## 3 The Proposed Decoupling Uplink and Downlink Access Scheme
### DUDA Protocol for Centralized Network Systems  
Without loss of generality, we consider two-tier satellites, i.e., \(k\in\{L,H\}\). Let \(\vartheta_{L_{0}}\) and \(\vartheta_{H_{0}}\) represent the off-axis angle of two typical NGEO satellites belonging to different tiers. Without loss of generality, we consider a scenario with two tiers of satellites, denoted as \(k\in\{L,H\}\). Let \(\vartheta_{L_{0}}\) and \(\vartheta_{H_{0}}\) represent the off-axis angles of two typical NGEO satellites belonging to different tiers.  
Within the proposed DUDA scheme, NGEO UTs invariably opt for the satellite exhibiting the maximum uplink SINR for uplink transmission. Similarly, these same NGEO UTs select the intended satellite boasting the peak downlink SINR for their downlink transmission. Thus, we can distinguish between four distinct scenarios: (a) Both link transmissions of the NGEO UT are accessed via \(Sat^{L}\). (b) Both link transmissions of the NGEO UT are accessed via \(Sat^{H}\). (c) The uplink of the NGEO UT is directly connected to \(Sat^{L}\) while the downlink utilizes \(Sat^{H}\). (d) The uplink transmission of the NGEO UT is linked to \(Sat^{H}\) while the downlink utilizes \(Sat^{L}\). These scenarios (a)-(d) correspond to four mathematical expressions, outlined as follows  
Case 1: Both access \(Sat^{L}\) in UL and DL:  
\[\{\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{ 0}})}>\frac{P_{H}}{P_{L}}\,\cap\,\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{ Z_{u_{0},H}(\hat{\vartheta}_{H_{0}})}>1\}. \tag{19}\]  
Case 2: Both access \(Sat^{H}\) in UL and DL  
\[\{\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{ 0}})}<\frac{P_{H}}{P_{L}}\,\cap\,\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{ Z_{u_{0},H}(\hat{\vartheta}_{H_{0}})}<1\}. \tag{20}\]  
Case 3: Access \(Sat^{L}\) in UL while access \(Sat^{H}\) in DL  
\[\{\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{ 0}})}<\frac{P_{H}}{P_{L}}\,\cap\,\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{ Z_{u_{0},H}(\hat{\vartheta}_{H_{0}})}>1\}. \tag{21}\]  
Case 4: Access \(Sat^{H}\) in UL while access \(Sat^{L}\) in DL  
\[\{\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{ 0}})}>\frac{P_{H}}{P_{L}}\,\cap\,\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{ Z_{u_{0},H}(\hat{\vartheta}_{H_{0}})}<1\}. \tag{22}\]  
From the perspective of routing, the DUDA scheme decouples the route table between uplink and downlink transmission. The centralized network framework is considered to facilitate the route table update. The rule of routing first hop, constrained by the SINR and the exclusion zones, is proposed as the DUDA scheme. The standard procedure of the DUDA protocol is encapsulated in Figure 3. The state data of step (1) incorporate the UT location and channel state information (CSI). Through the relay of the satellite, the SCC computes \(\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{ 0}})}\) and \(\frac{Z_{u_{0},L}(\hat{\vartheta}_{L_{0}})}{Z_{u_{0},H}(\hat{\vartheta}_{H_{0}})}\) to determine the associated satellites for uplinkand downlink access. The UT is informed by the associated satellite in downlink, subsequently, the UT transmits uplink data inclusive of confirm information and UT data to the associated satellite in uplink. The access process concludes and repeats periodically. It is straightforward to execute this strategy in MSS as the SCC can be the ground station or a satellite.