---
title: PAT-Aware CPD Framework for FSO Links
url: https://www.emergentmind.com/topics/pat-aware-cpd-framework
type: topic
---

# PAT-Aware CPD Framework for FSO Links

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 [2601.18148].

## 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 [2601.18148].

Source: https://www.emergentmind.com/topics/pat-aware-cpd-framework