# Machine Learning-Based 5G-and-Beyond Channel Estimation for MIMO-OFDM Communication Systems
## 5 Conclusions  
In this paper, we have presented the use of different DNN structures, including a fully-connected DNN, CNN, and bi-LTSM, to assist in the channel estimation process in a MIMO-OFDM system with different scenarios of fading multi-path channel models based on the TDL-C model defined in the 5G networks. The proposed DNN-based channel estimation framework was trained with the channel estimation from least squares estimation and the corresponding perfect channels to obtain the parameters as weights and biases. By utilizing the QAM modulation scheme, the performance of the proposed estimations was compared with the conventional LS and LMMSE estimations in terms of the channel estimation error and the bit error ratio as a function of the SNR levels. As the channel properties were learned effectively, we observed improvements of the proposed deep  
Figure 16: The impact of the Doppler frequency on the deep learning-based channel estimations.  
Figure 17: The impact of a Doppler frequency mismatch on the deep learning-based channel estimations.  
Figure 15: The impact of the pilot density on the deep learning-based channel estimations.  
learning-aided estimations in terms of reducing the channel estimation error and bit error ratio. Among the proposed deep learning-based channel estimation approaches, bi-LSTM showed the greatest reduction in channel estimation error as a consequence of its ability to exploit the time and frequency correlation among the channels. Furthermore, the proposed deep learning-based channel estimation approaches exhibited great robustness with different pilot densities as well as with changes of the Doppler frequency.  
[PERSON] proposed the concept and methodology, conducted software programming, and drafted the initial manuscript. [PERSON] provided feedback and revised the manuscript. [PERSON] revised the manuscript. H.C. provided the research funding and administered the project. [PERSON] co-proposed the concept, supervised the research, and revised the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part by the Korean government, under the ICT Creative Consilience program (IITP-2021-2020-0-01821) supervised by the IITP and Mid-Career Research program (NRF-2020R1A2C2008447) through NRF, and in part by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01-2019.07.  
Not applicable.  
The data for the simulation in this paper including noisy channel and theory channel can be found in this repository: [[https://drive.google.com/drive/folders/1](https://drive.google.com/drive/folders/1) KWCS9]([https://drive.google.com/drive/folders/1](https://drive.google.com/drive/folders/1) KWCS9) Yc3 jh-IEkXs/7 bj8 RGW8e4 uOzj4 usp=sharing accessed on 15 July 2021.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l}
5G & Fifth generation \\
3 GPP & Third generation partnership project \\ BER & Bit error ratio \\ CNN & Convolutional neural network \\ CP & Cyclic prefix \\ DNN & Deep neural network \\ FDNN & Fully connected deep neural network \\ FFT & Fast Fourier transform \\ ISI & Inter-symbol interference \\ LMMSE & Linear minimum mean square error \\ LS & Least Squares \\ LSTM & Long short-term memory \\ GRU & Gated recurrent unit \\ MIMO & Multiple-input multiple-output \\ MSE & Mean square error \\ OFDM & Orthogonal frequency-division multiplexing \\ QAM & Quadrature amplitude modulation \\ SNR & Signal to noise ratio \\ TDL-C & Tapped delay line type C model \\ \end{tabular}