## 3 Modulation Signal Generation
### Generation of Samples and Time-Frequency Analysis  
The RML2016.10A open source dataset [31], which features a wide selection of modulation modes, extensive coverage of SNRs, and a sufficient volume of data, is generated by GNU radio, simulating real communication channel environments. Being highly useful in reality, it can be employed for algorithm training and system development in various fields such as communication system monitoring and management, electronic warfare and signal intelligence analysis, radio spectrum monitoring, and satellite communication. The simulation data in this paper refer to the RML2016.10A dataset. There are a total of 11 modulations. Eight of them are digital modulations, namely BPSK, QPSK, BPSK, 16 QAM, 64 QAM, PAM4, GFSK, and CPFSK. Three of them are analog modulations, namely B-FM, DSB-FM, and AM-SSB. For each modulation, there are 400 IQ two-way data as samples at a fixed SNR. The samples, with a size of \(2\times 1024\), are in a small sample scale. The ratio of the number of samples in the training set to that in the test set is 3:1. The data cover four channel environments, namely, additive Gaussian white noise, selective fading, center frequency offset, and sampling rate offset, as well as a certain frequency bias. Let the SRO be \(\varepsilon\) and the CFO be \(\Delta f\); Equation (1) can be defined as follows. \[r(t)=(s(t)*h(t))e^{i2\pi\Delta ft}+n(t) \tag{6}\]  
In the discrete time domain, the received signal in the case of considering the SRO is given by  
\[r[n]=(s[n]*h[n])e^{i2\pi\Delta ftnT_{s}(1+\varepsilon)}+n[n] \tag{7}\]  
where \(n[n]\) denotes additive noise in the discrete time domain. In addition to the aforementioned channel environment, this paper focuses on multi-path fading as a channel environment. The impulse response of a multipath channel can be expressed as  
\[h(t)=\sum_{i=1}^{N}\alpha_{i}\delta(t-\tau_{i}) \tag{8}\]  
The delay time of the multipath paths and the average path gain are two important parameters that characterize the multipath effect. The channel model used in this paper's dataset contains three paths, namely, the main path and two reflection paths with specific delays, respectively. The gains of these paths are \(0\) dB, \(-2\) dB, and \(-10\) dB, respectively. Moreover, the Rician K-factor further describes the channel's statistical characteristics. When the value of K is larger, it indicates that the channel has less significant fading characteristics [32]. In this paper, we set the K-factor as 4. The experiments in Section 5.3 make necessary adjustments to the parameters of the channel model. The specific parameters are shown in Table 1.  
Although orthogonal two-way IQ data can characterize signals, merely relying on identifying only the IQ data input is insufficient to fully reflect the signal characteristics. At the same time, the conventional Fourier transform fails to represent the frequency components at arbitrary moments. For comprehensive analysis, the time-frequency analysis method that combines the frequency and amplitude of the signal over time is often employed. By transforming a one-dimensional time-domain signal into a two-dimensional time-frequency image, the relationship between the time domain and frequency domain of the signal can be visualized and correlated [33]. In this paper, we employed STFT [33] which has the following transformation expression. \[STFT(t,f)=\int_{-\infty}^{+\infty}x(\tau)g(\tau-t)\mathrm{e}^{-\
icefrac{{-2 \pi f\tau}}{{}}}\mathrm{d}\tau=\langle x(\tau),g(\tau-t)\rangle \tag{9}\]  
where \(t\) and \(\tau\) serve as the time factors, while \(f\) is the frequency factor. The window function \(g(t)\) is a symmetric real function, and it satisfies the conditions that \(\left\|g(\tau)\right\|=1\) and \(\left\|g_{t,f}(\tau-t)\right\|=1\). Parameter selection plays a crucial role in determining computational complexity and accuracy [34]. The window length in STFT impacts time-frequency analysis resolution and computational complexity.