## 2 System Model  
Figure 1 shows the architecture of the integrated wireless sensor and cognitive satellite terrestrial networks, where the mobile satellite terminal plays the role of the sink for the terrestrial sensor network. In this system, an uplink cognitive satellite terrestrial network consisting of one primary terrestrial network and one secondary satellite network is considered, where the satellite system shares the spectral resource with terrestrial system to improve the spectral efficiency. In the considered architecture, the satellite network (e.g., DVB-SH) acts as the secondary system, whereas the terrestrial cellular network (e.g., UMTS or LTE) corresponds to the primary system [16; 17]. Herein, we focus on the underlay scenario as mentioned above. In addition, the weak interference from primary terrestrial user to the satellite can be negligible due to the large distance [28]. In traditional WSNs, sensor nodes are distributed in the sensing field whereupon detecting some events of interest, nodes report the sensed event back to some static sink(s) through multi-hop or single hop communication. One major drawback of such communication infrastructures is that the sensor nodes close to the sink will consume more energy, and thus their energy supply will be rapidly depleted [29]. To deal with this issue, the concept of mobile sink was introduced in [30; 31], that not only results in balanced energy consumption among the nodes but can also be exploited to connect isolated segments of the network [32]. Moreover, some applications explicitly require sink mobility in the sensor field. For instance, a rescuer equipped with a PDA moves around in a disaster area to search any survivors [33], and a farmer while walking around a field would be interested in knowing which  
Figure 1: The architecture of the integrated wireless sensor and cognitive satellite terrestrial networks. segment of the field requires watering, fertilizers, etc. Thus, the sink in this paper i.e., the satellite user is selected as a mobile terminal. The operating power refers to the power needed for running the network equipment, e.g., the satellite terminal. In the considered system model, the satellite terminal is a vehicle equipment, which is commonly powered by on-board batteries, that is to say, the satellite terminal is limited in energy storage capacity. In this regard, energy efficiency is a fundamental constraint in the operation and design of communication networks consisting of battery-operated terminals. In addition, DVB-SH transmissions are subject to long-fading durations which degrade the quality of experience if not tackled efficiently. The long propagation delay in satellite networks (especially in GEO-based networks) and fast changing link conditions impose challenges on the energy efficiency optimizations [21]. Therefore, it is of importance to optimize the power allocation mechanism from the energy efficiency perspective of the satellite vehicle terminal. When the transmit power of the satellite user is \(P_{t}\), the receive power \(P_{r}\) at the satellite can be calculated as  
\[P_{r}=P_{t}G_{t}\left(\theta\right)G_{r}\left(\varphi\right)L_{S}h_{S}, \tag{1}\]  
where \(G_{t}\left(\theta\right)\) is the transmit antenna gain of the satellite user, \(G_{r}(\varphi)\) denotes the receive antenna gain at the satellite, which can be obtained as  
\[G_{t}\left(\theta\right)=\left\{ \begin{array}{ccc}G_{t,\max},&0^{\circ}< \theta<1^{\circ}\\ 32-25\log\theta,&1^{\circ}<\theta<48^{\circ}\\ -10,&48^{\circ}<\theta<180^{\circ}\end{array} \right., \tag{2}\]  
\[G_{r}(\varphi)=G_{r,\max}\left(\frac{{{I_{1}}\left(u\right)}}{2u}+36\frac{{{I _{3}}\left(u\right)}}{u^{3}}\right)^{2}, \tag{3}\]  
where \(\theta\) is the elevation angle, \(G_{r,\max}\) is the maximum beam gain at the onboard antenna boresight and \(J\left(\cdot\right)\) is the Bessel function.