# Resource Allocation for Cognitive LEO Satellite Systems: Facilitating IoT Communications
## 5 Simulations Results
When \(\frac{d}{\sigma^{2}}<12.5\) dB, the receive power limit dominates the power allocation scheme. Note that the tuning points in the two figures are related to the parameters design. With other parameters, the tuning points may change. reason is that the available interference margin increases with the decrease of the legacy user number. In addition, when \(\frac{\bar{q}}{\sigma^{2}}<6.5\) dB, the two schemes have the same performance since the legacy satellite system cannot tolerate the interference of the IoT system and the sum rate of the IoT users is equal to 0. Next, we evaluate the optimal legacy satellite receive power and the optimal sum rate of the IoT user based on the optimized joint power allocation scheme by varying the maximum receive SNR of the IoT users \(\frac{\bar{p}}{\sigma^{2}}\), as shown in Figures 6 and 7. Meanwhile, to show the effectiveness of the joint resource allocation scheme, we also plot the curves of Benchmark 2 in Figure 7, where we set the \(\frac{\bar{q}}{\sigma^{2}}=20\) dB. In the two figures, we set \(K=150\). From Figure 6, we can find that when \(\frac{\bar{p}}{\sigma^{2}}\) grows, the optimal receive SNR of the legacy user, i.e., \(\frac{\bar{q}_{1}}{\sigma^{2}}\), also increases. This indicates that the sum rate of the IoT users is maximized with higher \(\frac{\bar{q}_{1}}{\sigma^{2}}\), which is also shown in Figure 3. Meanwhile, the optimal receive SNR increase with \(\alpha_{1}\) due to less interference from the legacy satellite users. In Figure 7, we can observe that, for any \(\alpha_{1}\), as \(\frac{\bar{p}}{\sigma^{2}}\) increases, the optimal IoT sum rate increases since the higher \(\frac{\bar{p}}{\sigma^{2}}\) can help the IoT users to exploit more interference margin. Furthermore, we can find our  
Figure 4: Sum rate of the legacy satellite users vs. legacy satellite receive SNR. Figure 5: Sum rate of IoT and legacy satellite users vs. legacy satellite receive SNR. proposed joint resource allocation scheme performs better than Benchmark 2 for any legacy system load, which shows the effectiveness of the joint design. In addition, the optimal IoT sum rate decreases with \(\alpha_{1}\) since the available interference margin decreases with the increase of \(\alpha_{1}\). Finally, the optimal sum rate of the IoT users w.r.t. the number of the IoT users is shown in Figure 8. In this figure, we set \(U=50\). For every given \(K\), the calculation of the sum rate of the IoT users is based on the optimal \(p\) and \(q\) which can ensure the maximization of the IoT sum rate. It is observed that the optimal sum rate of the IoT users is quasi-concave over the number of the IoT users since the sum rate of the IoT system equals the user number times each user's rate, and when the user number increases, this, however, decreases the SINR in (19), resulting in the decrease of each user's throughput. We also know that the user number must be an integer. Thus, we can traverse \(K\) next to the peak in Figure 8 to confirm the user number of the IoT system which can make the IoT sum rate reaches the maximum. For example, from Figure 8, we can observe that when  
Figure 6: Optimal legacy satellite receive SNR vs. maximum IoT receive SNR. Figure 7: Optimal sum rate of IoT users vs. maximum IoT receive SNR. \(\frac{\rho}{\sigma^{2}}=25\) dB, the optimal secondary user number is around 180. Meanwhile, we can find that in this setup, the receive SNR \(\frac{P}{\sigma^{2}}\) has a trivial effect on the optimal number of the IoT users due to the huge effect of the QoS requirements of the legacy satellite users.