# A Joint Channel Estimation and Compression Method Based on GAN in 6G Communication Systems
## 4 Simulation Settings and Results
### Simulation Results  
In Figure 8, the comparisons between the magnitude of channel coefficients estimated by our proposed GAN based method and those of the ground truth channel samples in both medium- and high-speed mobile scenarios are provided. In particular, the pilot configuration setting follows the scheme shown in Figure 6a. As shown in this figure, the  
Figure 7: Illustration of used GAN model architecture.  
channel changes more dramatically in the high-speed scenario than that in the medium-speed scenario. The channel variation trends of the estimated results in both scenarios coincide well with those of the ground truth results from both the two-dimensional and three-dimensional perspectives. Moreover, Figure 8b,d show that the estimated results are only with a limited error, which verifies the feasibility of our proposed method.  
As shown in Figure 9, the evaluation for the accuracy performance of our proposed GAN-based channel estimation method is provided, where two mobile scenarios with speeds of 150 km/h and 300 km/h are considered in Figure 9a,b, respectively. In addition, the pilot configuration settings are given in Figure 6. In particular, the widely used conventional Wiener filtering interpolation method [30], a method that can achieve the MMSE criteria when SNR is high enough, is selected as the benchmark. The estimated data channels after Wiener filtering can be expressed as  
\[\hat{\mathbf{h}}_{d,w}=\mathbf{A}_{w}\hat{\mathbf{h}}_{p}, \tag{13}\]  
where \(\mathbf{A}_{w}=\mathbf{R}_{h_{d}h_{p}}\mathbf{R}_{h_{p},h_{p}}^{-1}\) denotes the filtering matrix, which is pre-estimated in the link-level simulation platform. In the mobile scenario with speed of 150 km/h shown in Figure 9a, compared with the conventional method, the GAN-based methods always outperform, even with a fewer number of pilots. However, when SNR is low, neither the conventional method nor the proposed GAN-based method can achieve good performance due to the existence of non-negligible error for the channel coefficients at pilot positions estimated by the LS method. The maximum gain can be obtained when SNR is 10 dB. Specifically, the performance gain is 3.4 dB, 3.0 dB and 2.7 dB when the number of pilot is 96, 48 and 24, respectively. It shows that the proposed method can reduce the pilot overhead by 75% with only 0.7 dB performance loss. As the SNR increases, the performance of the  
Figure 8: Comparison of GAN-based estimated channel samples and ideal channel samples (ground truth results) when SNR is set as 20 dB. In (**a,b**), the speed of terminal user is set as 150 km/h, while that in (**c,d**) is set as 300 km/h. Moreover, (**a,c**) show the channel magnitude from a two-dimensional perspective, while (**b,d**) show that from a three-dimensional perspective.  
proposed method will converge to a stable level due to the learning ability being limited by the experimental model structure. By re-designing a more complicated network structure, the error will converge to a smaller value.  
Moreover, in the mobile scenario with a speed of 300 km/h shown in Figure 9, the performance curves follow a similar trend with those in the mobile scenario with a speed of 150 km/h. In particular, the achieved accuracy performance is lower than that in Figure 9 due to the more variable channel environment. The maximum gain also appears in the case that SNR is 10 dB, where the performance gains under 96, 48 and 24 pilots conditions are 3.4 dB, 2.8 dB and 2.4 dB, respectively. It shows that the estimation error of the proposed method increases 1 dB when 75% pilots are removed. It can be observed that as the number of pilots decreases, the performance gain decays faster in the high speed scenario than that in the medium-speed scenario; as a result, the accurate acquisition of channel correlation in a complex channel environment needs sufficient pilots.