# Resource Allocation for Cognitive LEO Satellite Systems: Facilitating IoT Communications
## 5 Simulations Results  
In this section, simulation results are presented to evaluate the performance of the proposed cognitive LEO satellite communication system. The spreading gain for the legacy and IoT systems is set to \(N=256\), which is large enough to verify the asymptotic results obtained in this paper. Although the LEO satellite system involves the shadowed Rice channel, the resource allocation schemes in this paper focus on the receive signal-to-noise ratio (SNR). Due to the fact that the performance of the legacy and IoT systems is related to the SINR, here, we use the receive SNR, i.e., \(\frac{p}{\sigma^{2}}\) and \(\frac{d}{\sigma^{2}}\), to evaluate the performance of the proposed cognitive LEO satellite communication system. Specifically, the white Gaussian noise power is normalized to \(\sigma^{2}=1\). We set the target SINR threshold \(\beta^{*}\) for the legacy satellite system to 5 dB. To show the effectiveness of our proposed framework and algorithms, we set two benchmarks, which are illustrated as follows:  
* **Benchmark 1**: To show the advantages of spectrum sharing, we show the performance of the legacy satellite systems without spectrum sharing, whose SINR with the MMSE detector is given by \(\gamma_{l}=\frac{\gamma_{l}q}{1+\gamma_{l}+\sigma^{2}}\). Accordingly, the sum rate of the legacy satellite users is given by \(\frac{U}{N}\log(1+\gamma_{l})\). * **Benchmark 2**: To show the advantages of the joint resource allocation scheme, we show the performance by only optimizing the receive power of the IoT devices based on the analysis in Section 4.1. Firstly, we evaluate the asymptotic SINR of the legacy satellite system by comparing the simulated SINR with the theoretical SINR with the MMSE detector. We set \(U=50\), \(K=100\), and \(p=20\) dB. The calculation of simulated SINR is based on random spreading codes which are assigned to each user in the legacy satellite system, as shown in (9). The theoretical SINR with the MMSE detector can be calculated by (18). As shown in Figure 2, the dense small circles are the simulated SINRs, while the big circles are the theoretical SINRs for the MMSE detector. It is seen that the theoretical SINR can be considered as the statistical mean value of the simulated SINRs. Thus, it is reasonable to formulate the joint resource allocation problem based on the asymptotic SINR. In addition, we can find that the interference from the IoT users and other legacy satellite users leads to about 4 dB SINR loss with MMSE detector compared with the SNR of the effective legacy satellite user. Figures 3 and 4 present the sum rate of the IoT users and the sum rate of the legacy satellite users w.r.t. the legacy satellite receive SNR, i.e., \(\frac{d}{\sigma^{2}}\), respectively. Here, we set \(U=100\) and \(K=200\). From Figure 3, it can be found that the sum rate of the IoT users is quasi-concave over the legacy satellite receive SNR, which is consistent with the results in Lemmas 2 and 3. In addition, from Figures 3 and 4, we can find that when \(\frac{d}{\sigma^{2}}<6.5\) dB, the sum rate of the IoT users is equal to 0, while the sum rate of the legacy satellite users increases with the growth of \(\frac{d}{\sigma^{2}}\). The main reason is that when \(\frac{d}{\sigma^{2}}<6.5\) dB, we have \(\frac{d}{\sigma^{2}}<\frac{q_{0}}{\sigma^{2}}\), which means that the legacy satellite system cannot tolerate the interference of the IoT system. For \(\frac{p}{\sigma^{2}}=10\) dB, the sum rate of the IoT users increases with \(\frac{d}{\sigma^{2}}\), when \(\frac{d}{\sigma^{2}}<12.5\) dB. In this case, the sum rate of the legacy satellite users remains unchanged, which indicates that the legacy SINR requirement constraint dominates the power allocation scheme. When the IoT receive power limit is not achieved, for each value of \(\frac{p}{\sigma^{2}}\), the curves are coincident and all the interference margins can be exploited by the IoT system. Note that the interference margin refers to the tolerable interference of the legacy satellite system.