## 4 The Proposed STCA Protocol
### STCA Without SIC
Additionally, due to the difference in the duration between minislots and timeslots, when a traffic data packet in the service transmission channel is completed, several ground terminals will have already completed their access in the competition access channel. A transmission queue will be generated in the service transmission channel. When the normalized throughput of the access process is sufficient, continuous collision-free data packets will be sent to the satellite, and the channel utilization will always be 100%. The access probability \(P_{i}\) can be adjusted according to the access load to ensure maximum normalized throughput. The following will detail how to predict and estimate the number of ground terminals needing access in each frame and how to adjust the access probability \(P_{i}\) based on this estimate. For the air access control node, the real access load is unknown. Therefore, it needs to estimate how many ground terminals have data packets to send in the current frame. In  
Figure 5: Flowchart of system without SIC. discrete-time channels, the access load is proportional to the number of idle minislots. The probability of a minislot being idle is  
\[P_{idle}=\left(\frac{N_{\mathrm{C}}-1}{N_{\mathrm{C}}}\right)^{M_{i}P_{i}}. \tag{8}\]  
Thus, the estimated number of idle minislots in a competition access channel frame can be expressed as  
\[n_{idle}=N_{\mathrm{C}}P_{idle}=f(M_{i}). \tag{9}\]  
For the air access control node, the only unknown is \(M_{i}\). Thus, this expression can be written as a function \(f(M_{i})\). Additionally, its inverse function can be written as  
\[M_{i}=f^{-1}(n_{idle}). \tag{10}\]  
At the end of each frame, the air access control node can determine how many minislots are in the idle and successful states, which allows one to estimate how many ground terminals have data packets to send in the next frame:  
\[M_{i+1}=(M_{i}-M_{succ})+(M-M_{i}+M_{succ})\Big{(}1-e^{-N_{\mathrm{C}}T_{ \mathrm{C}}\lambda_{i}}\Big{)}, \tag{11}\]  
where \(M_{succ}\) is the number of ground terminals that successfully gained access in frame \(i\). Since the competition access information contains identity information, \(M_{succ}\) is known to the air access control node. The above equation consists of two parts: one part corresponds to the ground terminals that failed to access due to a probability of \(1-P_{i}\) and need to retransmit, while the other part corresponds to those that have just reached the need to access. \(\lambda_{i}\) can be iteratively estimated as  
\[\lambda_{i}=-\alpha\frac{\ln\Big{(}\frac{M_{i}-M}{M_{i-1}-M_{succ}-M}\Big{)}} {N_{\mathrm{C}}T_{\mathrm{C}}}+(1-\alpha)\lambda_{i-1}, \tag{12}\]  
where \(\alpha\) is a constant. Since the arrival rate does not change drastically in the short term, a portion of the previous frame's arrival rate is retained. \(M_{succ}^{\prime}\) is the number of successfully accessed ground terminals in the previous frame. Combined with Equation (1), the air access control node can set the access probability \(P_{i+1}\) for the next frame based on the predicted \(M_{i+1}\), in order to make \(G=0.368\), thereby maximizing the throughput per unit time. The above method maximizes throughput by controlling the access probability. However, considering that some ground terminals may never successfully access the system, leading to fairness issues, this paper also proposes an algorithm to adjust the frame length.