# A Joint Channel Estimation and Compression Method Based on GAN in 6G Communication Systems
## 1 Introduction  
Channel estimation is a fundamental issue to be addressed in wireless communication systems since its accuracy has a significant impact on the recovery of the received signals as well as the management of interference suppression and wireless resource allocation and other tasks [1]. According to whether prior information is used, the channel estimation methods can be divided into three categories, which are the blind estimation method, the pilot-based estimation method, and the semi-blind estimation method, respectively. In particular, blind estimation methods acquire channel state information (CSI) from the structure and statistics of the received signals, while pilot-based estimation methods allocate a part of wireless resource to transmit known signals to obtain CSI. To enable high precision channel estimation performance, the latter has been widely used [2]. For a future beyond 5G and 6G communication systems, it is more challenging to acquire channel estimation results with high accuracy since many higher mobility and denser-connection scenarios will appear [3]. As introduced in [4], the accuracy of channel estimation can benefit from the increase in the number of pilots. To support the estimation accuracy to satisfy the requirements of service in a complex channel environment, typical conventional channel estimation methods, such as the least square (LS) estimator and the minimum mean square error (MMSE) estimator, have to add many more pilots. However, it declines the spectral efficiency of communication systems due to more wireless resources being allocated to transmit pilot signals. In addition, both methods have their own shortcomings [5]. Specifically, the LS estimator cannot be used to estimate data channels directly,while the MMSE estimator needs to know the statistical characteristics of both pilot and data channels in advance and consumes extra computational resources to perform the matrix inversion operation. To overcome these bottlenecks, some deep learning-based channel estimation methods have been developed. According to whether the conventional channel estimation method is combined, the main idea of these methods can be classified in the following two categories. On the one side, there are some works focusing on designing neural networks as the denoising module embedded into existing conventional estimation methods. In [6], the authors employed two convolutional neural networks (CNNs) connected sequentially to denoise and smooth the channel matrix obtained by using conventional interpolation methods. A scheme that denoises the received signals based on CNN model at first and then estimates channel coefficients by using conventional estimation methods was proposed in [7]. On the other side, some studies are dedicated to learning the correlation between pilot channels and data channels by using neural networks. In [8], a CNN model was trained to learn the time-frequency correlation so that the complete channel matrix can be obtained by feeding pilot channels into the model. Moreover, [PERSON]. [9] designed a CNN model to learn the time-frequency-spatial correlation in massive multiple-input-multiple-output (MIMO) systems. However, it is worth pointing out that although the performance can be improved significantly by comparing with conventional methods, most of the designed structure of neural networks is very dependent on the specific pilot configuration. It means that the model needs to be retrained once the pilot configuration changes, which cannot provide adaptive deployment. As a newly emerging neural network structure, GAN has shown powerful performance in generating synthetic samples following real data distribution [10], which has been applied in many aspects, including image generation [11], image restoration [12], dataset extension [13], communication networks [14] and others. In the wireless communication domain, the GAN-based channel modeling in complex channel environment has attracted a lot of attention. In particular, [PERSON].