# A Joint Channel Estimation and Compression Method Based on GAN in 6G Communication Systems
## 1 Introduction
[15] has studied the feasibility of using the conditional GAN model to replace the modeling channel transfer function. Therefore, a more precise parametric backpropagation can be guaranteed during the training process of an end-to-end communication system. By employing the federated learning framework [16; 17], a distributed conditional GAN framework was proposed in [18] to enable multiple users to train a global model collaboratively. In terms of the channel estimation problem, some GAN-based schemes have been proposed to enhance estimation accuracy and reduce pilot overhead. In [19; 20], GAN was employed to learn the distribution of channel correlation matrix in vehicular millimeter wave systems and frequency division duplex massive MIMO systems, respectively. Moreover, [PERSON]. [21] provided a scheme aiming to learn the gradient of any point in high-dimensional channel space, in which any channel to be estimated can be recovered by following the learned gradient direction. However, consuming a large amount of storage resource is the shortcoming of this scheme. In addition, [PERSON]. [22] proposed a virtual pilot generation-based scheme, where GAN is used to learn the correlation between pilot signals. By combining real pilots with generated virtual pilots, the channel estimation accuracy can be improved without extra cost of wireless resource. Furthermore, GAN has been used to learn the correlation between elements of channel matrix directly in [23]. With the aid of compressed sensing, the channel can be estimated without a significant loss of accuracy when more than a half of the number of pilots is reduced. Although the above GAN-based works have explored the ability of GAN to learn the distribution of multiorder statistics for wireless channels in depth, they mainly focus on low-speed mobile users and neglect to be compatible with high-speed mobile users. In this paper, a novel two-stage channel estimation method based on GAN is proposed to guarantee flexible channel estimation under any pilot configuration and the performance evaluation is extended into the medium- and high-speed mobile scenario for OFDM systems. In particular, a GAN model is designed to learn the correlation between elements of the channel matrix in the first stage. During the second stage, a channel recovery method is given to achieve channel estimation via using the pretrained GAN model. In particular, our proposed scheme can estimate data channels directly via the given pilots without generating extra virtual pilots at first and then using the conventional interpolation method as introduced in [22], which facilitates the efficiency of channel estimation. Moreover, compared with [23], our proposed scheme does not need to find a measurement matrix that is necessary for compressed sensing. The main contribution of this paper is summarized as follows:  
* Firstly, a novel GAN-based channel estimation method is proposed, in which the coefficients over all data channels are obtained by matching the coefficients of real channels and generated channels at pilot positions. Meanwhile, the compressed low-dimensional latent variable is obtained simultaneously, which can be used to support the CSI feedback service with a low communication overhead. * Secondly, the simulation results are provided to show the performance gain obtained by using our proposed method. In particular, by comparing with the conventional Wiener filtering interpolation method, our proposed method can improve the accuracy performance by more than 2 dB with a 75% reduction of the number pilots when the signal-to-noise (SNR) is 10 dB. It shows the potential to reduce the pilots overhead drastically. The achieved compression ratio in this experiment is 2.4%.