Joint Laser Inter-Satellite Link Matching and Traffic Flow Routing in LEO Mega-Constellations via Lagrangian Duality

Low Earth orbit (LEO) mega-constellations greatly extend the coverage and resilience of future wireless systems. Within the mega-constellations, laser inter-satellite links (LISLs) enable high-capacity, long-range connectivity. Existing LISL schemes often overlook mechanical limitations of laser communication terminals (LCTs) and non-uniform global traffic profiles caused by uneven user and gateway distributions, leading to suboptimal throughput and underused LCTs/LISLs – especially when each satellite carries only a few LCTs. This paper investigates the joint optimization of LCT connections and traffic routing to maximize the constellation throughput, considering the realistic LCT mechanics and the global traffic profile. The problem is formulated as an NP-hard mixed-integer program coupling LCT connections with flow-rate variables under link capacity constraints. Due to its intractability, we resort to relaxing the coupling constraints via Lagrangian duality, decomposing the problem into a weighted graph-matching for LCT connections, weighted shortest-path routing tasks, and a linear program for rate allocation. Here, Lagrange multipliers reflect congestion weights between satellites, jointly guiding the matching, routing, and rate allocation. Subgradient descent optimizes the multipliers, with provable convergence. Simulations using real-world constellation and terrestrial data show that our methods substantially improve network throughput by up to $35%$–$145%$ over existing non-joint approaches.

💡 Research Summary

The paper tackles the joint design of laser inter‑satellite link (LISL) establishment and traffic routing in large low‑Earth‑orbit (LEO) mega‑constellations. While previous works have either focused on static link‑selection heuristics or on routing without considering the physical constraints of laser communication terminals (LCTs), this study integrates both aspects into a single optimization framework.

System and Physical Model
Each satellite carries a limited number (N′) of LCTs. An LCT has a fixed mounting direction and a steering capability limited by a field‑of‑regard (FOR) half‑angle θ. Pointing jitter, caused by vibrations and attitude control errors, is modeled as a Rayleigh‑distributed angular deviation ν with scale σ_J. The optical beam follows a Gaussian profile; the received intensity and consequently the link capacity are expressed as a lower bound that depends on the distance z between satellites and the jitter‑induced offset y≈z·ν. This yields a capacity formula C(z,ν)≈B·log₂