## 4 FTN Detection Scheme in Multipath Channels Based on Neural Network
### Detection via CNN  
In the CNN model, we treat FTN detection as a classification problem, select the signal that has not been matched and filtered at the receiving end as the sample set, and theabel set is the symbol sequence of the transmitted signal.The specific structure of using a convolutional neural network as a classification model is shown in Figure 2. Both convolutionalayers use Relu as a non-linear activation function. Finally, after passing through the fully connectedayer, the output probability distribution is obtained from the activation function SoftMax, where the symbol corresponding to the maximum probability is the estimated signal \(\mathbf{\hat{a}}\).  
The rationality of using CNN as the detection algorithm can be explained as follows. In FTN, the influence of the value of the symbol before and after the symbol on the judgment of the current symbol must be considered. From this perspective, the process of the filter sliding on the input data in the CNN model to extractocal features can be regarded as a series of related operations of a small-sized matched filter at different time positions, which measures the magnitude of interference generated by symbols at different moments and uses this as a feature to help subsequent classification judgments.  
For high-order modulation, since the information bits are stored in the real and imaginary parts of the signal, the signal at the receiving end is separated according to the real and imaginary parts and then integrated into the corresponding transmission symbol sequence. Specifically, IQ signals can be connected in parallel and the real and imaginary parts can be input into the networking byine, which is equivalent to processing single-channel two-dimensional images (such as grayscale images). A more reasonable method is to put the real and imaginary signals on different channels, that is, treat the real and imaginary data as different images. This process can be analogous to the three-channel processing of RGB in digital image processing. Furthermore, as the noise interference of FTN signaling in the multipath channel is independent and identically distributed, the correlation between the real part and the imaginary part of the noise is fares clear than the correlation between the adjacent real part or imaginary part signals. Therefore, it can consider using the real part and the imaginary part to be connected to different channels respectively, and the corresponding feature information is extracted, and then the classified results are merged and outputted.  
The advantage of the symbol-by-symbol detection of the CNN model is that the model is simple, but the sample signal is not clear enough to express ISI. Therefore, on this basis, we try to use the idea of discrete signal sequence detection to deal with the problem of strong correlation in the time dimension of the FTN--RNN network model.  
RNN allows information to persist, that is, the current output depends on all previous inputs. From a computational point of view, as the current state depends on previous calculations, and the network performs the same task for each element of the input sequence. In the next section, the Deep-Bi-LSTM network based on RNN will be introduced in detail, and the effectiveness of FTN detection in multipath channels will be analyzed.