## 2 System Model  
### Dual-LEO-Satellite System Model  
Considering the cooperative transmission of dual-satellite communication system, there are two satellites that transmit data to the single IoT user terminal (UT). Each satellite is equipped with a planer antenna array containing antenna elements. The user terminal is equipped with two reflector antennas. The signals received by terminal's antenna 1 and antenna 2 at a certain time can be expressed as  
\[y_{1}(n) =G_{R1}G_{T1}h_{1,1}w_{1}x_{1}(n)+G_{R2}G_{T1}h_{1,2}w_{2}x_{2}(n)+z _{1}(n) \tag{1}\] \[y_{2}(n) =G_{R1}G_{T2}h_{2,1}w_{2}x_{2}(n)+G_{R2}G_{T2}h_{2,2}w_{1}x_{1}(n)+ z_{2}(n) \tag{2}\]  
Figure 1: The dual-stream transmission for LEO satellites-assisted IoT network. where \(G_{T1}\) and \(G_{T2}\) are the antenna gain of satellite 1 and satellite 2. \(G_{R1}\) and \(G_{R2}\) are the antenna gain of the terminal's antenna 1 and terminal's antenna 2, respectively. \(h_{1,1}\), \(h_{1,2}\), \(h_{2,1}\), \(h_{2,2}\in C^{1\times N_{t}}\) represent the channel response. \(w_{1}\), \(w_{2}\in C^{N_{t}\times 1}\) denote analog beamforming weighting vectors of satellite 1 and satellite 2. \(x_{1}(n)\), \(x_{2}(n)\) denote the transmit signal of satellite 1 and satellite 2. \(z_{1}(n)\), \(z_{2}(n)\) represent the additive noise of the terminal's antenna 1 and antenna 2. \(y_{1}(n)\), \(y_{2}(n)\) denote the receive signal of antenna 1 and antenna 2, respectively. Note that \(G_{R1}G_{T1}h_{1,1}w_{1}x_{1}(n)\) in (1) denotes signal from satellite 1 received by antenna 1, and \(G_{R2}G_{T1}h_{1,2}w_{2}x_{2}(n)\) represents the signal from satellite 2 received by antenna 1. \(G_{R1}G_{T2}h_{2,1}w_{2}x_{2}(n)\) denotes signal from satellite 2 received by antenna 2, and \(G_{R2}G_{T2}h_{2,2}w_{1}x_{1}(n)\) represents the signal from satellite 1 received by antenna 2. To evaluate the performance of the dual-stream transmission with two LEO satellites, we set up a simulation platform. As shown in Figure 2, the system simulation model mainly includes two parts: the satellite simulation model and the downlink physical channel simulation model. The satellite simulation model includes satellite orbit model and power control module. The satellite orbit model mainly models the satellite orbit according to the satellite simulation parameters and obtains the position parameters of two satellites at any time. Then, calculate the relative position of ground users and satellites. The power control module mainly realizes power optimization by controlling power parameters. Downlink physical channel simulation includes signal transmitters, channel, signal receiver, bit error rate(BER) statistics and other modules to verify the system performance. Satellite model simulation can be divided into three parts. First, according to the six orbital elements of satellite, simulate the satellite orbit, which can calculate the location parameters, such as the distance between the satellite and the user, the angle of arrival and angle of elevation. Second, calculate the parameters required by the channel model through the position parameters. Third, the power optimization scheme is adopted to adjust the power control parameters. Finally, the channel model parameters and power control parameters are output to the physical downlink channel simulation model. The physical downlink channel simulation model process is shown in Figure 2, which consists of transmitters, channel model and receiver. At the transmitter, two satellites send two different data streams. The receiver demodulates the data separately by two receiving antennas. Set the user's two receiving antennas as antenna 1 and antenna 2. Figure 2: System simulation model. Assuming at the receiver, antenna 1 expects to receive the transmitted data from satellite 1, antenna 2 expects to receive the transmitted data from satellite 2. Satellite 1 and satellite 2 generate different data followed by encoding, scrambling, modulation and power control at the transmitter.