# Low-Complexity Convolutional Neural Network for Channel Estimation
## 4 DL-Channel Estimation
### Proposed Convolutional Neural Network
The real (**a**) and imaginary (**b**) parts are processed in parallel. channels translate in less data to store and process, which reduces the memory requirements and quickens the training process. Every design choice of the proposed CNN is a strategic decision aimed at balancing the model's performance, computational efficiency, and resource constraints for practical real-world applications. This was achieved by a combination of empirical testing and insights from relevant prior research. Each parameter involved in the neural network, such as dimension of the kernel, padding, and number of channels, was tuned at each layer. This allowed us to notice that it is more advantageous in term of accuracy to include larger kernels in the first layers rather than later ones. Instead, the number of channels was identified as a parameter that could be minimized to reduce computational costs. This is due to the fact that the channel, seen as an image, does not have highly detailed information. A similar investigation was conducted for the padding method and the location of the size increments. Three different types of padding methods were considered: replication of the edges, zero-padding, and symmetric padding. The latter result was more effective thanks to propagation of the DMRS structure in the resource grid, while the location of the size increment was found to be more effective when placed at the beginning of the network. In order to assess the advantages of this model, two additional CNN structures with pre-interpolation stages have been implemented. These two architectures are going to differ in the number of layers; one is composed of three layers while the other is designed with six layers. Increasing the number of layers should increase the accuracy, compromising the computational cost, giving good benchmarks in the subsequential analysis. An illustrative comparison is also included in Figure 6, where Figure 6 describes the traditional approach using interpolation, and Figure 6 shows in detail all of the settings at each layer in the proposed CNN. The model reported in Figure 6 receives the preliminary estimation provided by LS and the results are interpolated, increasing the size of the input from 288 \(\times\) 3 to 288 \(\times\) 14. The Input Image Layer forwards the input image to the first CONV Layer, which adopts 3-D filters with planar sizes of 9 \(\times\) 9. Padding sizes are set to \(P_{H}=P_{W}=4\) in order to preserve the sizes of _fmaps_. A sequence of \(L\)-2 CONV Layers, with \(L\) being the number of layers, is stacked throughout the model. Each of them consists of several filters with 5 \(\times\) 5 planar sizes. Moreover, in this case, the sizes of the generated _fmaps_ are preserved by setting \(P_{H}=P_{W}=2\). Finally, the last CONV Layer performs the remaining computations to generate the estimated channel. It is worth underlining that the stride \(S_{H}=S_{W}=1\) throughout the CNN and the Rectified Linear Unit are used as non-linear activation. The model reported in Figure 6 receives the original symbols after application of LS without an interpolation stage (288 \(\times\) 3). The Input Image Layer forwards the input image to the first CONV Layer, which adopts 3-D filters having planar sizes 5 \(\times\) 5. In this scenario, CONV layers are responsible for progressively increasing the size of input symbols to build the full-size channel grid. To reach this goal, the padding sizes are tuned in each layer. In this case, \(P_{H}=2\) allows the number of subcarriers to be kept unchanged, while \(P_{W}=4\) allows the size \(N_{OFDM}\) to grow from 3 to 7. The second CONV layer adopts 9 \(\times\) 9 filters, which lead to 288 \(\times\) 13 planar representations. The last three CONV layers, having \(K_{H}=K_{W}=5\), extract further features from internal data and specifically the fifth layer increases the size from 13 to 15. At the end, a Resize layer is used to crop 1 column to meet the desired number of OFDM symbols (288 \(\times\) 14).