# Machine Learning-Based 5G-and-Beyond Channel Estimation for MIMO-OFDM Communication Systems
## 1 Introduction
We emphasize that several sophisticated techniques have been applied to estimate channel state information (CSI) to date. In a MIMO system, we could assume in practice that the CSI from each antenna at the BS shares the same autocorrelation pattern for enhancing the channel estimation quality of a particular terminal [22]. By effectively deploying this property and arranging the CSI from the multiple antennas into a matrix, the system can exploit a well-known technique from the fields of image recognition and image denoising [15; 23; 24; 25] to predict the pattern of CSI variation by means of the channel structure. In particular, a convolutional neural network (CNN) is applied in [26] for channel estimation in a mmWave Massive MIMO system to reduce noise from the estimated channel, thus outperforming the traditional counterparts. In [27], the authors proposed a CNN-based scheme to predict channels in a large-scale MIMO system as the channels age. The authors in [28] used a deep CNN to enhance the channel estimation quality while retaining high performance compared to the traditional methods by utilizing less pilot overhead. The numerical results showed that the data-driven method remarkably improved the prediction quality. However, the authors in those papers did not consider the influences of Doppler frequencies, which can cause significant changes in the channels over time and even make the channels nonstationary. In addition, the velocity of the receiver may often vary; thus, it is important to evaluate the effect of the mismatch of the Doppler frequency between the training and testing stages of a DNN model. Another approach is to treat instantaneous channels as a time series data and then consider the CSI estimation as a typical time series learning problem to model the problem. In this case, there exist several powerful architectures in the literature that can track the long-term correlation of the channel profile effectively, including long short-term memory (LSTM) [29] and the gated recurrent unit (GRU) [30]. The authors in [31] suggested a scheme that integrates an LSTM network and a feed-forward neural network (FNN) in a unified structure to track time-varying channels, but without mobility. Apart from this, the authors in [32] reported the use of a bidirectional GRU network to estimate time-selective fading channels. Because of the ability to learn and predict the relationship among the various realizations of the propagation channels, those recurrent neural network structures showed unprecedented improvements over the traditional suboptimal channel estimation methods. Nonetheless, in both papers, the authors only considered channel estimation in SISO systems. Since MIMO technology has been widely used in many modern wireless communication systems, the evaluation of the use of a recurrent neural network for estimating channel information under the Doppler effect is necessary. In this paper, we extend our preliminary work [6], which only used a fully-connected deep neural network (FDNN) model to enhance the channel estimation of a MIMO-OFDM system over frequency-selective fading channels. We show the system performance of the proposed deep learning-based channel estimation framework with different receiver velocities and different neural network structures. The channel parameters in each scenario are generated based on the tapped delay line type C model (TDL-C) that was reported by 3 GPP [33]. Our main contributions are summarized as follows:  
* We construct a MIMO-OFDM system with the channel profile suggested by 3 GPP for 5G-and-beyond systems, accounting for the effects of mobility and frequency selective fading. We make a practical assumption that the receiver does not know the instantaneous channels and that the transmitted data symbols should include pilot signals for the channel estimation;
* We propose a general deep neural network that assists with the traditional channel estimation technique. Our framework does not require any prior information of channel statistics.