# Intelligent Beam-Hopping-Based Grant-Free Random Access in Secure IoT-Oriented Satellite Networks
## 2 System Model and Procedure of BH-GFRA
### System Model
Each active device that wants to transmit uplink data sends a predetermined preamble as its signature in the preamble section to allow the satellite to identify which devices have attempted GFMA as compared to the random preamble selection. We can utilize the Zadoff-Chu (ZC) sequence as the preamble signal. The satellites then detect ZC sequence-based priors by calculating the correlation value and investigating whether the correlation value exceeds the detection threshold for each prior detection region. After identifying the active devices, the satellite obtains an active list of all devices on a specific GFMA block. Moreover, we analyze the time-domain composition of the PRACH resource form mentioned above. We conclude that there are \(\textit{pr}_{slot}\) PRACH time slots in a cycle \(T_{PRACH}\), and each time slot has \(Num_{Ro}\) access occasions. Therefore, the entire PRACH time slot resource can be represented by a function matrix:  
\[\xi(T_{PRACH})= \begin{bmatrix}\text{RO}_{11}&\text{RO}_{12}&\cdots&\text{RO}_{ \text{j}}\\ \text{RO}_{21}&\text{RO}_{22}&\cdots&\text{RO}_{\text{j}}\\ \vdots&\vdots&\ddots&\vdots\\ \text{RO}_{11}&\text{RO}_{22}&\cdots&\text{RO}_{\text{j}}\end{bmatrix}  \tag{1}\]  
The formula \(\xi(T_{PRACH})\) represents the distribution of RO resources in a PRACH cycle, and \(RO_{ij}\) is denoted as the \(j\)th RO resource in the \(i\)th PRACH time slot, where \(i=1,2,3\dots\), \(\textit{pr}_{slot}\) and \(j=1,2,3,\dots,Num_{Ro}\). Figure 1: Scenario of BH-GFRA. Based on the PRACH resource matrix, this paper establishes the resource consumption and model of the satellite and the space-time distribution constraint model of the device side to achieve access resource demand [41]. In this scenario, beam-hopping satellite coverage is used, and devices in a specific region are configured to be \(U=\{u_{1},u_{2},\ldots,u_{n}\}\), the satellite coverage type in this scenario is beam-hopping coverage, and the devices are classified as \(U_{sens}=\{u_{ts1},u_{ts2},\ldots,u_{tsi}\}\) time-sensitive devices and \(U_{sparse}=\{u_{ts1},u_{ts2},\ldots,u_{tsj}\}\). \(U_{num}=\{U_{sens}+U_{sparse}\}\) is the total number of connected devices, where \(U_{sens}\) represents the number of devices with time constraints and \(U_{sparse}\) represents the number of regular devices, which just send some sparse data traffic. By constructing a device distribution constraint model [42], \(\mathcal{F}(\mathcal{S},\mathcal{D},\mathcal{P})=F_{S}*F_{D}*F_{P}\) based on the spatial location \(S\), device density intensity \(D\), and device distribution model \(P\)[43]. The device distribution location \(S\) is associated with the global latitude and longitude coordinates \((X,Y)\), and a certain device is set to be \(U=\{u_{1},u_{2},...,u_{n}\}\). Then, the location where and when traffic occurs is set as \((X_{r},Y_{r})\) and the space range as \(\mathcal{L}_{s}\). \(U_{sparse}(\mathcal{L}_{s})\) and \(U_{sens}(\mathcal{L}_{s})\) represent the variances in the number of time-sensitive and normal devices in different locations. Along with the time parameter \(t\) of the number of devices' time expression for \(U_{sparse}(\mathcal{L}_{s},t)\) and \(U_{sens}(\mathcal{L}_{s},t)\), different moments of the number of devices will also vary [44]. The probability of an overall device initiating access, which indicates changes in the number of devices gaining access, is the main topic of this work. The probability of access for a time-sensitive device is \(prob_{sens}\), whereas that of a normal device is \(prob_{sparse}\). As a result, the number of applicants in a region at a given time during the random access procedure can be written as follows:  
\[U_{num}(\mathcal{L}_{s},t)=U_{sparse}(\mathcal{L}_{s},t)*prob_{sparse}+U_{sens }(\mathcal{L}_{s},t)*prob_{sens} \tag{2}\]