## 2 System Model
### Transmission Model  
In this paper, we design the periodic frame structure, and the time duration of each frame is \(T\). As shown in Figure 2, each frame duration consists of two parts: the sensing slot and the data transmission slot. During the sensing slot \(\tau\), the satellite user that acts as the sink of the sensor network can monitor the terrestrial network state through the sensor data. In addition, during the transmission slot \(T-\tau\), the satellite user adapts its power control scheme to access the channel assigned to a terrestrial network without degrading the communication quality of the terrestrial user. The probabilities of the busy/idle states of terrestrial network are denoted by \(\mathcal{P}(\mathcal{H}_{b})\) and \(\mathcal{P}(\mathcal{H}_{i})\), respectively, and obviously \(\mathcal{P}(\mathcal{H}_{b})+\mathcal{P}(\mathcal{H}_{i})=1\). The paper introduces \(\mathcal{H}_{b}/\mathcal{H}_{i}\) to represent the sensor results of busy/idle state of the terrestrial network, and the expressions are as follows:  
\[ \begin{array}{l}\mathcal{H}_{b}:y(i)=cx(i)+n(i),\\ \mathcal{H}_{i}:y(i)=n(i),\end{array}  \tag{8}\]  
where \(i=1,2,\cdots,N\), \(N\) is the sample number of one frame and follows \(N\geq\tau f_{s}\), \(f_{s}\) is sample frequency, \(y(i)\) is the signal received by the satellite user that acts as the sensor sink, \(x(i)\) denotes the signal sent by the terrestrial user, \(c\) represents the channel gain of sensor network which is changed in different frame but fixed in one frame, and \(n(i)\) is AWGN with zero mean and variance \(\sigma_{n}^{2}\). Under this assumption, the sensing results contain two types, which are called busy state and idle state. The sensing result of busy state can be caused by two possibilities: (a) when the primary terrestrial network is busy, which happens with the probability \(\mathcal{P}(\mathcal{H}_{b})\), and the sensing result is correct. The procedure is defined as the perfect detection and the probability of detection is denoted by \(P_{d}\); (b) when the primary terrestrial network is idle, which happens with the probability \(\mathcal{P}(\mathcal{H}_{i})\), but the sensing result is false. It is defined as a false alarm and the probability of the sensing result is represented by \(P_{f}\). Likewise, the idle state also contains two possible causes: (c) if the primary terrestrial network is busy with the probability of \(\mathcal{P}(\mathcal{H}_{b})\), but the sensor result is idle, the procedure is called error detection with probability of \((1-P_{d})\); and (d) the sensing result is idle and the primary terrestrial network is just idle too, and the detection probability is denoted as \((1-P_{f})\). Considering the lowest complexity and the high efficiency [35], the energy detection approach is adopted to deal with the sensor data. In addition, then, the detection probability \(P_{d}\) and the false detection probability \(P_{f}\) can be calculated as [21]:  
\[P_{d}\left(\varepsilon,\tau\right)=Q\left(\left(\frac{\varepsilon}{\sigma_{n }^{2}}-\gamma-1\right)\sqrt{\frac{\tau f_{s}}{2\gamma+1}}\right), \tag{9}\]  
Figure 2: Periodic spectrum sensing frame structure. \[P_{f}\left(\varepsilon,\tau\right)=Q\left(\left(\left(\frac{\varepsilon}{\sigma_{n} ^{2}}-1\right)\sqrt{\tau f_{s}}\right), \tag{10}\]  
where \(\varepsilon\) is the detection threshold, \(\gamma\) refers to the signal-to-noise ratio (SNR) of received sensing signals, and \(Q(\cdot)\) denotes the complementary distribution function of the standard Gaussian, i.e.,  
\[Q(x)=\frac{1}{\sqrt{2\pi}}\int_{x}^{\infty}\exp{\left(-\frac{t^{2}}{2}\right)}dt. \tag{11}\]  
The satellite user can adopt a different power control scheme to access the channel based on the sensing results.