# Intelligent Detection Method for Satellite TT&C Signals under Restricted Conditions Based on TATR
## 3 Problem Definition  
Satellite TT&C signals are transmitted by satellites to monitor and transmit data, playing a crucial role in various fields such as aerospace, meteorology, and Earth remote sensing observations. TT&C signals wirelessly transmit information from sensors and monitoring parameters to ground stations or other receiving devices. Detecting TT&C signals is a prerequisite for signal reception and estimation. However, the electromagnetic space is cluttered with various types of noise and interference signals of different frequency bands and mechanisms, intertwining satellite and background signals. Figure 1 illustrates the transmission scenario of the satellite downlink, where the satellite communicates with the ground station through the downlink channel. The ground station, while receiving signals, also encounters intentional or unintentional interference from ground-based sources. Due to the extended transmission distance and the presence of shading, severe channel attenuation occurs, resulting in a diminished signal-to-noise ratio (SNR). Consequently, the signal is often submerged in complex backgrounds, exhibiting extremely low spectral density characteristics. The blind detection problem of non-cooperative satellite signals, determining the presence of satellite downlink signals from the received raw data, essentially represents a binary hypothesis testing problem:  
\[ \begin{cases}&H_{0}:y(t)=\sum\limits_{k=1}^{M}b_{k}(t)+n(t)\\ &H_{1}:y(t)=\sum\limits_{i=1}^{N}x_{i}(t)+\sum\limits_{k=1}^{M}b_{k}(t)+n(t) \end{cases}  \tag{1}\]where \(x_{i}(t)\) is the TT&C signal, \(N\) is the number of signals contained in the original data, \(b_{i}(t)\) is the background signal or interference signal present in the environment, and \(M\) is the number of background signals or interference signals present in the environment. \(n(t)\)is the noise introduced by the channel environment. In this paper, we model it as Gaussian white noise with a distribution function of \(f_{n}(\varsigma)=1/\sqrt{2\pi\sigma_{n}{}^{2}}\exp\left(-\varsigma^{2}/2\sigma_ {n}{}^{2}\right)\). \(H_{0}\) indicates that the satellite signal does not exist, with \(H_{1}\) indicating that the satellite signal is present. Traditional time-domain detection methods construct test statistics based on observed values of \(y(t)\), seeking differences between \(x(t)\) and \(b(t)\) in various representation domains, setting thresholds to make decisions and obtain results. However, due to limitations in non-collaborative information or constraints on the data volume of intermediate frequency signals, practical processing or real-time monitoring often only provides amplitude information of the signal spectrum, lacking phase information. Therefore, under restricted conditions, based on the amplitude sequence of the spectrum of \(y(t)\), the detection problem can be modeled as  
\[\hat{H}=\arg\max_{j\in\{0,1\}}P\big{(}H_{j}\mid|DFT(y(t))|\big{)} \tag{2}\]  
where \(\hat{H}\) represents the detection result, and \(||\) represents the modulus operation. This problem is easily solvable using deep learning methods. Deep neural networks, as data-driven models, are well-suited for handling complex, nonlinear relationships and patterns. The black box model \(\mathcal{F}\) within deep neural networks can be seen as a mapping function between inputs and outputs:  
\[\hat{H}=\mathcal{F}(|DFT(y(t))|)\quad\mathcal{F}:\mathbb{R}^{d}\to \mathbb{R}. \tag{3}\]  
By training on a large amount of labeled data, deep neural networks capture the relationship between the received signal spectrum and the TT&C signal spectrum fea  
Figure 1: The transmission scenario of the satellite TT&C signal downlink. Ground receiving stations, while receiving downlink TT&C signals, may receive intentional or unintentional interference signals and multipath clutter from ground-based stations. Furthermore, there may be obstacles such as trees and buildings which lead to the submergence of TT&C signals within the ambient signal environment.