# 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
In other words, the average delay when there are \(N^{success}\) users successfully accessing is

\[t_{RO}^{delay}=\frac{\sum_{i=1}^{N^{success}}t_{u_{i}}^{delay}}{N^{success}} \tag{17}\]

The access success rate refers to the probability that a user will successfully access the randomized access system within a given number of retransmissions, denoted as \(T_{time}\), that the user experiences when attempting to initiate access. A user access failure occurs when the user attempts to retransmit the system after surpassing the maximum number of retransmission attempts. In this article's system, the reason for re-initiating the calculation is that the beam has scanned past this beam position, that is, the number of times the satellite has scanned past the beam position during the time it took to cover this cell. Suppose that the \(L_{device}^{\text{GFRA}}\) user initiates a connection but only the \(L_{device}^{\text{success}}\) user can successfully connect to it. The connection delay for this user is

\[\text{prob}_{RO}=\frac{L_{device}^{\text{success}}}{L_{device}^{\text{GFRA}}} \tag{18}\]

The following metrics block error rate (BLER) was utilized as the metric to evaluate and contrast different kinds of frequency-hopping systems with the already employed grant-based RA technique. In the existing contention-based resource allocation system, each device sends data in Msg3 for a four-step access or MsgA for a two-step access. The satellite is not obligated to cache the device data during the first access. Furthermore, during the competition for the preamble in the initial phase of RA, any device can transmit data utilizing identical resources in the subsequent phase; however, the quantity of devices that disrupt the transmission may differ. Furthermore, if the quantity of detected pilot symbols exceeds the number of devices, the Random Access Response (RAR) message required to identify the frequency position for subsequent signaling transmission may not be received. Consequently, data cannot be sent. Therefore, the reasons that the collision will occur are as follows: W1) the target device can receive the RAR, and W2) the RAR cannot correctly transmit to the device, with probabilities P[W1] and P[W2], respectively, applicable. The block error rate (BLER) of the present solution may be calculated using the subsequent formula:

\[P[\text{BLER}]=P[\text{BLER}\mid W_{1}]P[W_{1}]+P[W_{2}] \tag{19}\]

## 5 Analysis of Simulation Results

The simulation specifically examines the collision in the random access process and thoroughly examines the impact of different factors on the user collision process. The random access collision simulation is conducted by adjusting the simulation parameters and scenarios, and utilizing data such as user activities during various time periods. The Table 2 explained the simulation parameters. This allows for the analysis and evaluation of access performance metrics such as access delay, access success rate, and BLER. The efficacy of the proposed access framework is validated, as it can effectively guarantee timely user access and enhance overall access performance. Figure 4 shows a comparison of the access delay of different random access (RA) schemes when the number of devices is 100, 500, and 1000, respectively. The abscissa indicates the access probability, and the ordinate indicates the delay in the system. The exact access delay numerical value is listed in Table 3. The figure compares the theoretical performance of the traditional 2-step RA, BH-GFRA schemes, and the proposed scheme. It can be observed from the figure that, as the access probability increases, the system delay shows a rapid growth trend, especially when the number of devices is large (e.g., 1000 devices), the delay increase is more obvious. This shows that the traditional RA scheme is difficult to effectively reduce the delay under high access load.