# The Extended SLM Combined Autoencoder of the PAPR Reduction Scheme in DCO-OFDM Systems
## 3 Results and Discussion  
In this section, simulation results are presented to demonstrate the PAPR and BER performances of the proposed scheme in different channels. The parameters of the network are shown in Table 1.  
In the training of the proposed network, a total of 64,000,000 independent random bits are used for training, 12,800,000 bits for validation and 12,800,000 bits for testing, respectively. Taking \(SNR=15\) dB for an example, the corresponding average PAPR and BER results of training set, validation set, and test set are given in Table 2. Note that all the following simulation and discussion of the proposed ESLM-AE and AE schemes are based on the results of test set. For comparison, we also investigate the performances of other PAPR reduction schemes such as basic AE network without ESLM method, classical SLM [41] using \(U=128,\mathrm{B}_{\mathrm{DC}}=7\) dB and amplitude clipping [30] with a different clipping ratio \(\gamma\). All the simulation results are taken from 100000 OFDM symbols, and 4-quadrature amplitude modulation is adopted. The number of phase sequences for SLM considered here are significantly high to maintain the SLM performance depicted here close to the upper-bound on the scheme's performance. The schemes are listed as follows:  
Clipped DCO-OFDM and Clipping with clipping ratio \(\gamma\) refer to the conventional DCO-OFDM sample values which are larger than the upper levels or less than the lower levels are directly upper or lower clipped without any other recovery methods. ESLM-AE and AE with clipping ratio \(\gamma\) refer to the ESLM-AE and AE sample values are symmetrically clipped similar to the direct upper and lower clipping implementation. To compare the computation complexity of SLM and the proposed ESLM-AE, the Big \(O\) notations of the two methods are given below. For SLM with U groups of phase factors. For each group, the most time-consuming part is the process of the IFFT, with time complexity of \(O(N^{2})\), where \(N\) is the number of subcarriers. To select the best phase factor for PAPR reduction, the time complexity of the SLM algorithm is \(O(UN^{2})\), where \(U\) is the total number of phase vectors. For the ESLM-AE algorithm, \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Transmitter (TX) dimensions & \\ Input & 128 \\ Dense (ReLU) & 2048 \\ Dense (ReLU) & 2048 \\ Dense (ReLU) & 128 \\ Receiver (RX) dimensions & \\ Input & 128 \\ Dense (ReLU) & 2048 \\ Dense (ReLU) & 2048 \\ Dense (sigmoid) & 128 \\ Optimizer & SGD with [PERSON] [40] \\ Learning rate \(\lambda\) & 0.0001 \\ Batch size & 32 \\ Weight parameter \(\eta\) & 0.01 \\ Dropout probability & 0.1 \\ Number of subcarriers & 128 \\ Length of cyclic prefix & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the proposed network. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Results** & **Average PAPR** & **BER** \\ \hline Training set & 2.0198 & 0.0003976 \\ Validation set & 2.0499 & 0.0004077 \\ Test set & 2.0439 & 0.0004059 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results Comparison of the training set, validation set and test set. the training process is offline. Once the network weights are determined, when new messages come, only the forward propagation of network are needed. Assume there are \(L_{f}\) hidden layers in encoder network, and \(L_{g}\) hidden layers in the decoder network. All the hidden layers are assumed to have \(M\) neurons. The computation complexity of encoder network is \(O(2*N*M+(L_{f}-1)*M*M)\). Similarly, the computation complexity of decoder network is \(O(2*N*M+(L_{g}-1)*M*M)\). In the ESLM-AE, the phase factor is also determined in the training phase, and only one IFFT is needed to be computed which computation complexity is \(O(N^{2})\). Therefore, the computation complexity of ESLM-AE is \(O(4*N*M+(L_{f}+L_{g}-2)*M*M)+N*N)\). In practice, \(U\), \(N\) and \(M\) are in the same scale.