## 3 System Model
### An Adaptive Packets Segmentation Scheme Based on the Irregular Gradient Algorithm  
In the multi-beam satellite communication system, optimal resources are taken as the weight of gradient segmentation. The packets are segmented in an irregular way to adapt to the discontinuous optimal resources, which are transmitted cooperatively by multi-satellite to improve the spectrum efficiency and maximize the utilization of resources. According to 3 GPP, radio resources are divided into time domain resources and frequency domain resources. In the time domain, they are sequentially divided into frames, subframes, slots, and symbols. In the frequency domain, they are divided into resource blocks (RB) and resource elements (RE). Unlike LTE, in order to adapt to the multiple scenarios of 5G, the transmission time interval (TTI) of 5G is defined as a slot. Moreover, in the frequency domain, subcarrier spacing can be set as 15 kHz, 30 kHz, 60 kHz, 120 kHz, and 240 kHz according to different scenarios. The uplink and downlink channels are no longer fixed slots, and the slots can be flexibly allocated according to the demand for packets. Similar to the 3 GPP 5G Non-Terrestrial Network (NTN), the radio resources of the NTN in 3 GPP are also divided into time domain resources and frequency domain resources. The difference from the ground is that a higher frequency band is used in NTN for transmission. As shown in Figure 6, we use the same resource division method as 3 GPP. In the time domain, the slot is the smallest unit of TTI, which contains 14 OFDM symbols. In the frequency domain, the system bandwidth is divided into multiple RBs and each RB contains 12 consecutive subcarriers. Each RB occupies 12 consecutive subcarriers and a symbol. In each TTI, we allocate RBs according to user demands. The maximum allocatable slot resources are 14 OFDM symbols in a TTI, and the maximum frequency domain resources that can be allocated are related to the allocatable bandwidth and subcarrier spacing. Different from 3 GPP, the relative movement between satellites and users and long distances cause large delays, so we mainly use 120 kHz subcarrier spacing to reduce the interference of carriers and frequency offset in our system. Figure 6 shows a detailed explanation of the adaptive packet segmentation scheme based on the irregular gradient algorithm. In this paper, the user generates packets with different delays, different QoS requirements, and different sizes at the application layer. After processing by high layers, the packets are multiplexed at MAC. It is different from the rule in which packets are multiplexed into fixed-size transmission blocks in the 5G MAC. In this paper, the packets are segmented according to optimal resources. The segmented packets are padding zeros according to the size of the transmission block to ensure that packets can be sent when resources are insufficient. In the PHY, the packets are coded and modulated, and mapped to the corresponding RB. In this paper, while ensuring transmission quality, the scattered radio resources are integrated to transmit packets to improve spectrum efficiency. As mentioned above, the optimal resources RB are found according to the cross-layer and cross-dimension radio resources optimization model based on the weighted discrete firefly algorithm. When the size of the optimal continuous RB is smaller than the size of the packet that needs to be transmitted, the packet is divided into smaller packets at the MAC according to the size of the optimal continuous RB. Then, zero padding is performed according to the fixed size of the transmission block. The above steps are cyclically executed until the RB in this TTI is used up or all packets are successfully transmitted. At the receiver, the user completes frame synchronization and slot synchronization in the PHY according to Primary Synchronization Signal (PSS) and Secondary Synchronization Signal (SSS) to receive the physical signal in each beam.