# Intelligent Beam-Hopping-Based Grant-Free Random Access in Secure IoT-Oriented Satellite Networks
## 3 Beam-Hopping-Based Grant-Free Random Access
### Optimization of Activation Factors by Exploiting Space-Time Distribution Constraint
\begin{split}& U_{u}(\mathcal{L}_{s},t)=U_{\text{num}}\left( \mathcal{L}_{s},t\right)+U_{\text{num}}\left(\mathcal{L}_{s},t\right)*\rho_{t- 1}-U_{\text{num}}(\mathcal{L}_{s},t)*\rho_{t+1}+\leftarrow\\ &\sum_{i=\mu_{t}-t_{\text{win}}\,/2}^{\mu_{t}+t_{\text{win}}\,/2}U _{\text{num}}\left(\mathcal{L}_{s},t-T-i\right)*\\ &\left(1-\frac{\text{preamble}_{\text{sens}}\,*\,(\,\text{Psens }_{\text{success}}\,+\,\text{Psens}_{\text{ collision}}\,)}{U_{\text{sens}}\left(\mathcal{L}_{s},T-i \right)*\,\text{probsens}}\right)\frac{1}{\sqrt{2\pi}\sigma}\exp\Bigl{(}- \frac{(T-i-\mu)^{2}}{2\sigma^{2}}\Bigr{)}\end{split}  \tag{16}\]  
Once the requisite access resources have been obtained, the network will ascertain whether these resources are sufficient to meet the access requirements of all time-sensitive users, taking into account the current number of time-sensitive and sparse traffic users. In the event that the aforementioned conditions are not satisfied, the user will determine whether the access demand of the time-sensitive user is satisfied in the subsequent time slot, according to the time-sensitive user change curve. In the event of satisfaction, the user in question will refrain from accessing the network with some time-sensitive users, in accordance with the constraints outlined. In the event of non-satisfaction, the user will proceed with initiating access within the designated time slot. Based on the probability of time-sensitive \(Pro_{sens}\) and collision \(Psens_{collision}\) situations, the active rate mentioned above will always change. The specific algorithm is detailed in Algorithm 1. ``` Input :Device situation \(U_{u}(L_{s},t)\);Access delay \(T_{delay}\);Access success rate \(Pro_{parse}\);Initial preamble allocation rate \(rate_{preamble}\);Density \(\rho_{t}\);Number of RO \(Num_{RO}\);Number of preamble \(Num_{preamble}\);Activation probability \(v\);
1 if\(\mathcal{F}_{sens}<0\& U_{num}(\mathcal{L}_{s},t+1)>U_{num}( \mathcal{L}_{s},t)\)then
2\(\rho_{t}=0\&rate_{preamble}=0\& v=\alpha_{group}\)
3 end if
4 elseif\(\mathcal{F}_{sens}>0\& U_{num}(\mathcal{L}_{s},t+1)>U_{num}( \mathcal{L}_{s},t)\&\mathcal{F}_{parse}<0\)then
5\(\rho_{t}=0\&rate_{preamble}\
eq 0\& v=\beta_{random}\)
6 end if
7 elseif\(\mathcal{F}_{sens}>0\& U_{num}(\mathcal{L}_{s},t+1)<(\mathcal{L}_{s},t) \&\mathcal{F}_{parse}<0\)then
8\(\rho_{t}\
eq 0&rate_{preamble}\
eq 0&\delta v=\delta_{group}\)
9 end if
10 Output :\(Pro_{sens}\);\(Psens_{collision}\);

## 4 Performance Metrics of the Proposed GFRA

In this scenario, performance limitations include random access success rate, random access delay, and block error rate. A BH-GFRA is then continuously implemented to maximize user performance. A user collision occurs when the satellite decodes a preamble and receives multiple CSI. Only one device can send successful data to a satellite, while the rest must send access failure information, per the collision resolution rule. Thus, random access collisions are caused by multiple users selecting the same resource. The user-access delay refers to the time it takes for the user to send the access request message to the gateway station via satellite, following the initiation of the random access process. It is the duration between the user's action and the gateway station's response message, which is provided after processing the request. The access initiation moment of user \(u_{i}\) is denoted as \(t_{u_{i}}^{start}\), and the access completion moment is denoted as \(t_{u_{i}}^{end}\). Therefore, the access delay of this user can be calculated as \(t_{u_{i}}^{delay}=t_{u_{i}}^{end}-t_{u_{i}}^{start}\). To effectively evaluate the optimization performance of the algorithm, the statistical user-access delay focuses on the average delay experienced by the user \(u_{i}^{success}\) who successfully accessed it in an access RO. Users who failed to access it and did not receive the feedback message are not considered when calculating the delay statistics.