# Assessing the Capacity and Coverage of Satellite IoT for Developing Countries Using a CubeSat
## 3 Coverage and Capacity Evaluation
### Efficiency Factor (\(\eta\))
#### 3.5.1 Efficiency Factor due to Temperature (\(\eta_{\mathrm{T}}\))  
The effects of temperature variations on LoRa modulation have been tested and found to reduce the received signal strength when the ambient temperature increased in [42; 43]. Inverse correlation between low temperatures and signal-to-noise ratio (SNR) was observed in [43], but extensive tests for low temperatures have not been performed, especially in the space environment. To deduce the impact of temperature on the data reception quality, an experiment was performed to derive the efficiency factor.  
A test with SloT receiver board and backplane was conducted in Peltier-based Thermal Testing (PeTT) Chamber located at Kyutech. The chamber pressure was maintained below 1 \(\times\) 10\({}^{-3}\) Pa throughout the test and the temperature was varied between \(-\)22 \({}^{\circ}\)C to +72 \({}^{\circ}\)C. The center frequencies of the eight receivers were set 5 kHz apart from 433.060 MHz to 433.085 MHz, and data from the GST were transmitted at 433.080 MHz.  
The reception of the data was evaluated on the weighted success that is a measure of number of packets received for transmitted packets and the success rate of the bytes in the data. The test results are summarized in Figure 17 for the three receivers; RX7 is the tuned frequency, RX6 is receiver with 5 kHz lower CF and, RX8 with 5 kHz higher CF.  
It was observed that the receiver performance was not affected by increase in temperature up to 72 \({}^{\circ}\)C; however, only 3 packets out of 105 packets were received by RX6 and RX7 with a byte success rate of 64% at 72 \({}^{\circ}\)C. The performance of the receivers deteriorated when the temperature was reduced below 20 \({}^{\circ}\)C, an apparent change in the center frequency was noted since the receiver RX6 received more packets with correct bytes than RX7 and RX8. At cold temperatures, the center frequency of the receiver increased. The performance of the RX-7 further reduced at lower temperatures while RX6 continued to receive packets with 50%-byte success rate. At the minimum of \(-\)22 \({}^{\circ}\)C, the success rate was low for all the receivers, nevertheless RX6 continued to perform better than the other two. The temperature was increased to set the receivers to ambient temperature and just over 10 \({}^{\circ}\)C, and all receivers received the correct data packets.  
This temperature dependence could be correlated to the temperature profile in-orbit for deriving the efficiency factor for temperature. The on-orbit temperature of the backplane, which is similar to the temperature of the SloT board, was below 10 \({}^{\circ}\)C when the beta angle was below 25 degrees and increased up to +42 \({}^{\circ}\)C at maximum beta angle. Figure 18 shows the temperature of SloT board obtained from on-orbit housekeeping data with error bars for varying beta angles.  
Figure 17: Summary of temperature dependence test of receivers in PeTT chamber.  
The efficiency factor for temperature can hence be derived from the performance of the receivers with a threshold of 10 \({}^{\circ}\)C, which is true when the beta angle is above or below 25 degrees, as shown in Equation (7).  
\[\eta\mathrm{T}\ =\ \begin{cases}0.85\text{ for beta angles}>25\text{ degrees}\\ 0.50\text{ for beta angles}<25\text{ degrees}\end{cases} \tag{7}\]  
The absolute beta angles in the LEO orbit of 400 km vary between 0-74 degrees, and the beta angle simulation is performed in STK software for the period of one year, as shown in Figure 19. The beta angle is above 25 degrees for 59% of the total simulated duration. Using Equation (7) for the total amount of data that can be collected inclusive of temperature impact, about 70% from the total estimated data for one year could be retrieved.