## 2 System Model  
This paper refers to the space-air-ground integrated network architecture, as discussed in [9], which addresses random access congestion issues for user equipment in massive IoT networks within such a network framework. The network studied in this work is divided into three layers: the satellite layer, the access control node layer (ACN layer), and the satellite user equipment layer (SUE layer). Based on this framework, we construct an integrated space-air-ground (ISAG) network by introducing airborne devices into the traditional satellite communication system. This ISAG network utilizes three types of spectrum to connect devices across different layers. The names and functions of these spectra are described as follows:  
1. The Contention Access Spectrum (CAS) connects the ACNs to SUE and is used for contending access and broadcasting the indices of traffic transmission allocated by the satellite;
2. The Resource Allocation Spectrum (RAS) connects satellites to the ACNs and is used for allocating traffic transmission resources to ACNs according to the load of each ACN;
3. The Traffic Transmission Spectrum (TTS) connects the satellites to SUE and is used to convey the traffic data within the traffic transmission resources that the SUE has competed for from the ACNs. Using these three types of spectra, we can separate the transmission plane from the control plane. As shown in Figure 1, the considered ISAG network consists of one satellite, \(J\) ACNs, and several pieces of SUE. ACNs can take various forms, such as unmanned aerial vehicles, high-altitude platforms, airplanes, etc., and each ACN needs to have a base station. The base station manages SUE access and processes access results, establishing connections with SUE by receiving its contention packets, determining access status (success, collision, or idle), and feeding back results. Each ACN \(j\) is associated with \(M_{j}\) pieces of SUE. For ACN \(j\), a subset of SUE \(M_{i,j}\) has incoming traffic packets in frame \(i\) (\(M_{i,j}\leqslant M_{j}\)). SUE must obtain permission to transmit. Since each ACN operates independently without communicating with others, the subsequent content will be described using one ACN as an example, without using the ACN index \(j\). The random multiple access procedures for systems with and without transmission and control separation are illustrated in Figure 2. As depicted, when a service request arrives at a slot, it defers transmission until the beginning of the next slot to avoid collisions. A transmission is deemed successful if only one service request occupies a slot. If two or more requests attempt simultaneous transmission, a collision occurs, triggering a retransmission process after a random backoff period. Prior to transmission and control separation, each data packet has encapsulated both service payload and access control information. Consequently, collisions result in the loss of both components. Following separation, access control information is confined to the access phase, while service payloads are transmitted exclusively in the dedicated transmission phase. Collisions are thus restricted to the access phase, enabling collision-free transmission of service data over the satellite channel. This architecture maximizes channel utilization by eliminating contention during payload transmission. This procedure is formalized in the Algorithm 1. Figure 1: System model. Figure 2: Schematic diagram of transmission–control separation architecture.