## 2 System Model  
### System Model  
Figure 1 depicts the integrated wireless sensor and cognitive satellite terrestrial network architecture, which is composed of the cognitive satellite network, the terrestrial network, and the terrestrial sensor nodes. The satellite fixed/portable user acts as the sink of the wireless terrestrial sensor network, and they communicate with a number of wireless sensors via a radio link while providing the interface between the terrestrial sensor network and the satellite system. More details are presented as follows. Terrestrial sensor nodes: In the sensor field, the sensor nodes monitor the terrestrial network state and transmit the monitoring results to the satellite user. Terrestrial network: The terrestrial network plays the role of PU, and the link between the mobile user and base station, which is pre-allocated, is called the primary link. Cognitive satellite network: The cognitive satellite network acts as the SU in the architecture. The satellite user, which acts as the sink of the wireless terrestrial sensor network, can dynamically access the cognitive link that was allocated to the terrestrial network according to the results of sensing results. In addition, \(h_{ss}\) denotes the gain of the cognitive link. However, considering the impact of the antenna patterns and propagation issues, the satellite user would interfere the terrestrial network when the two systems working simultaneously and \(h_{sp}\) refers to the gain of interference link. Nowadays, WSN plays an important role in assisting us to understand the world, which is widely applied in environmental monitoring, health monitoring, and so on. In traditional WSNs, the sensor nodes collect and transmit the data to the fixed sink for the states in which the energy of the nodes closed to the fixed sink always deplete quickly, and the fixed sink is easy to be attacked. Some research pays attention to the mobile sink that just meets the requirements such as rescue mission, agricultural irrigation, and so on. Thus, the satellite user is introduced as a mobile sink in this paper. Figure 1: Integrated wireless sensor and cognitive satellite terrestrial network. \(P_{t}\) and \(P_{r}\) denote the transmit power of the satellite user and the satellite receive power, respectively. In addition, \(P_{r}\) is formulated as:  
\[P_{r}{=}P_{t}G_{t}(\theta)G_{r}(\varphi)L_{ss}h_{ss}, \tag{1}\]  
where \(G_{t}(\theta)\) and \(G_{r}(\varphi)\) represent the gain of the satellite user antenna and satellite receiver antenna, respectively. In addition, \(G_{t}(\theta)\) and \(G_{r}(\varphi)\) can be obtained as follows:  
\[G_{t}(\theta){=}\left\{\begin{array}{cl} \begin{array}{cl}G_{t,\max},&0^{ \circ}<\theta<1^{\circ},\\ 32-25\log\theta,&1^{\circ}<\theta<48^{\circ},\\ -10,&48^{\circ}<\theta<180^{\circ},\end{array} \right. \tag{2}\]  
where \(\theta\) is the elevation angle of the satellite user, \(G_{t,\max}\) is the maximum beam gain at the onboard antenna boresight:  
\[G_{r}\left(\varphi\right){=}G_{r,\max}\Big{(}\frac{f_{1}(u)}{2u}+36\frac{f_{ 1}(u)}{u^{3}}\Big{)}^{2}, \tag{3}\]  
where \(\varphi\) is the angle between the beam center of the satellite antenna and connection from the satellite user to satellite, and \(J(\cdot)\) is the Beseel function. In addition, \(u=2.07123\frac{\sin\varphi}{\sin\varphi_{34\text{B}}}\), where \(\varphi_{34\text{B}}\) denotes 3 dB angle. \(L_{ss}\) represents the free space loss, which mainly relates to frequency and distance. Considering that the satellite communication is line-of-sight and the user operates in various propagation environments, we adopted the Shadowed-Riced fading channel model to express the channel characteristic.