## 5 Capacity Trends Analysis
### Actualized Factors  
Recall that nodes in the network may not maintain perfect links due to some actualized factors, e.g., antenna slewing and acquisition maneuvers, unknown noise that degrades the SNR and system failures. Figure 4: Effects of a growing set of sensor nodes on space network utilization. Figure 5: The effects of the growing ratio between the ground sensor nodes and satellite nodes on failed access time for the sensor nodes. The failed access time is the time when sensors cannot access satellites due to the capacity constraints of the satellite network. The scenario of this result is identical to the one of Figure 4. When the ratio between ground sensor nodes and satellite nodes is 50, there are 3500 sensor nodes in the network. In high fidelity network capacity models, these inefficiencies and constraints of the network should be considered, both from the satellite-satellite and sensor-satellite perspectives. A path \(p\) from the source node \(v_{i}\) to the destination node \(d\) may contain ISLs and sensor-satellite links (SSLs). ISLs are usually based on high frequency band (Ka, EHF or laser), and their beam-widths are narrow. In addition, the attitude control of each satellite usually has certain errors. All of these make the transmitting and receiving antennas off the trail, _i.e._, alignment errors. Alignment errors also exist in SSLs, but the beam-widths in SSLs are broader, so the performance deteriorations are not as obvious as that in ISLs. Due to the alignment errors of the transmitting and receiving antennas, the actual antenna gain is lower than the antenna peak gain. The decrease of the gain, _i.e._, alignment loss, can be approximately calculated using \(Loss=11.1\left(\phi_{e}/\phi_{\rm 3 dB}\right)\left(\rm dB\right)\) from [49], where \(\phi_{e}\) is the alignment error angle, \(\phi_{\rm 3 dB}\approx 70\lambda/D\) is the 3-dB beam-width of the antenna. In \(\phi_{\rm 3 dB}\), \(\lambda\left(\rm m\right)\) denotes the carrier wave length and \(D\left(\rm m\right)\) denotes the antenna diameter. Figure 6 shows the antenna gain when alignment error angle \(\phi_{e}\) varies from \(0^{\circ}\) to \(0.2^{\circ}\). As a result, if \(\phi_{e}=0^{\circ}\), antenna gain increases with the rise of antenna diameter and carrier frequency. When \(\phi_{e}\
eq 0^{\circ}\), antenna gain increases until the highest point and then decreases. Alignment loss makes node \(\forall v_{r}\in p\) not be able to operate perfectly, _i.e._, \(\eta_{r}\left(t\right)<1\), \(\eta_{i}\left(d,p,t\right)=\prod\limits_{v_{r}\in p}\eta_{r}\left(t\right)<1\). Additionally, from Figure 6, the optimal antenna diameter and carrier frequency of the space nodes can be selected for a maximum network capacity before they are injected into the IWSSN. When focusing on the sensor-satellite perspective, more actualized factors should be considered. The actual time that a link can be maintained is usually less than the total visibility duration. Let \(\beta_{t}\) be the actual time the data link is maintained relative to the total visibility durations between the sensor and satellite. \(\beta_{t}\) is usually less than 100% and is tightly related to the actualized factors, such as maximum  
Figure 6: Gain of the inter-satellite links (ISLs) antenna of different alignment error angles. (**a**) Variation with antenna diameter (the carrier frequency is 60 GHz, and the efficiency of the antenna is 0.6); (**b**) Variation with carrier frequency (the antenna diameter is 0.6 m, and the efficiency of the antenna is 0.6). elevation angle \(e_{\max}\), carrier frequency \(f_{c}\), average rainfall rate \(R_{rain}\), altitude of the sensor node \(h_{s}\), _etc_. What is more, considering the above actualized factors and based on the minimum SNR requirement, the maximum transfer rate of the SSLs may also vary when using adaptive coding and modulation (ACM) [50,51]. Obviously, higher fidelity satellite and sensor models will further decrease the network capacity and limit the optimal solution space of the network scheduling.