# Machine Learning-Based 5G-and-Beyond Channel Estimation for MIMO-OFDM Communication Systems
## 4 Simulation Results
### Performance Comparison with the Conventional Estimators  
To evaluate the performance of the proposed estimators, the simulation was carried out and the results compared with the conventional LS estimation and LMMSE estimation by utilizing the bit error rate (BER) and mean square error (MSE) versus signal to noise ratio (SNR). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline MIMO & 4 \(\times\) 4 \\ FFT size & 256 \\ Subcarrier spacing & 15 kHz \\ Cyclic prefix & 24 \\ Type of modulation & 16-QAM \\ Channel PDP & TDL-C \\ Maximum Doppler frequency & 36 Hz, 200 Hz \\ Noise model & Gaussian Noise \\ Sample frequency & 3.84 MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameter setup for the considered MIMO-OFDM system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Kernel** & \(f(.)\) \\ \hline Input layer & 16 \(\times\) 256 & - \\ Conv1 layer & 3 \(\times\) 3 \(\times\) 64 & ReLU \\ Conv2 layer & 3 \(\times\) 3 \(\times\) 64 & ReLU \\ Conv3 layer & 3 \(\times\) 3 \(\times\) 64 & ReLU \\ Conv4 layer & 3 \(\times\) 3 \(\times\) 32 & ReLU \\ Linear layer & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Architecture of CNN model for channel estimation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Nodes** & \(f(.)\) \\ \hline Input layer & 32 & - \\ Hidden layer 1 & 64 & tanh \\ Hidden layer 2 & 64 & tanh \\ Hidden layer 3 & 64 & tanh \\ Output layer & 32 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The architecture setup of the FDNN-based channel estimation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of input feature layers & 32 \\ Number of LSTM layers & 2 \\ Hidden layer size & 100 \\ Sequence length & 256 \\ Activation function & Tanh and Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Architecture of bi-LSTM model for channel estimation. To investigate the performance of all the considered channel estimations used in the MIMO-OFDM system through the 5G channel model, two different scenarios corresponding to the velocity of mobiles were exploited. In the first scenario, the receiver moved with a low speed such that the maximum Doppler frequency was 36 Hz. The pilot symbols were inserted along with data in both frequency and time domains. In the frequency domain, we referred to the type 1 configuration of DM-RS as in [36]. In this configuration, six subcarriers were defined for the DM-RS signal for each physical resource block that contained 12 subcarriers. Thus, the pilot spacing in the frequency domain was \(D_{f}=2\) for both scenarios. In the time domain, the 5G system supported up to 4 pilot symbols in 1 slot that included 14 OFDM symbols. Therefore, in the first scenario, since the channel slowly changed over time, the pilot spacing in the time domain was \(D_{t}=14\). In the second scenario, the system exhibited high-speed mobility, which resulted in the maximum Doppler frequency of 200 Hz. In this scenario, the setup \(D_{t}=7\) was used to cope with the rapid change of the channels over time. Figures 9 and 10 show the MSE of different channel estimations in the first and second scenarios, respectively. The 16-QAM (quadrature amplitude modulation) method was deployed to modulate the transmitted data in the simulation. As shown in Figures 9 and 10, all the channel estimation methods led to the MSE declining gradually as the SNR increased. In both the scenarios, LS estimation yielded the worst MSE performance, which was because it does not take the statistical channel information into account when performing the channel estimation. On the contrary, LMMSE estimation exploits the mean and covariance matrices, which resulted in better MSE performance than its LS counterpart. Our proposed deep learning estimators yielded the best MSE performance compared to the two conventional methods. In detail, the FDNN model showed the smallest MSE compared to the two other deep learning models.