# Low-Complexity Convolutional Neural Network for Channel Estimation
## 6 Numerical Simulation and Analysis  
To evaluate the performance of the proposed CNN-channel estimation in terms of accuracy in the channel matrix estimation, the MSE is analyzed over a range of SNR values. The main setup parameters are summarized in Table 4, and the simulated system is shown in Figure 9.  
Figure 8: Computational cost analysis among several implemented DL channel estimations varying the number of antennas at the receiver. The transmitting UT uses eight antennas. The calculation is obtained from the above table considering the implemented designs and those reported in the literature [3; 8; 25]. Two antennas for the receiver and the transmitter are considered. The transmitted grid is generated considering only the DMRS signals in the PDSCH. At the receiver, the channel information is estimated using five different types of channel estimation designs and compared with the perfect knowledge of the full channel. These are the conventional LS estimation, the MMSE estimation, the pre-interpolated CNN channel estimation with 3L and 6L, and an FCDNN-based channel estimation proposed in [3]. The MSE results are obtained using MATLAB's 5G Toolbox [26] and are presented in the logarithmic scale in Figure 10.  
All of the MSE curves improve as the SNR increases, following a linear trend. The difference is in the rate of decreasing MSE. The LS technique decreases faster with the SNR growth, while the rest of the curves present a slower trend. However, as expected, the traditional LS technique generates the highest MSE, becoming competitive only at high SNR values. On the other hand, the neural networks (CNN-6L, CNN-3L, FCDNN, and the proposed CNN-based channel estimation) are all very close to the MMSE technique, commonly considered the most accurate. The lowest MSE values are obtained by the technique described in [3] and the CNN-6L design. However, they are not convenient in terms of complexity considering their dependency with the number of antennas and the evolution of this parameter in the communication systems (e.g., Massive MIMO and Gigantic MIMO [27]), especially for the FCDNN network where the number of neurons is proportional to the total number of antennas in the system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Settings** \\ \hline Antennas & 2 Rx and 2 Tx \\ Resource blocks & 24 \\ Subcarrier spacing & 15 \\ Mapping type & A \\ Layer & 1 \\ Symbol Allocation & [0 14] \\  & DMRS Configuration type = 2 \\ DMRS configuration & DMRS length = 1 \\  & DMRS Additional Position = 2 \\ Nift & 512 \\ Channel & Channel profile = TDL-A \\ Channel & Doppler Shift = 36 \\ Delay spread = 300 \(\times\) 10\({}^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main setup parameters for the simulated system. Figure 9: Diagram of the simulated system comparing the channel estimation from the proposed structure with CNNs with pre-interpolation, LS with post-interpolation, and MMSE with post-interpolation. Despite a slightly reduced accuracy achieved by the proposed technique, its overall performance is very much in line with the state-of-the-art methodologies. This reduction is expressed in an increase of the MSE at each SNR level, and it is expected due to the approximation introduced for reducing the complexity. The first factor which played an important role is the use of the padding method to increase the dimensions in favor of the computational cost. Therefore, the interpolation stage is not needed, and the full-channel dimensions are achieved symmetrically mirroring the reference information. Two other important factors in the reduction of accuracy are the low number of channels and layers in the proposed CNN. As already mentioned, each layer helps to denoise the input and the channels collect the feature information. Indeed, the impact of increasing the number of layers and channels is also proven by the CNN-6L and CNN-3L neural network performances.