Stackelberg Game for Dynamic Spectrum Allocation over Nakagami-m Channels in LEO Collaborative Networks

The proliferation of Low Earth Orbit (LEO) satellite constellations has precipitated a critical scarcity in available radio frequency spectrum. Collaborative networking among satellites offers a viable pathway to mitigate this congestion, yet static allocation strategies fail to address the highly dynamic topology and time-varying channel conditions inherent to orbital communications. This paper investigates a dynamic spectrum allocation framework utilizing a Stackelberg game theoretic approach, specifically tailored for environments characterized by Nakagami-m fading channels. Unlike traditional models that assume Gaussian or Rayleigh fading, the Nakagami-m distribution provides a more versatile representation of the line-of-sight and multipath scattering conditions encountered in satellite-to-ground and inter-satellite links. We model the spectrum management problem as a leader-follower game where a primary network operator acts as the leader, determining pricing strategies to maximize revenue, while LEO satellites act as followers, competing for bandwidth to optimize their transmission utility. We derive the existence and uniqueness of the Nash Equilibrium analytically, considering the statistical properties of the channel. Simulation results demonstrate that the proposed scheme significantly enhances spectral efficiency and system utility compared to fixed allocation schemes, adapting robustly to varying fading severity.