# Hierarchical Resource Management for Mega-LEO Satellite Constellation
## 6 Approaches and Algorithms
### Game-Based Spectrum Planning  
Multi-satellite resource management is a core task for the RRSC. The RRSC schedules and allocates spectrum resources to SBSs based on the current spectrum usage and network topology. The SBSs then configure these allocated resources among the beams and user terminals. However, traditional fixed spectrum scheduling strategies cannot adapt to dynamic changes in system topology, spectrum usage, and user demand. To address this, dynamic optimization of spectrum resources throughout the network is required. One effective approach is to allocate spectrum resources using pricing mechanisms and competitive bidding, similarly to the commodity market. For this reason, game theory has been introduced into the resource scheduling of wireless communication systems to provide a framework for efficient resource allocation. In our architecture, the competition and game for spectrum resources among SBSs are managed by the RRSC. SBSs apply to RRSC for usage rights of spectrum based on their individual demands. The NCC formulates the rules and regulations for spectrum usage and sets prices for the spectrum according to the resource allocation strategy and pricing principles. Each SBS then participates in a game-theoretic bidding process to secure usage rights of the spectrum based on these rules and prices. The optimization goal of this game and bidding process is to maximize the utility function of RRSC, which represents the overall efficiency and performance of the network. After the RRSC prices, the spectrum resource as unit price \(p\) and \(q_{i}\) is the resource requirement of the \(i\)-th SBS. Suppose that the resource requirment set of \(M\) SBSs is \(\mathcal{Q}=\{q_{1},q_{2},\ldots,q_{M}\}\) and the total demand is \(Q=\cup_{i=1}^{M}\{q_{i}\}\). Generally, the acquisition of the equilibrium solution of the single-master multi-slaver Stackelberg game between the RRSC and SBSs is completed in two stages. In phase 1, the RRSC firstly announces its pricing strategy \(p\) to all SBSs. The SBSs determine their resource demand strategy \(q\) according to the received pricing strategy \(p\). In phase 2, the RRSC adjusts its price to achieve larger utility after it obtains the resource demands \(\mathcal{Q}\) of the SBSs. The utility function at the RRSC is equal to the difference between its benefit and cost, i.e.,  
\[G(p,\mathcal{Q})=(p-c)Q \tag{1}\]  
Figure 9: Software architecture of spectrum planning module. where \(c\) is the unit cost of the spectrum and \(Q\) is volume of resource demand when using \(\mathcal{Q}\) strategy. The revenue of the RRSC is influenced not only by its own price strategy, but also by the demand of the SBSs. When the RRSC prices too high, the demands of the SBSs reduce and leave more spectrum idle. Contrarily, a low price at the RRSC results in excessive demand and a large network load, which reduce the user experience and system revenue. Therefore, the RRSC is apt to set a reasonable price to maximize its own revenue during the game. Assuming that the optimal price strategy of the RRSC is \(p^{*}\), and its maximum revenue is satisfied by \(max\{G(p^{*},\mathcal{Q}^{*})\}\), where \(\mathcal{Q}^{*}\) is the optimal resource demand strategy of all the SBSs, then \((p^{*},\mathcal{Q}^{*})\) represents an equilibrium point of the single-master multi-slaver Stackelberg game. The task of the RRSC is to provide a reasonable pricing mechanism so as to lay a price foundation for the game of spectrum for the whole network. In the non-cooperative game problem, when all SBSs have reached a state of no further strategy changes, and if any SBS unilaterally changes its strategy, it will not result in an increase in overall system revenue, and the utility of each SBS will be maximized.