# Improved Performance in the Detection of ACO-OFDM Modulated Signals Using Deep Learning Modules
## 4 Simulation Results  
In this section, we describe the simulation results of our DL models and compare them with the simulation results of regular ACO-OFDM schemes in terms of performance and energy consumption. Our aim is to replace the regular ACO-OFDM receiver with the DL systems that we built. In order to check our DL models, we needed to generate datasets of input and output data vectors. The input to the DL system is the modulated data received at the input to the receiver. The output of the DL system is the detected data bits. Through the training process, the DL system tries to learn to recover the data in a number of iterations until it succeeds in reaching the minimum distance between the original and the recovered data bits. The dataset of our DL systems includes 10,000 random input-output vectors built by the MATLAB program. We built our DL decoders using Tensorflow software. The output vectors are the output of the DL decoder and are of size 256 data bits of 0 and 1. The input vectors are input ACO-OFDM data bits modulated by 16 subcarriers. We run our simulations on a computer with a CPU Intel Core i7-7500U 2.7 GHz. We tested our DL models and compared them with the standard ACO-OFDM decoder system for different levels of turbulence in the channels. We passed our modulated ACO-OFDM data through weak and strong turbulence in cases of slow fading with a stationary channel and fast fading with a non-stationary channel. The strength parameters for the different turbulence channels that we used and the hyperparameters of our DL systems are presented in Table 1.  
The BER performance results of our DL models compared with the regular ACO-OFDM decoder system when the channel is with fast fading and non-stationary are presented in Figure 5 for strong turbulence. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Number of generated data bits & 256 \\ Number of subcarriers & 16 \\ Channel 1: weak turbulence & \(\alpha_{\text{B}}^{2}=0.1\) \\ Channel 2: strong turbulence & \(\sigma_{\text{R}}^{2}=3.5,\ \alpha=4.2,\ \beta=1.4\) \\ Number of iterations & 50 \\ Dataset size & 10,000 \\ Activation function & Relu \\ Loss function & Softmax cross entropy \\ Optimizer & Adam \\ Learning rate & 0.01 \\ Batch size & 10 \\ Train data percentage & 90\% \\ Test data percentage & 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. The red curve is the BER performance of the ACO-OFDM decoder using the MMSE estimator, the black curve is the results of our FCNN model, and the blue curve is the results of our FC DL model. We see that the results of our DL models are very close to each other and very close to results of the regular ACO-OFDM until SNR = 13. After this, our DL models improve the performance of the ACO-OFDM system and lead to a significant decrease in BER compared to the regular ACO-OFDM decoder. For example, after SNR = 14, the BER performance of our models decreases rapidly to values less than \(10^{-6}\). On the other hand, the BER performance in regular ACO-OFDM for the same SNR is equal to \(10^{-4}\), and at SNR = 25, it reaches \(5.10^{-4}\) and does not decrease further, because the channel is non-stationary, and it is difficult for the MMSE estimator to estimate the CSI in order to get optimal performance. The results of our FCNN DL model when the channel is stationary with slow fading and strong turbulence are presented in Figure 6.  
The results of our FCNN DL model when the channel is stationary with weak turbulence are shown in Figure 7.  
Figure 5: Bit error rate (BER) performance against normalized SNR for ACO-OFDM with minimum mean square error (MMSE) estimator, our FC model, and the FCNN model for strong turbulence and non-stationary channel. Figure 6: BER performance against normalized SNR for ACO-OFDM with MMSE estimator and our FCNN model when the channel is stationary with strong turbulence.