# Adversarial Sample Generation Method Based on Frequency Domain Transformation and Channel Awareness
## 5 Channel Aware Adversarial Sample Generation Method Based on Frequency Domain Transformation  
Channel estimation guarantees communication quality and is related to the accuracy and stability of signal transmission. Modulation classification, as the basis of communication systems, is a key prerequisite for subsequent signal processing and information interpretation. The two are closely related and jointly promote the development of communication technology. Under this broad background, the security and stability of communication systems have become key research directions, and adversarial attacks and channel estimation are precisely the core issues among them. In recent years, the research on adversarial attacks based on frequency-domain information has revealed the frequency-domain sensitivity characteristics of deep learning from two dimensions: attack methods and model mechanisms. At the level of attack methods, researchers have found that low-frequency components and high-frequency components have the same influence on model decision-making. Although the existing defense mechanisms can effectively suppress high-frequency disturbances, there are still significant loopholes in the defense against low-frequency disturbances. At the model mechanism level, research shows that deep neural networks have significant frequency-domain perception preferences. On the one hand, the model can capture high-frequency features that are difficult for humans to detect, but is extremely sensitive to high-frequency noise. On the other hand, network decision-making overly relies on spectral amplitude information while ignoring the robustness characterization of phase characteristics. Further research has found that the key discrimination frequency bands of samples of different categories are specific. This category difference in frequency sensitivity provides an opportunity for targeted frequency-domain attacks. The current defense methods enhance robustness through strategies such as high-frequency noise suppression and phase protection. However, breakthroughs are still needed in cross-band attack defense and dynamic spectrum registration, which points out the direction for subsequent research. From the above content, it can be known that different frequency components in the existing research contribute differently to the model decision-making. Then, different frequency components also have guiding significance for the generation of adversarial samples. Based on this, this paper proposes an adversarial sample generation method based on channel awareness for frequency-domain transformation. At the same time, it can verify the importance of accurate channel estimation in adversarial attacks on communication systems. Provide new solutions for the security and reliability of communication systems. In this section, the Fourier transform is adopted to transform the signal from a continuous time series signal in the time-domain to the frequency domain for analysis. The specific mathematical expression is as follows:  
\[F(w)=\int_{-\infty}^{\infty}f(t)\times e^{-jwt}dt \tag{36}\]  
\[e^{-jwt}=\cos(wt)-j\times\sin(wt) \tag{37}\]  
where \(e^{-jwt}\) represents an odd function. When both the function and its Fourier transform undergo discretization processing, the discrete Fourier transform (DFT) can be obtained. For radio signals that are usually modulated by I/Q modulators, the I/Q two-channel signals can be expressed as:  
\[x(t)=I(t)+jQ(t)=e^{j\varphi(t)} \tag{38}\]  
For a signal with a sampling length of \(L\), it can be expressed as:  
\[x=\left[ \begin{array}{c}I\\ Q\end{array} \right]\text{, }\left\{ \begin{array}{c}I=[i_{1},i_{2},\ldots,i_{L}]\\ Q=[q_{1},q_{2},\ldots,q_{L}]\end{array}