  In this paper, we investigate the performance of large-scale heterogeneous
low Earth orbit (LEO) satellite networks in the context of three association
schemes. In contrast to existing studies, where single-tier LEO satellite-based
network deployments are considered, the developed framework captures the
heterogeneous nature of real-world satellite network deployments. More
specifically, we propose an analytical framework to evaluate the performance of
multi-tier LEO satellite-based networks, where the locations of LEO satellites
are approximated as points of independent Poisson point processes, with
different density, transmit power, and altitude. We propose three association
schemes for the considered network topology based on: 1) the Euclidean
distance, 2) the average received power, and 3) a random selection. By using
stochastic geometry tools, analytical expressions for the association
probability, the downlink coverage probability, as well as the spectral
efficiency are derived for each association scheme, where the interference is
considered. Moreover, we assess the achieved network performance under several
different fading environments, including low, typical, and severe fading
conditions, namely non-fading, shadowed-Rician and Rayleigh fading channels,
respectively. Our results reveal the impact of fading channels on the coverage
probability, and illustrate that the average power-based association scheme
outperforms in terms of achieved coverage and spectral efficiency performance
against the other two association policies. Furthermore, we highlight the
impact of the proposed association schemes and the network topology on the
optimal number of LEO satellites, providing guidance for the planning of
multi-tier LEO satellite-based networks in order to enhance network
performance.
