# Going Deeper into OSNR Estimation with CNN
## 2 Principle of Proposed Scheme
### Proposed Scheme: OptInception  
Figure 3 shows the whole architecture of the proposed network, OptInception, and its advanced version, OptInception-Pro, in this paper. We deepen the OptInception by cascading multiple Inception-ResNet modules in OptInception-Pro, which is inspired by Inception-v4. The input length of the network is \(1\times 1024\) for four channels, which correspondingly represents sampled data from the optical field of in-phase and quadrature-phase components in both horizontal and vertical polarization. The detailed structures of Inception blocks and Reduction blocks are shown in Figures 4 and 5, respectively. In the Figures, the sizes of data flowing in the networks and convolutional kernels are in the form of _Channels@\(1\times Length\) of data(kernel) in every channel_. The same padding is the default strategy, while 'Valid' is marked in the convolutional layer if valid padding is used. Layers  
Figure 2: Structure of the Inception block.  
without an activation function are noted with 'Linear' in parentheses. Concatenation of branches in Inception blocks is named 'Filter concat' for short.  
In order to estimate OSNR with neural networks, the key is the acquisition of characteristics of signal and noise power from raw data, as clarified above in (2). As clarified in (25), convolutional layers fed with four channels of raw data asynchronously sampled by ADC act as filters to extract various components of signals. Meanwhile, these filters in convolutional layers can be automatically trained by a back-propagation algorithm without any manual intervention. On this basis, longer convolutional kernels are applied for signal processing with higher resolution when feature separation of signal and noise can be more precise in an Inception-FIR block in a proposed scheme. Inspired by the structure of the Inception block itself, different lengths of CNN kernels are deployed in parallel and then concatenated by channels. Furthermore, it maintains integration of signals without the negative part being cut off, meaning that ReLU or other nonlinear activation functions are not applied to the convolution results. For max pooling in particular, pooling can lose a lot of information, ending with a deteriorating feature extraction effect in the successive  
Figure 3: Whole architecture of (**a**) OptInception and (**b**) OptInception-Pro.  
network section, as explained in Section 2.2. Pooling layers which will not contribute to the separation were not laid out in this block.  
Next, residual connections were introduced into subsequent Inception blocks to improve computation efficiency in deep network training. Considering that the network we design is definitely deep with multiple Inception blocks and fully connected layers, this practical structure is necessary and useful.  
Following the Inception-ResNet blocks, reduction blocks named Reduction-1 and Reduction-2 were designed to help aggregate features and decrease the grid sizes of the feature maps. In the Reduction module, average pooling and \(1\times 1\) convolution were both used. Only one of them should be used in a single branch of the Inception parallel structure as usual.  
Figure 4: Structures of Inception blocks.  
After three Inception-ResNet and two Reduction blocks, the trained feature maps were sent to average pooling before being flattened. Four fully connected layers with two hidden layers and without an activation function applied at the output of the network were arranged in order to fit the mapping to OSNR that is a continuous value.  
All in all, the general architecture of OptInception can be divided into three procedures. In the beginning, the Inception-FIR is responsible for the reception of input data and feature separation. Secondly, feature extraction is conducted in Inception-ResNet and Reduction blocks. Finally, the features learned previously are mapped to a corresponding OSNR value in FC networks.