## 5 Proposed Neural Network Solution
### Proposed Dataset Compilation and Network Selection  
A 3-D training dataset, \(\mathcal{D}\), is formed by running Algorithm 1. Initially, \(\mathcal{D}\) is propagated by zeros. The dataset, \(\mathcal{D}\), is comprised of multiple 2-D slices as shown in Figure 4. The \(i\)-th 2-D slice, \(\mathcal{D}(i,\ldots)\)\(\forall\)\(i=1,2,\ldots,S\), is filled with a random selection of a group of \(\eta N\) time-domain samples. The samples are obtained by generating a vector of samples of an original OFDM symbol, \(x_{i}[n]\)\(\forall\)\(n=1,2,\ldots,\eta N\), which is then fed to an ICF-based clipping algorithm to generate the corresponding output training vector, \(x_{o}[n]\)\(\forall\)\(n=1,2,\ldots,\eta N\). SCF-based training can be applied alternatively. The samples of the two generated vectors are jointly scattered across the slices in a random fashion as shown in Figure 4. The process is repeated until all the slices within \(\mathcal{D}\) are filled with the training data. Figure 4: Proposed dataset compilation mechanism. Figure 3: FFMLP neural networks: (**a**) general structure; and (**b**) OFDM signal processing. Figure 5 illustrates the concept of the proposed SNN-CF scheme. Unlike conventional NN solutions, we propose using a synchronous FFMLP-based network structure to achieve a more accurate performance with a slight increase in computational cost. In this scheme, instead of processing the correlated (I) and (Q) parts independently, only one FFMLP module is employed to process both parts simultaneously, using 2-dimensional (2-D) input and output sequences (\(M=2\) and \(P=2\) in Figure 3a). This synchronous approach can emulate SCF with higher flexibility and handle underfitting and overfitting problems more gracefully than ANN where two modules are trained separately. Therefore, SNN-CF essentially models \(\mathcal{R}\left\{\tilde{x}[n]\right\}\) as a function of both \(\mathcal{R}\left\{x[n]\right\}\) and \(\mathcal{I}\left\{x[n]\right\}\). Similarly, \(\mathcal{I}\left\{\tilde{x}[n]\right\}\) is modeled as a function of both \(\mathcal{R}\left\{x[n]\right\}\) and \(\mathcal{I}\left\{x[n]\right\}\). Thus, SNN-CF has potentially higher chances of capturing the essence of the SCF peak-limiting mapping algorithm. ```
- Initialize\(s=0,\mathcal{D}=0_{S,\eta N,2}\)
- While\(s<S\) repeat the following steps: 1. Generate training samples:
- Apply IFFT to compute the time-domain OFDM signal, \(x[n]\), of (1):
- Append \((\eta-1)N\) trailing zeros to \(X[k]\) for oversampling. - Compute IFFT of \(X[k]\) with size \(\eta N\). - Save the generated OFDM signal: \(x_{i}[n]\gets x[n]\)
- while \(l<L\), repeat the following steps:
- Generate clipped OFDM signal, \(\hat{x}[n]\), by replacing all samples of \(x[n]\) with amplitudes exceeding the limiting value, \(R\), according to, \(\hat{x}[n]=R\hat{e}^{j\angle x[n]}\ \forall\ n\ \
i|x[n]|>R\,,\) where \(R=C\sqrt{\overline{x[n]}}\) and \(C\) is the desired clipping ratio. - Filter the resulting OoB radiations: - Compute FFT of \(\hat{x}[n]\) with size \(\eta N\) to generate \(\hat{X}[k]\). - Zero out the trailing \((\eta-1)N\) frequency-domain samples of \(\hat{X}[k]\) to generate filtered OFDM signal, \(\hat{X}[k]\). - Recompute the corresponding time-domain OFDM signal, \(\hat{x}[n]\), using IFFT with size \(\eta N\). - \(x[n]\leftarrow\hat{x}[n]\,\ l\gets l+1\) - end while - Save the generated OFDM signal: \(x_{o}[n]\leftarrow\hat{x}[n]\) 2. Scatter the \(\eta N\) input and output OFDM samples across \(\eta N\) random empty locations within \(\mathcal{D}\): \[\mathcal{D}(i,j,1)=x_{i}[n],\] \[\mathcal{D}(i,j,2)=x_{o}[n]\] 3. \(s\gets s+1\) - endwhile
```  
**Algorithm 1** Proposed Dataset Compilation. Figure 5: The proposed SNN-CF scheme. Unlike conventional NN solutions, we propose using a synchronous FFMLP-based network structure to achieve a more accurate performance with a slight increase in computational cost.