Downlink Performance of Cell-Free Massive MIMO for LEO Satellite Mega-Constellation

Low-earth orbit (LEO) satellite communication (SatCom) has emerged as a promising technology to improve wireless connectivity in global areas. Cell-free massive multiple-input multiple-output (CF-mMIMO), an architecture proposed for next-generation networks, has yet to be fully explored for LEO satellites. In this paper, we investigate the downlink performance of a CF-mMIMO LEO SatCom network, where multiple satellite access points (SAPs) simultaneously serve the corresponding ground user terminals (UTs). Using tools from stochastic geometry, we model the locations of SAPs and UTs on surfaces of concentric spheres using Poisson point processes (PPPs) and present expressions on transmit and received signals, signal-to-interference-plus-noise ratio (SINR). Then, we derive the coverage probabilities in fading scenarios, considering significant system parameters such as the Nakagami fading parameter, the number of UTs, the number of SAPs, the orbital altitude, and the service range affected by the dome angle. Finally, the analytical model is verified by extensive Monte Carlo simulations. Simulation results indicate that stronger line-of-sight (LoS) effects and a more comprehensive service range of the UT result in a higher coverage probability, despite the presence of multi-user interference (MUI). Moreover, we found that there exist optimal numbers of UTs that maximize system capacity for different orbital altitudes and dome angles, providing valuable insights for system design.