## 5 Proposed Neural Network Solution
### Proposed Dataset Compilation and Network Selection
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. During training the network model in Figure 5, each training data point is formed from \(\mathcal{D}\) by constructing an input training vector, \([\mathcal{R}\{\mathcal{D}(i,j,1)\},\mathcal{I}\{\mathcal{D}(i,j,1)\}]^{T}\), and a corresponding target vector, \([\mathcal{R}\{\mathcal{D}(i,j,2)\},\mathcal{I}\{\mathcal{D}(i,j,2)\}]^{T}\). The training process goes on until the mean square error (MSE) between the actual output of the NN module and the target output is minimized. An SNN-CF network is found once the training process halts. The network is then ready and can be deployed for the processing of raw OFDM signals that it has not processed before while learning SCF patterns. Compared to ANN, the proposed SNN-CF scheme is able to converge within fewer iterations during the training stage. When deployed for operation, SNN-CF starts by reformatting the original OFDM input \(x[n]\) to produce \([\mathcal{R}\{x[n]\},\mathcal{I}\{x[n]\}]^{T}\), a 2-D vector representation of the in-phase and quadrature components of \(x[n]\). The input vector is then applied to the network's Hidden Layers section which is preconfigured during the training stage to implement a map \(f:\mathbb{R}^{2}\rightarrow\mathbb{R}^{2}\) in the neighborhood of conventional ICF or SCF. The output layer processes the 2-D signal vector produced by the vector mapper \(f\) to generate a close estimate to \(\hat{x}[n]\), which would be the output of conventional ICF or SCF for the same input \(x[n]\). Attaining a higher performance than conventional CF-based schemes is accomplished by exploring the space of different maps in the neighborhood of ICF or SCF. This is performed by repeatedly training different SNN-CF modules until a network providing the highest positive performance gap is found under certain quality of service (QoS) requirements. Thus, to ensure the fidelity of the solution, we impose a threshold BER, \(\mathcal{E}_{t}\), for the trained SNN-CF network at an arbitrary \(E_{b}/N_{0}|_{t}\). Therefore, in order to find a mapper \(f\) with desirable characteristics, we explore the neighborhood of a conventional CF map during the offline training stage. The outline of the proposed network-selection algorithm is given in Algorithm 2. The basic concept of the algorithm is to optimize the network structure to achieve the lowest possible CM value while maintaining a given QoS requirement. Although a maximum allowable BER level is used as a metric to enforce the required QoS, other metrics can be applied, such as the sum-rate and error vector magnitude (EVM). In fact, EVM is used as a metric to achieve the target BER in [20]. The algorithm starts by initializing an SNN-CF network, _Net(0)_, with a random parameter set \(\phi\) and updates it using a random batch of training data points from the dataset \(\mathcal{D}\) in order to find a mapping solution that minimizes the MSE mentioned previously. For a  
Figure 5: The proposed scheme: (**a**) training; and (**b**) deployment. preset number of iterations, different SNN-CF networks are generated.