Ergodic Capacity and Optimal Handover in Satellite Mega-Constellations under Finite Serving Times

Technical Summary: Ergodic Capacity and Optimal Handover in Satellite Mega-Constellations under Finite Serving Times

Problem Statement
Existing analyses of ergodic capacity in Low-Earth Orbit (LEO) satellite mega-constellations face a trade-off between tractability and realism. Deterministic models, while accurate for specific system simulations, are often intractable for theoretical analysis of ultra-dense constellations. Conversely, purely stochastic models lack the temporal persistence required to optimize handover strategies when serving times are long enough for link statistics to evolve. Furthermore, traditional handover criteria (e.g., minimum distance or maximum serving time) often fail to account for the time-dependent evolution of channel quality, particularly in the presence of shadowing, leading to suboptimal aggregate performance. The paper addresses the need for a framework that characterizes ergodic capacity under arbitrary handover strategies and finite serving times, explicitly modeling the "persistence" of the satellite link.

Methodology
The authors develop a semi-stochastic framework that bridges the gap between purely stochastic point processes and fully deterministic orbit simulations.

• Channel Modeling: The user-satellite link is modeled as a shadowed-Rician fading channel. The satellite constellation is represented using a Non-Homogeneous Binomial Point Process (NBPP) to sample visible satellites at each handover event. Crucially, the framework introduces a "persistent satellite channel" where the selected satellite's trajectory is propagated using circular orbit dynamics (or SGP4 for realistic simulations) over a finite serving time.
• Handover Process: The handover is modeled as a stochastic point process where decisions are made independently at each trigger event. The serving time is constrained by minimum ($T_{min}$) and maximum ($T_{max}$) limits, clamping the satellite's natural visibility time.
• Capacity Formulation: The paper defines Persistent Capacity as the long-term average throughput derived via the renewal-reward theorem. This is formulated as the ratio of the expected total capacity accumulated over a serving period to the expected duration of that period.
• Optimization: The optimal handover strategy is formulated as a non-linear fractional program aimed at maximizing persistent capacity. The authors employ a variant of Dinkelbach's algorithm to derive an explicit decision rule. This involves iteratively solving for a threshold capacity value that equates the residual between instantaneous serving capacity and the average maximum capacity.
• Simulation: The theoretical framework is validated using Monte Carlo simulations based on the NBPP model and compared against realistic orbit propagation using the Simplified General Perturbations 4 (SGP4) model with Starlink Two-Line Element (TLE) data. Simulations cover users in Melbourne (low latitude) and Helsinki (high latitude).

Key Contributions

1. Semi-Stochastic Framework: The paper introduces a tractable semi-stochastic model for user-centric handovers that incorporates orbit prediction and arbitrary serving times, termed the "persistent satellite channel." This extends prior work by providing closed-form orbit prediction equations and an efficient NBPP sampling method.
2. Persistent Capacity Derivation: The authors derive the ergodic capacity of this persistent channel, relating it to the "non-persistent" capacity found in prior literature. They provide closed-form upper and lower bounds for this capacity, facilitating efficient evaluation.
3. Optimal Handover Strategy: A closed-form decision rule for optimal handover is derived using a Dinkelbach-type algorithm. The strategy selects the satellite that maximizes the difference between its instantaneous serving capacity and the product of the optimal persistent capacity and its serving duration.
4. Approximation Analysis: The paper demonstrates that a simpler strategy, which maximizes the "serving capacity" (capacity per unit time) without explicit knowledge of the global optimal capacity, closely approximates the theoretical optimum.

Results

• Capacity Bounds: The derived upper bound on persistent capacity is shown to be tight, particularly for high-latitude users where satellite density is higher.
• Strategy Performance:
  • In scenarios with unconstrained serving times (long persistence), the optimal strategy ($H^\star$) provides only a marginal gain (approx. 0.03–0.07 dB) over the simpler maximum serving capacity strategy ($H_{MSC}$).
  • Under realistic SGP4-based orbit predictions, the $H_{MSC}$ strategy often outperforms the theoretical $H^\star$ derived from the NBPP model, likely due to the independence assumptions in the stochastic model not perfectly holding in deterministic trajectories.
  • For fixed serving times (e.g., 15 seconds, mimicking current Starlink operations), the distinction between optimal and sub-optimal strategies diminishes, and $H_{MSC}$ performs best.
  • Compared to a worst-case random handover strategy, utilizing side-information (position and fading statistics) yields a significant gain of approximately 1.07–1.15 dB.
• Model Accuracy: The semi-stochastic model shows close agreement with SGP4 and circular orbit simulations, validating its use for theoretical analysis.

Significance
The paper establishes persistent capacity as a tractable information-theoretic benchmark for LEO mega-constellation handover. It clarifies the relationship between non-persistent (instantaneous) and persistent (time-averaged) formulations, showing that purely stochastic models are most appropriate for short serving times. The primary practical significance lies in the finding that a low-complexity strategy—maximizing serving capacity—closely approximates the theoretical optimum. This provides a principled, computationally efficient basis for designing handover algorithms in large-scale satellite networks, reducing the search space for multi-user coordination without sacrificing significant performance. The work does not claim to solve the multi-user allocation problem itself but provides the physical-layer utility metric necessary to inform higher-layer scheduling algorithms.