Mean Gain Is Not a Guarantee: Risk-Controlled Open-Loop Scheduling for Ka-Band LEO Semantic Downlinks

Technical Summary: Risk-Controlled Open-Loop Scheduling for Ka-Band LEO Semantic Downlinks

Problem Statement
Low-Earth-orbit (LEO) satellites face severe constraints in downlinking imagery, operating within limited power budgets and short contact windows. While adaptive scheduling strategies that allocate more power to favorable channel conditions (based on weather statistics) theoretically increase the number of delivered images, they rely on open-loop planning due to the latency and mobility of LEO, which render real-time Channel State Information (CSI) stale.

The core problem identified is that conventional scheduling metrics focus on average gain over a non-adaptive reference (uniform power). The author argues this metric is misleading for operators who have only one attempt per pass. A scheduler might show a positive average gain yet fail to deliver more images than uniform power on a significant minority of individual passes (a "backfire" event). Furthermore, even a "genie" with perfect knowledge of the weather trajectory cannot eliminate this risk if the underlying semantic codec has a "shallow" response curve where deferred slots result in certain failure.

Methodology
The paper proposes a risk-controlled open-loop scheduling framework that shifts the design objective from maximizing average gain to guaranteeing a bound on the probability of underperforming uniform power.

1. System Model:

   • Channel: A Ka-band LEO pass is modeled with deterministic geometric components (elevation, path loss) and a stochastic weather component (rain attenuation) synthesized using ITU-R P.1853 and a Gauss-Markov stress model.
   • Codecs: Three semantic codecs are evaluated on the same latent representation:
     • Learned Receiver: A variational autoencoder-based receiver with refinement steps conditioned on estimated SNR and rain. It exhibits a "shallow" response where quality degrades gracefully but rarely reaches a hard "cliff."
     • ACM Ladder: An Adaptive Coding and Modulation scheme with multiple discrete steps (staircase response).
     • Cliff Codec: A single-rate system with an ideal capacity-achieving code that fails completely if the rate is not met (step response).
   • Scheduler: An open-loop scheduler selects a subset of time slots to transmit based on a predicted rain margin $m_t(s) = \mu(\epsilon_t) + s\sigma(\epsilon_t)$, where $s$ is a multiplier. Power is allocated inversely to the predicted gain.

2. Calibration Targets:

   • Conventional Target (Forecast Reliability): Sizing the margin $s$ such that the forecast covers the actual rain for a high percentage of slots (e.g., 95%). The author shows this is not the binding constraint for system performance.
   • Proposed Target (Decision Risk): Sizing the margin to control the per-pass shortfall rate. The loss function is defined as $L_s(P) = \mathbb{I}[D_u(P) - D_s(P) > c]$, where $D$ is the number of delivered images, $u$ is uniform power, $s$ is the scheduled power, and $c$ is a threshold (set to 1 image). The goal is to ensure the probability of this loss occurring is below a user-specified risk budget $\epsilon$.

3. Risk Control Mechanism:
   The paper employs the Learn-then-Test procedure (a form of conformal risk control).

   • Candidates (margin multipliers $s$) are ordered by estimated performance on a design split.
   • Each candidate is tested against a null hypothesis $H_s: R(s) > \epsilon$ (where $R(s)$ is the true risk) using an exact binomial test on a calibration set.
   • Testing stops at the first non-rejection. This guarantees that, with high confidence, the selected schedule will not underperform uniform power by more than $c$ images on more than an $\epsilon$ fraction of future passes.

Key Results
Experiments were conducted using EuroSAT RGB imagery and 800 calibration/500 evaluation passes.

• Average Gain vs. Per-Pass Risk: For the learned receiver, the best margin improved the mean number of delivered images by 0.83 to 1.69 images per pass. However, this positive average coexisted with a shortfall rate of 0.260 to 0.316 for the best margin (with a minimum shortfall of 0.250 across the sweep), meaning the scheduler performed worse than uniform power on 26–32% of passes.
• The "Genie" Limit: A scheduler with perfect knowledge of the rain trajectory (genie-CSI) also failed on 0.314 of passes. This demonstrates that the risk is inherent to the codec's shallow response and the open-loop nature of the problem, not merely a lack of feedback.
• Codec Dependency:
  • The Learned Receiver could not be certified at a strict risk budget ($\epsilon = 0.10$); the procedure correctly returned "uniform power" as the only safe option.
  • The ACM Ladder (at +8 dB) successfully certified 6 out of 19 candidates, achieving a measured shortfall rate of 0.060 (within the budget) while delivering ~7.33 more images on average.
  • The Cliff Codec certified all candidates but offered a vacuous guarantee because its uniform baseline was zero (it never delivered anything without scheduling).
• Risk Budget Trade-off: The paper quantifies the relationship between the operator's tolerance for risk ($\epsilon$) and the number of schedulable candidates. For the learned receiver, certification only became possible at a high risk budget ($\epsilon \approx 0.35$), whereas the ACM ladder was certifiable at $\epsilon = 0.10$.

Significance and Claims
The paper claims that for LEO semantic downlinks, average gain is an insufficient metric for scheduling decisions. A scheduler that improves the average can still be detrimental to a significant minority of passes, a risk that perfect channel knowledge cannot mitigate if the codec response is too shallow.

The primary contribution is a certified scheduling procedure that:

1. Replaces the conventional goal of "reliable weather forecasting" with a direct guarantee on the scheduling decision's risk.
2. Uses Learn-then-Test to provide a statistical guarantee that the scheduler will not backfire more often than a specified rate.
3. Demonstrates that this procedure acts as a filter: it refuses to schedule learned codecs with shallow responses (recommending uniform power instead) but certifies scheduling for codecs with sharper response curves (like ACM ladders).

The author concludes that operators can use this framework to set a tolerable backfire rate and determine, based on historical data, whether scheduling is a viable strategy for their specific codec and channel conditions, rather than blindly relying on average performance gains.