This paper investigates the coexistence of heterogeneous Low Earth Orbit (LEO) satellite networks, aiming to analyze the basic performance of downlink communications. The authors propose a tractable spatial model using Cox point processes to represent the complex spatial distribution of LEO satellites across multiple constellations. They consider two access technologies: closed access, where users can only communicate with satellites of the same constellation, and open access, where users can communicate with any type of satellite. The main contributions include: 1. **Modeling the Heterogeneous LEO Satellite Network**: The authors model the network using Cox point processes, ensuring that satellites are located on various orbits and altitudes, which is a significant improvement over existing models that assume uniform distribution on a sphere. 2. **Analysis of Closed Access**: They derive the coverage probability for closed access, considering both no-satellite scenarios and SINR coverage probability. The analysis shows that the coverage probability is influenced by the number of orbits, the number of satellites, and the altitude of the constellations. 3. **Analysis of Open Access**: For open access, they derive the association probability, which is the fraction of users that can be served by each constellation. They also derive the SINR coverage probability for open access, showing that it is generally higher than that of closed access due to the ability to communicate with a wider range of satellites. 4. **Performance Metrics**: The paper provides key distributional parameters and evaluates the impact of geometric parameters on the performance of downlink communications. It highlights that the Cox point process accurately models the target constellation with minimal error. 5. **Conclusion**: The study offers insights into the design and optimization of heterogeneous LEO satellite networks, emphasizing the importance of considering the geometric characteristics of constellations and the choice between closed and open access technologies.This paper investigates the coexistence of heterogeneous Low Earth Orbit (LEO) satellite networks, aiming to analyze the basic performance of downlink communications. The authors propose a tractable spatial model using Cox point processes to represent the complex spatial distribution of LEO satellites across multiple constellations. They consider two access technologies: closed access, where users can only communicate with satellites of the same constellation, and open access, where users can communicate with any type of satellite. The main contributions include: 1. **Modeling the Heterogeneous LEO Satellite Network**: The authors model the network using Cox point processes, ensuring that satellites are located on various orbits and altitudes, which is a significant improvement over existing models that assume uniform distribution on a sphere. 2. **Analysis of Closed Access**: They derive the coverage probability for closed access, considering both no-satellite scenarios and SINR coverage probability. The analysis shows that the coverage probability is influenced by the number of orbits, the number of satellites, and the altitude of the constellations. 3. **Analysis of Open Access**: For open access, they derive the association probability, which is the fraction of users that can be served by each constellation. They also derive the SINR coverage probability for open access, showing that it is generally higher than that of closed access due to the ability to communicate with a wider range of satellites. 4. **Performance Metrics**: The paper provides key distributional parameters and evaluates the impact of geometric parameters on the performance of downlink communications. It highlights that the Cox point process accurately models the target constellation with minimal error. 5. **Conclusion**: The study offers insights into the design and optimization of heterogeneous LEO satellite networks, emphasizing the importance of considering the geometric characteristics of constellations and the choice between closed and open access technologies.