# Machine Learning-Based 5G-and-Beyond Channel Estimation for MIMO-OFDM Communication Systems
## 1 Introduction  
The exponential increases in wireless throughput for many different types of users with high quality of service demands have been predicted to continue in upcoming years [1]. Fifth-generation (5G) and beyond wireless communication has been developed by integrating several disruptive technologies such as Massive MIMO, mmWave communications, and reconfigurable intelligent surfaces to handle the fast growth in wireless data traffic and reliability communications [2, 3, 4]. The orthogonal frequency division multiplexing (OFDM) technique has been verified to be a contributor due to its inevitable successes in wide-band communication networks. In fact, OFDM is still deployed in 5G systems to combat the frequency selective fading effects, therefore offering good communication quality in multi-path propagation environments [5]. Specifically, the OFDM technique increases the spectrum efficiency significantly compared with a single-carrier approach. When the transmitted signals propagate through the wireless multi-path channels, they are distorted by many detrimental effects; for example, large obstacles, multi-path propagation, local scattering, and mutual interference by sharing the same time and frequency radio resources. To decode the desired signal effectively, the channel state information and itseffects should be estimated and compensated at the receiver. For this purpose, the pilot signals should be known to both the transmitter and receiver, which are exploited to perform the channel estimation. In a 5G system, the structure of the pilot symbols in each data frame could be varied depending on the different use cases in practice [6]. We note that, among the traditional channel estimation methods, least squares (LS) estimation is well-known as a low computational complexity method because this estimation requires no prior channel statistics [7; 8]. However, LS estimation provides relatively high channel estimation errors in many practical applications, especially for multi-path channels. As an alternative solution, minimum mean square error (MMSE) estimation yields much better channel estimation quality than LS estimation by minimizing the channel estimation errors on average [9]. The closed-form expression of the channel estimates obtained by the MMSE estimation relies on the assumption that, for instance, the propagation channels are modeled by a linear system, while each channel response follows a circularly symmetric complex Gaussian distribution [10; 11]. Nonetheless, the MMSE estimation usually has high computational complexity since channel statistic information--i.e., the mean values and the covariance matrices of the propagation channels--is required. In many propagation environments, this statistical information is either extremely difficult to obtain or varies quickly in a short coherence time, making MMSE estimation challenging to implement [12; 13]. Machine learning has recently attracted a great deal of attention in both academia and industry for various applications of wireless communications, such as radio resource allocation, physical security, signal decoding, and channel estimation [14; 15; 16; 17; 18]. Regarding the channel estimation application, the authors in [19] reported the use of a trained deep neural network (DNN) model with the help of a pilot signal to estimate underwater channels in an efficient manner. In [20], the authors suggested to exploit the channel correlation in both time and frequency domains with a DNN model to perform channel estimation for the IEEE 802.11p standard. Furthermore, in [21], the authors investigated the effects of the channel estimation phase for a wireless energy transfer system and demonstrated that downlink channel estimation is necessary to harvest energy feedback information. In the considered system, a DNN structure makes better channel estimates than the traditional estimations comprising the LS estimation and the linear MMSE (LMMSE) estimation.