(j\) to 0. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Number of data subcarriers & 100 \\ Number of pilot subcarriers & 12 \\ Total of subcarriers used & 122 \\ Subcarrier frequency spacing & 4.125 MHz \\ IFFT/FFT period & 242.42 ns \\ Zero padded suffix duration & 70.08 ns \\ Symbol interval & 312.5 ns \\ Number of samples per zero padding suffix & 37 \\ Total number of samples per symbol & 165 \\ Symbol rate & 3.2 MHz \\ Subcarrier modulation & QPSK or DCM \\ Code rates & 1/3, 1/2, 5/8, 3/4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: OFDM parameters for the ECMA-368 standard. Figure 2: PHY frame structure. 2. Clip all \(|x^{j}[k]|\geq B\) (where B represents the signal's magnitude), then \(x[k]\) becomes: \[\overline{x}[k]=\left\{ \begin{array}{ll}x^{j}[k]&|x^{j}[k]|\leq B,\\ Be^{\mu B[k]}&|x^{j}[k]|>B.\end{array} \right.\] (2)
3. Calculate the added clipped signal portion: \[c_{clip}[k]=\overline{x}[k]-x^{j}[k].\] (3)
4. Obtain \(C_{clip}\) by applying an \(FFT\) on \(c_{clip}\)
5. The only \(C_{clip}\) components with acceptable extension directions respecting the given sub-channel constellations are kept, the rest is set to 0. \[C_{clip}[k]=\left\{ \begin{array}{ll}0&(|\Re(C_{clip}[k])|+|\Re(x^{j}[k])|) \leq Q,\\ 0&(|\Im(C_{clip}[k])|+|\Im(x^{j}[k])|)\leq Q,\end{array} \right.\] (4) where \(Q\) represents the allowable regions of QPSK modulation. 6. Obtain \(c_{clipnew}\) using \(IFFT\) and compute: \[X^{j}_{new}[k]=X^{j}[k]+c^{j}_{clipnew}[k].\] (5)
7. If the target PAPR requirement is not achieved or the maximum number of iterations (\(j\)) is not reached, go to Step 2. Otherwise, the algorithm finishes and the output is the obtained signal. For less complexity and fast convergence, authors in [11] proposed a novel NN architecture designed and trained to obtain low PAPR signals by synthesizing the behavior of the ACE-AGP algorithm, but with much less complexity. The idea is to design an NN that would be able to obtain similar signals than ACE-AGP but with less complexity and without the iterative process that takes time and resources. To do this, as explained in [11], the NN is trained with time-domain and frequency-domain signals obtained from ACE-AGP as references. Thus, once the NN is trained, it is able to generate similar signals (with low PAPR) directly from the original ones without the iterative process and with less complexity. Thus, authors in [11] developed NN models based on the time-domain and frequency-domain OFDM signal, respectively, and provide the theoretical framework. Here, a brief description is provided for clarity purposes.