# Deep-Learning-Based Stream-Sensing Method for Detecting Asynchronous Multiple Signals
## 5 Learning-Based Asynchronous Stream Sensing
### Asynchronous Stream-Sensing Network
#### 5.2.2 Autoencoder Extractor  
In ASensNet, the AutoEncoder Extractor is based on the deep autoencoder that is widely used for efficient encoding and reduction of dimensionality [40]. Such a deep autoencoder structure is specialized to extract low-dimensional core features from high-dimensional data. Therefore, using the autoencoder structure, this extractor is responsible for extracting features from covariance matrices \(\mathbf{D}_{i,s},\forall i,s\) in \(\mathbf{I}\). Specifically, for the autoencoder network, each subnetwork regenerates the input \(\mathbf{I_{R}}\) (or \(\mathbf{I_{I}}\)) in the output. For real and imaginary subnetworks, 'Encoding Block' extracts real and imaginary latent vectors denoted as \(\mathbf{z_{R}}\) and \(\mathbf{z_{I}}\), respectively. 'Decoding Block' generates \(\mathbf{I_{R,reen}}\) and \(\mathbf{I_{I,reen}}\) based on \(\mathbf{z_{R}}\) and \(\mathbf{z_{I}}\), respectively.  
**Feature Extraction**: Since 'Decoding Block' aims to make \(\mathbf{I_{R,reen}}\) and \(\mathbf{I_{I,reen}}\) the same as \(\mathbf{I_{R}}\) and \(\mathbf{I_{I}}\), 'Encoding Block' should generate \(\mathbf{z_{R}}\) and \(\mathbf{z_{I}}\) that include low-dimensional necessary information for 'Decoding Block' to regenerate the input. In other words, for subnetworks, the latent vectors \(\mathbf{z_{R}}\) and \(\mathbf{z_{I}}\) are bound to contain the most essential features that represent \(\mathbf{D_{R,(i,s)}}\) and \(\mathbf{D_{I,(i,s)}}\) in the input \(\mathbf{I_{R}}\) and \(\mathbf{I_{I}}\), respectively.  
As a result, from \(\mathbf{D_{R,(i,s)}}\) and \(\mathbf{D_{I,(i,s)}}\) in \(\mathbf{I_{R}}\) and \(\mathbf{I_{I}}\), 'Encoding Block' extracts distinct low-dimensional features depending on the number of rescue signals in a received signal.  
**2D Dilated Encoder**: In our AutoEncoder Extractor, there are two types of two-dimensional encoder: a '2D Encoder' and a '2D Dilated Encoder'. The 2D dilated encoder is constructed by stacking 2D dilated convolution layers, while the 2D encoder consists of 2D convolution layers, similar to a typical convolutional neural network. By inserting zero between the values in a kernel, a 2D dilated convolution performs convolution with non-adjacent values in an input matrix, which provides a wider field of view at the same computational cost [41].  
For this block, we attach a 2D dilated encoder. Due to the structural feature of the kernel of the 2D dilated convolution, the 2D dilated encoder considers the relationship among non-adjacent values of \(\mathbf{D_{R,(i,s)}}\) (or \(\mathbf{D_{I,(i,s)}}\)). Since \(\mathbf{D_{i,s}}=\mathbf{d_{i,s}}\cdot(\mathbf{d_{i,s}})^{\text{H}}\), considering between non-adjacent values in \(\mathbf{D_{R,(i,s)}}\) (or \(\mathbf{D_{I,(i,s)}}\)) has the same effect as taking non-adjacent values of \(\mathbf{d_{i,s}}\) into account (Note that the \(r\)-th element of \(\mathbf{d_{i,s}}\) is the signal value obtained from the \(r\)-th receive antenna).  
The matrix \(\mathbf{D_{R,(i,s)}}\) is a covariance matrix of a vector \(\mathbf{d_{i,s}}\) that is obtained from a received signal. The received signal consists of multiple signals transmitted from multiple devices and propagating over wireless channels. In the case, the independence of wireless channels can theoretically be preserved only when all transmitted signals are well synchronized. Otherwise, if signals are transmitted asynchronously from devices, the independence is no longer maintained (This is also why the existing mathematical schemes AIC and MDL cannot work with asynchronous transmission, because they were developed based on the assumption of synchronous transmission). The asynchronicity in a received signal could cause in \(\mathbf{d_{i,s}}\) channel correlation among non-adjacent antennas. As a result, through '2D Dilated Encoder' using 2D dilated convolution layers, our AutoEncoder Extractor produces \(\mathbf{z_{R}}\) and \(\mathbf{z_{I}}\) considering spatial correlation among non-adjacent antennas.