Exploring the Throughput Capacity Limits of LEO Satellite Constellation Networks: Mathematical Models and Analysis

The throughput capacity of low earth orbit (LEO) satellite constellation networks has become increasingly significant for satisfying the high demands of future communication systems. However, the misalignment between the constellation topology and traffic distribution can lead to network congestion, negatively impacting the throughput capacity of LEO networks. To address this issue, we propose a theoretical framework that elucidates the relationship between throughput capacity and constellation parameters, aiming to identify the achievable throughput capacity upper bound in LEO networks. It is proved that the upper bound is given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$C_{UB}=3\sqrt{2N}(W_{lx}+W_{ly})$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> represents the size of the constellation, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W_{lx}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W_{ly}$</tex> represent the inter- and intra-plane data rates of the inter-satellite links (ISLs), respectively. Moreover, it indicates that a constellation topology with an average path length (APL) of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline{L}_{min}=\sqrt{2N}/3$</tex> can closely approach the upper bound. Besides, it is shown that indiscriminately reducing the APL of the LEO network without considering traffic distribution may degrade throughput capacity.