# Intelligent Detection Method for Satellite TT&C Signals under Restricted Conditions Based on TATR
## 4 Signal Model  
TT&C signals in satellite downlinks often employ composite modulation types, undergoing multi-level modulation of information. Among them, PCM-BPSK-PM is a commonly used type of command and measurement signal [43]. The initial information undergoes sequential pulse code modulation (PCM) encoding, binary phase-shift keying (BPSK) modulation, and outer phase modulation (PM), resulting in the following expression:  
\[{}_{\text{\tiny{PCM-BPSK-PM}}}(t)=A_{c}e^{i[2\pi f_{c}t+K_{p}s_{PSK}(t)]} \tag{4}\]  
where \(A_{c}\) represents the main carrier amplitude, \(f_{c}\) is the main carrier frequency, and \(K_{p}\) is the phase modulation sensitivity, indicating the phase shift in the PM signal caused by unit modulation signal amplitude.  
\(s_{BPSK}\) represents the inner BPSK signal, where BPSK modulation adds the original information to the phase, and the carried information is represented through phase changes. The time-domain expression of a BPSK signal is as follows:  
\[s_{BPSK}(t)=A_{B}\cos[2\pi f_{B}t+\varphi] \tag{5}\]  
The PCM-BPSK-PM signal has PM modulation as the main carrier and BPSK modulation as the subcarrier. The main carrier is primarily used for detection, while the subcarrier is mainly employed to convey information for communication. Figure 2 depicts the spectrograms of the satellite downlink PCM-BPSK-PM signal under different phase modulation sensitivities. The envelope illustrates the spectral characteristics of the inner modulation signal. Whether these features are distinct is closely related to the phase modulation sensitivity. When the modulation sensitivity is small, the spectrogram shows only a particularly strong carrier component. When the modulation sensitivity is large, the spectrogram exhibits both the inner modulation signal and the carrier frequency of the inner modulation signal, along with symbol rate information.  
Ground receiving equipment needs to choose a suitable data transmission method based on the requirements, balancing data volume, real-time performance, and the level of detail in the signal information. The original data quantity of intermediate-frequency signals is substantial, making real-time transmission impractical. Therefore, in scenarios requiring fast detection and analysis, typically only the spectrum amplitude information of TT&C signals can be utilized.  
In addition, the downlink channel, often subject to losses like shadowing and multi-path fading, results in a decline in SNR. Background interference signals, whether intentional or unintentional, may possess significantly higher energy than the satellite TT&C signal when close to the ground receiving station. Figure 3 illustrates a schematic spectrum received by a ground station in a complex scenario, displaying a wideband spectrum of signals, where the frequency range is from 2100 MHz to 2400 MHz. The scene includes persistent signals from multiple sources, such as 3G and 4G base stations, as shown in Table A1 of Appendix A, making the TT&C signal nearly submerged in the spectrogram. Notably, 3G and 4G signals commonly employ code-division multiple access (CDMA) or orthogonal frequency-division multiple access (OFDMA) [44] technologies, with a wide bandwidth ranging from a few to tens of megahertz. These 3G and 4G signals are reflected in the spectrogram as continuous multi-carrier spectral bands. In contrast, TT&C signals have a narrower bandwidth and often appear as discrete, concentrated spectral bands in specific frequency ranges. As a result, TT&C signals demonstrate modulation characteristics that distinguish them from background signals in the spectrogram. Effective detection can be achieved by observing the spectrogram of the received signal and extracting envelope features.