# Adversarial Sample Generation Method Based on Frequency Domain Transformation and Channel Awareness
## 7 Simulation Result  
### Channel Estimation  
In this section, the experiments for verifying the effectiveness of the proposed method are described in detail, and the experimental results are presented. This experiment is built based on the OFDM communication system. The application scenario is set as transmission by a single antenna and reception by a single user. The channel model selected is the Rayleigh channel. The Pytorch toolkit is selected as the deep learning development tool, and all deep learning models are trained on NVIDIA Tesla V100-PCIE. We make full use of its powerful functions of deep learning model construction and training to provide strong support for the implementation of the SDNet and SDRNet frameworks. The sample size is set at 2000, and the signal data are generated by using the QPSK modulation method. To obtain the test set, the output of the OMP algorithm is used as the input data of the neural network, thereby providing basic data support for the subsequent network performance evaluation. In the network compilation stage, the Adam optimizer is selected for training because it performs well in parameter optimization and can effectively adjust network parameters to improve model performance. The learning rate is set to 0.0005 to maintain a stable update during the training process. The mean square error is adopted as the loss function throughout the training process, and the loss of the validation set is taken as the key evaluation index to measure the training effect and generalization ability of the model. Furthermore, in all experiments, other parameters were kept uniform, and the number of loop iterations was fixed at 100 times to ensure the scientificity and comparability of the experimental results, facilitating the accurate evaluation of the performance of different methods. Secondly, the default system parameters used in the channel simulation are summarized as shown in Table 1.  
Figures 7 and 8 present a detailed analysis of the mean square error (MSE) and bit error rate (BER) of different channel estimation algorithms under a signal-to-noise ratio of 0-20 dB. The results show that the MSE and BER of all methods decrease as the signal-to-noise ratio increases. This is because a higher transmission power can effectively resist noise interference. Based on the LS algorithm in low SNR and poor performance, a high signal-to-noise ratio is better. This is because the LS algorithm regards the channel as a definite but unknown constant and uses linear estimation, which is extremely sensitive to noise. In comparison, the performance of the MMSE algorithm is slightly better because it takes into account the prior statistical characteristics of the channel and uses weighted coefficients for linear estimation. The OMP algorithm estimates by gradually selecting the most relevant sparse channel components, which can effectively utilize the channel sparsity and have a higher estimation accuracy than the previous two. Different from traditional algorithms, the framework proposed in this paper adopts a nonlinear and multi-layer neural network structure, which can estimate more complex channels. Overall, SDNet and SDRNet perform exceptionally well across the full signal-to-noise ratio range, with their MSE significantly lower than that of OMP, LS, and MMSE. Among them, SDRNet performed the most prominently. At 20 dB, the MSE was as low as 0.0004, showing significant advantages. This is attributed to SDRNet integrating multiple residual blocks on the basis of SDNet, retaining the output results of the previous module, and making full use of the features. Therefore, regardless of the environment of low signal-to-noise ratio (0-4 dB), medium signal-to-noise ratio (6-12 dB), or high signal-to-noise ratio (14-20 dB), the MSE and BER of SDRNet remain at a relatively low level, highlighting its superiority and robustness in channel estimation. These data strongly prove the effectiveness of SDNet and SDRNet in channel estimation, and further verify the performance advantages of the proposed method.