PAT-Aware CPD Framework for FSO Links

• The paper introduces a mathematically rigorous MILP scheduler that integrates explicit PAT delay modeling to improve FSO interplanetary communications with a throughput gain over 30%.
• It employs a mixed-integer linear programming formulation over time-extended graphs, capturing orbital dynamics, physical constraints, and mechanical retargeting overhead for precise contact planning.
• The framework emphasizes longer, well-coordinated contact windows, fairness constraints, and solver warm-starting to ensure near-uniform capacity allocation across Mars orbiters, MEO relays, and Earth ground stations.

The PAT-aware Contact Plan Design (CPD) framework represents a mathematically rigorous and system-architectural solution for scheduling high-throughput free-space optical (FSO) interplanetary backhaul links in space communications. Its distinctive contribution is the explicit modeling of pointing–acquisition–tracking (PAT) retargeting delays, a previously unaddressed impairment in FSO contact planning, which alters the feasible schedule space and operational capacity for both direct-to-Earth and relay-based multi-hop networks. The framework leverages a mixed-integer linear programming (MILP) formulation over a time-extended graph (TEG), integrating orbital motion, network topology, and physical link constraints to deliver executable contact schedules that maximize end-to-end scientific telemetry throughput, fairness, and duty-cycle efficiency (Gerard et al., 26 Jan 2026).

1. System Model and Key Assumptions

The framework is instantiated on a Mars–Earth optical backhaul scenario comprising three node classes:

• Sources: Deep-space Mars orbiters equipped with SWaP-C constrained single FSO terminals.
• Relays: Medium-Earth–orbit (MEO) satellites with dual FSO heads, implementing DTN bundle protocol (mirroring NASA’s LCRD).
• Sinks: Optical ground stations (OGSs) on Earth, each with one FSO head.

Link connectivity is time-varying and directional:

• Direct-to-Earth (DTE) Links: Mars orbiter-to-OGS, single hop, nominally 50 Mbps over ≈$10^8$ km.
• Two-hop Relays: Mars orbiter→MEO relay (50 Mbps)→OGS (1.2 Gbps).

A scheduled link is defined by contact windows $c=(u,v,k)$, specified by start/end times $(\tau^\mathrm{start}_c, \tau^\mathrm{end}_c)$ and duration $T_k$. Before usable transmission, each FSO terminal must disengage previous links and slew to new line-of-sight, incurring a PAT retargeting delay:

$$T_\mathrm{retarget} = T_\mathrm{pointing} + T_\mathrm{acq}$$

with $T_\mathrm{pointing}$ (mechanical gimbal slew, $\approx1^\circ/\mathrm{s}$) and $T_\mathrm{acq}$ (narrow-beam acquisition dwell, $\approx$0.5 s). The resulting effective transmission period is:

$T^\mathrm{eff}_k = T_k - T_\mathrm{retarget}$

2. Mathematical MILP Formulation

The CPD scheduling problem is cast as a mixed-integer linear program over a TEG, constructed by time-stamping node and edge instances for each slice $k$:

• Variables:
  • $L_{e_k}\in\{0,1\}$: contact selection indicator for edge $e_k=(u,v,k)$.
  • $C_{e_k}\geq0$: data-carrying capacity of the scheduled contact.
  • $C_v$: aggregate capacity received/relayed at node $v$.
• Objective:

$$\max\;\sum_{v\in V'_\mathrm{relay}\cup V'_\mathrm{sink}} C_v$$

Maximizes total backhaul delivery to relays and sinks.

• Constraints:
  • Edge capacity bounds:

  $C_{e_k}\;\leq\;L_{e_k}\,T_k\,B_e$

  $$C_{e_k}\;\leq\;(T_k - T_\mathrm{retarget})\,B_e = T^\mathrm{eff}_k\,B_e$$

  with $B_e = \min(B_u,B_v)$ (modem rate). - Flow conservation (at relays):

  $$C_v\leq\min(\mathrm{inflow}_v,\,\mathrm{outflow}_v)$$ - Optical terminal constraint:

  $\sum_{(u,v,k):\,u=u_0}L_{(u,v)_k}\;\leq\;1$

  ensuring one contact per terminal, per slice. - Fairness soft constraint (optional):

  $$\mathrm{ECT}_u = \sum_{(u,v,k)\in E'}L_{(u,v)_k}\,T^\mathrm{eff}_k$$

  $$\mathrm{ECT}_u\geq\epsilon\cdot\overline{\mathrm{ECT}},\quad\forall u\in V'_\mathrm{source}$$

  controls minimum relative enabled-contact-time ($0<\epsilon\leq1$) across sources.

3. Optical Duty-Cycle Metric

The framework introduces an operational quality metric—the optical network duty-cycle (ODC):

$$\mathit{ODC} = 100\times\frac{\sum_{(u,v,k)\in L}T^\mathrm{eff}_{u,v,k}}{\sum_{(u,v,k)\in L}T_k}$$

for all scheduled contacts $L$. ODC estimates the proportion of window time used for data transfer (avoiding PAT-induced wastage), essential for identifying capacity lost to retargeting. In two-hop relay chains, sequential scheduling enables amortization of retargeting overhead over higher aggregate throughput.

4. Scheduler Implementation and Algorithmic Strategy

The MILP is solved in Python (PuLP/Gurobi), using the following scheme:

• Edge pruning: the initial TEG is reduced by a DAG journey-preservation method, removing infeasible source–sink paths and preserving computational tractability with linear scaling in temporal paths.
• Solver warm-start: global MILP branch-and-bound search (via Gurobi) is initialized with a greedy baseline solution (“LLS_Greedy”), expediting convergence within a wall-clock budget (2.5 h per schedule).

Greedy baseline algorithm: At each slice $k$, maximum-weight matchings (per Edmonds’ blossom algorithm) are computed for the instantaneous graph, with edge weights as $T^\mathrm{eff}_k\cdot B_e$. This approach, $O(|E'|\sqrt{|V'|})$ per time slice, fails to model cross-slice link coupling imposed by PAT retargeting.

5. Performance Evaluation

Evaluation involves a 24 h scheduling horizon, up to 32 Mars orbiters, 3 MEO relays, and 3 OGSs, integrating NASA DSOC/LCRD/TBIRD parameters, real orbital data, and PAT delays.

Metric	PAT-aware MILP (LLS_MIP)	Greedy (LLS_Greedy)	Zero-delay CPD
Aggregate Capacity	>30% higher	Baseline	-35–40%
Duty Cycle (ODC)	>90%	60–70%	N/A
Schedule Morphology	Few, long contacts	Many, short hops	Unphysical
Fairness (ECT, $\epsilon=0.95$)	Near-uniform, <30 min latency	Variable, >40 min for some	N/A
Scalability	16 sources, exponential growth, 2.5 h cap	Up to 50 sources tractable	N/A

MILP schedules consistently favor fewer long-duration contacts, amortizing PAT delay and maximizing throughput in contrast to the greedy algorithm, which is prone to producing infeasible sequences when retargeting is ignored.

6. Insights, Implications, and Design Guidelines

The findings demonstrate that ignoring PAT retargeting results in overestimation of achievable capacity and infeasible contact schedules. The MILP framework, with explicit modeling of $T_\mathrm{retarget}$, shifts the optimal schedule toward longer contacts of lower instantaneous diversity but higher net throughput.

Emergent design recommendations include:

• Explicit PAT modeling: Required for networks with mechanical steering times beyond the subsecond regime.
• TEG pruning: Journey-preserving DAG reduction prior to optimization is crucial.
• Solver warm-starting: Use of greedy schedules accelerates global MILP convergence.
• Fairness tuning: ECT soft constraints with $\epsilon\approx0.9–1.0$ balance equity and total capacity.
• Scalability strategies: For large networks, utilize problem decomposition or rolling-horizon MILPs.

The PAT-aware CPD framework constitutes the first implementation of temporal max-flow scheduling integrated with physical link setup delays for FSO networks, delivering executable contact plans with a throughput gain exceeding 30% versus traditional heuristic methods. This approach enables high-rate, autonomous, and physically realistic optical interplanetary communications, accounting for both orbital dynamics and mechanical PAT constraints (Gerard et al., 26 Jan 2026).