# Improved Performance in the Detection of ACO-OFDM Modulated Signals Using Deep Learning Modules
## 4 Simulation Results
In Figures 6 and 7, the red curve represents the BER performance of the regular ACO-OFDM decoder using the MMSE estimator, and the black curve represents the results of our FCNN model. We see that our FCNN DL model yields performance very close to that of the MMSE estimator when the channel is stationary with weak turbulence or with strong turbulence. However, the advantages of our DL models are clearly shown in Figure 8. When the channel is characterized by weak turbulence and is non-stationary with fast fading, the regular ACO-OFDM decoder using the MMSE estimator does not succeed in recovering the corrupted data. Since for the same BER this method requires higher SNR, it consumes much more energy compared to our DL models, which succeed in recovering the data with less energy consumption and manage to decrease BER by more than 8 dB. For example, when the SNR is larger than 25, the regular ACO-OFDM decoder yields a BER performance equal to \(10^{-6}\) and does not achieve a lower value than this, even at higher SNR. However, in our FCNN DL model, when the SNR is 17 dB, we succeed in getting BER performance equal to \(10^{-7}\), and with this SNR, we recover the transmitted data without errors. In other words, we get a BER equal to zero. In addition to this, another advantage of our DL models is that they are faster than the regular ACO-OFDM decoder. The prediction time of our DL models after the training process is faster than that of the regular ACO-OFDM decoder, as shown in Figure 9.  
Figure 8: BER performance against normalized SNR for ACO-OFDM with an MMSE estimator and our FCNN model when the channel is non-stationary with weak turbulence. Figure 7: BER performance against normalized SNR for ACO-OFDM with MMSE estimator and our FCNN model when the channel is stationary with weak turbulence. Our FCNN DL model recovers the data more than 10 times faster than the regular decoder. In addition, the prediction time is three times faster than for our FC DL model. This is because the nodes in each layer in the FC model are connected to all the nodes in the next layer. This take time, but the nodes in each layer in the FCNN model are not connected to all the nodes in the next layer. The DL method consumes less time and less energy than the FC model and the regular ACO-OFDM detector. After the training process, we do not need, as in the regular ACO-OFDM decoder, to go through all the blocks of the decoder one by one, which would consume time and energy. After the training process, the weights are saved in the system, and any online received modulated ACO-OFDM can be recovered directly. Therefore, in this work, our DL models succeed in recovering the received ACO-OFDM data when the channel is with strong and weak turbulence, when the channel is stationary with slow fading, and when the channel is non-stationary with fast fading. Our DL models offer performance very close to that of ACO-OFDM using the MMSE estimator, and it is even slightly better when the channel is stationary. However, when the channel is fast fading and non-deterministic, our DL models can recover the data with better performance than the MMSE estimator. When the channel is variable, this estimator does not manage to reach optimal performance because the channel is not stationary. In addition to these advantages, our models work faster than the regular ACO-OFDM decoder, so they are very efficient for use in real environments where energy saving is important.