## 3 Transmission Protocol Configuration and Resource Allocation Scheme
### Transmission Protocol Configuration  
To realize the practical and high-quality transmission of the diversified services carried by a system, according to the characteristics of integrated networks, the overall performance optimization problem of the system is divided into two stages: long-period and sub period optimization stages. Considering the whole system performance, the long-period optimization goal is to maximize the expected throughput of the system. Then the frame structure of the TDD transmission mechanism can be figured out, that is, the configuration ratio of normal subframe and LP-ABS. The normal subframe is divided into uplink time slots and downlink time slots configurations. Then, from the perspective of cell performance optimization, the goal is to maximize the cell utility function based on the QoS requirements of different traffic flows and the limitations of system resources. The objective of sub-period optimization is to maximize the utility of the system. Due to many users and various service types in an integrated network, the proportion of uplink and downlink data flow of the system is relatively stable when many traffic flows are generated. Therefore, the strategy for setting the frame structure of integrated networks in this paper is that: (1) the proportion of frames consumed by the uplink is equal to the system resource requirement of the uplink traffic flow; (2) the proportion of frames consumed by the downlink is equal to the system resource requirement of the downlink data flow. On the one hand, the resource demand of traffic flow depends on the number of services. The more the traffic flows, the more system resource is needed. On the other hand, it depends on the data rate. Therefore, the transmission subframe configured by the system can be expressed as:  
\[\frac{\Phi^{n,u}}{\Phi^{n,d}+\frac{\sum\limits_{i\in\Gamma^{u}}\frac{\Gamma^{ d}}{\Gamma^{d}}}{\sum\limits_{i\in\Gamma^{d}}\frac{\Gamma^{d}}{\Gamma^{d}}}}= \frac{\sum\limits_{i\in\Gamma^{u}}\frac{\Gamma^{d}}{\Gamma^{d}}}{\sum\limits_{ i\in\Gamma^{d}}\frac{\Gamma^{d}}{\Gamma^{d}}} \tag{12}\]  
\[\Phi^{n,d}+\Phi^{n,u}+\Phi^{l}=1 \tag{13}\]  
Figure 3: Algorithm design flow diagram. Let \(X=\sum_{i\in\Gamma^{d}}\frac{c_{i}^{l,d}}{c_{i}^{d}\left|A\right|_{0}^{d}}|\), \(Y=\frac{\sum_{i\in\Gamma^{d}}\frac{1}{c_{i}^{d}}}{\sum_{i\in\Gamma^{u}}\frac{1}{c _{i}^{d}}}\), from Equations (12) and (13):  
\[\Phi^{n,d}=\frac{1+(X-1)\Phi^{l}}{1+Y} \tag{14}\]  
\[\Phi^{n,u}=\frac{Y-(X+Y)\Phi^{l}}{1+Y} \tag{15}\]  
The expected throughput of an integrated network is:  
\[C=\frac{\sum_{i\in\Gamma^{d}}c_{i}^{n,d}}{\left|\Gamma^{d}\right|}\[PERSON]^{n,d}+ \frac{\sum_{i\in\Gamma^{u}}c_{i}^{n,u}}{\left|\Gamma^{u}\right|}\[PERSON]^{n,u}+ \frac{\sum_{i\in\Gamma^{d}}\frac{1}{c_{i}^{d}}+\sum_{i\in\Gamma^{u}}c_{i}^{l,u }}{\left|\Gamma^{d}\right|+\left|\Gamma^{d}\right|}\[PERSON]^{n} \tag{16}\]  
By maximizing the expected throughput of the system, \(\Phi^{l}\) can be determined as  
\[\Phi^{l}=\underset{\Phi^{l}\in(0,1,\ldots,1)\in B}{\arg\max}\sum_{i\in B}C_{i }(\Phi^{l}) \tag{17}\]  
Then, by bringing Equations (14) and (15) into (17), the expected throughput of the system can be obtained. The transmission power \(P_{0}^{l}\) of the HAPS on the LP-ABS is a one-dimensional discrete variable. Therefore, we consider fixed power \(P_{0}^{l}\) to eliminate the coupling relationship firstly. When \(P_{0}^{l}\) is given, the specific frame allocation strategy \(\left(\Phi^{n,u},\Phi^{n,d},\Phi^{l}\right)\) is determined by Equation (16). Then, the network utility maximization problem is an optimization problem about resource allocation variable \(s_{i}\), which can be further decomposed into \(N+1\) independent sub-problems. Each subproblem is the maximization of the utility of the cell, where the utility of the cell is defined as the sum of the utility of all the business flows in the cell. Each base station distributes resources to maximize cell utility independently so as to realize network utility maximization.