Opportunistic Scheduling for Single-downlink Satellite-based Quantum Key Distribution

Satellite-based quantum key distribution (QKD), leveraging low photon loss in free-space quantum communication, is widely regarded as one of the most promising directions to achieve global-scale QKD. With a constellation of satellites and a set of ground stations in a satellite-based QKD system, how to schedule satellites to achieve efficient QKD is an important problem. This problem has been studied in the dual-downlink architecture, where each satellite distributes pairs of entanglements to two ground stations simultaneously. However, it has not been studied in the single downlink architecture, where satellites create keys with each individual ground station, and then serve as trusted nodes to create keys between pairs of ground stations. While the single downlink architecture provides weaker security in that the satellites need to be trusted, it has many advantages, including the potential of achieving significantly higher key rates, and generating keys between pairs of ground stations that are far away from each other and cannot be served using the dual-downlink architecture. In this paper, we propose a novel opportunistic approach for satellite scheduling that accounts for fairness among the ground station pairs, while taking advantage of the dynamic satellite channels to maximize the system performance. We evaluate this approach in a wide range of settings and demonstrate that it provides the best tradeoffs in terms of total and minimum key rates across the ground station pairs. Our evaluation also highlights the importance of considering seasonal effects and cloud coverage in evaluating satellite-based QKD systems. In addition, we show different tradeoffs in global and regional QKD systems.

💡 Research Summary

This paper addresses the scheduling problem for satellite‑based quantum key distribution (QKD) in the single‑downlink architecture, where each low‑Earth‑orbit (LEO) satellite establishes a secret key with individual ground stations using a prepare‑and‑measure protocol (e.g., BB84) and then acts as a trusted node to relay keys between pairs of ground stations. The single‑downlink model contrasts with the dual‑downlink approach that distributes entangled photon pairs to two stations simultaneously; the former requires trusted satellites but offers higher key rates, lower hardware complexity, and the ability to connect stations that are far apart and never simultaneously visible to the same satellite.

The authors first formalize the scheduling problem. Time is discretized into slots; a satellite s can serve up to M_s ground stations in a slot, while a ground station g can be served by up to R_g satellites. For each feasible satellite‑ground pair (s,g) at time t, the number of successfully received photons λ_{s,g}^t is derived from the instantaneous free‑space optical channel model, which incorporates distance‑dependent free‑space loss, atmospheric transmissivity (computed with MODTRAN for four representative seasonal profiles), elevation‑angle dependence, internal optics loss, and a cloud‑coverage factor obtained from the Visual Crossing Weather API. Background solar photons and detector dark counts are also modeled to obtain the quantum bit error rate (QBER) E_{s,g}^t, from which the asymptotic secret‑key rate r_{s,g}^t = 1‑2h(E_{s,g}^t) follows.

The objective is two‑fold: (i) maximize the aggregate secret‑key volume across all ground‑station pairs, and (ii) guarantee fairness by maximizing the minimum key volume among all pairs. To benchmark performance, two integer‑linear‑program (ILP) formulations are introduced: Min‑Total (optimizes total key volume) and Min‑Min (optimizes the minimum key volume). While optimal, these ILPs become computationally prohibitive for realistic constellations and daily schedules.

To overcome this, the paper proposes a two‑phase opportunistic scheduling framework. Phase 1 adapts opportunistic scheduling ideas from classical wireless networks to the multi‑satellite, multi‑ground setting. In each slot, the scheduler estimates the instantaneous channel transmissivity η_{s,g}(t) and QBER, computes the corresponding secret‑key rate, and greedily matches satellites to ground stations that can deliver the highest instantaneous rate, respecting the M_s and R_g constraints. This phase exploits the time‑varying nature of satellite visibility and atmospheric conditions, ensuring high link utilization with low computational overhead.

Phase 2 takes the satellite‑ground assignments from Phase 1 and performs an iterative key‑pairing optimization. For each ground‑station pair (g_i,g_j), the scheduler selects a satellite s that possesses key pools K_{s,g_i} and K_{s,g_j}. The usable key size for that pair is min(|K_{s,g_i}|,|K_{s,g_j}|), because the larger pool can encrypt the smaller one via a one‑time‑pad. The algorithm iteratively reallocates satellite resources to increase the smallest pairwise key volume while keeping the total key volume high, thereby achieving a balanced trade‑off between total throughput and fairness.

Key insights emerging from the analysis are:

1. Dynamic channel exploitation – Satellite‑ground visibility changes rapidly; static schedules waste many high‑quality windows. Real‑time opportunistic allocation captures these peaks.
2. Multi‑transmitter/receiver capability – Allowing a satellite to serve several ground stations simultaneously (M_s>1) and a ground station to receive from several satellites (R_g>1) dramatically improves system utilization.
3. Fairness via minimum‑key monitoring – Continuously tracking the smallest pairwise key volume and preferentially assigning resources to those pairs prevents starvation and yields a more equitable service.
4. Environmental realism matters – Seasonal atmospheric profiles and cloud coverage have a pronounced impact on link loss; incorporating MODTRAN‑derived transmissivities and hourly cloud factors yields realistic performance estimates.

Simulation studies evaluate a global scenario (30 ground stations worldwide, 40 polar‑orbiting satellites) and a regional scenario (clusters of stations within a continent). Time horizons of one day and one year are examined, with four seasonal atmospheric profiles and four daily background‑photon levels (midnight, dawn, noon, dusk). Results show that the opportunistic framework outperforms Min‑Total by ~12 % in total key volume and outperforms Min‑Min by ~18 % in the minimum pairwise key volume. The advantage is especially pronounced under cloudy conditions, where the opportunistic scheduler naturally avoids obstructed windows, whereas static ILP schedules suffer from reduced availability. In regional deployments, comparable performance is achieved with fewer satellites, indicating cost‑effective scalability.

In conclusion, the paper delivers the first comprehensive opportunistic scheduling strategy tailored to single‑downlink satellite QKD. By jointly leveraging dynamic channel state information, multi‑access hardware, and a two‑phase fairness‑aware optimization, it achieves superior throughput and equitable key distribution while remaining computationally tractable. The work opens avenues for future extensions such as inter‑satellite cooperation, incorporation of pointing‑error models, and integration with quantum memory‑assisted hybrid networks.