OECN

1. Executive Summary

The project successfully validated the Edge Compute Bus (Power/Thermal/Compute) but failed on the Payload Physics (RF Interception & Uplink). The decision to terminate is based on the inability to close the link budget for passive interception and the logistical impossibility of maintaining ML models via current S-Band infrastructure.

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2. Platform Success Validation (The "Truck")

2.1 Power Budget Simulation

We validated the ability to support 3x Jetson Orin NX modules. The critical constraint was the Energy Balance ($E_{bal}$) over one orbital period ($T_{orbit}$).

The simulation modeled the battery State of Charge ($SoC$) as:

$$SoC(t) = SoC_{initial} + \int_{0}^{t} (P_{gen}(t) - P_{load}(t)) \, dt$$

Where:

• Generation ($P_{gen}$): Modeled using a Variac/Rectifier setup simulating Solar Flux ($\Phi_{solar} \approx 1360 W/m^2$) adjusted for incidence angle $\theta$ and eclipse duty cycle. $$P_{gen}(t) = \eta_{mppt} \cdot A_{array} \cdot \Phi_{solar} \cdot \cos(\theta(t)) \cdot \delta_{sun}(t)$$
• Load ($P_{load}$): The dynamic load of 3x Orin NXs running YOLO inference. $$P_{load} \approx 3 \times (15W \text{ to } 25W) + P_{bus}$$

Result: With a calculated duty cycle of $\approx 30\%$ (firing compute only over Areas of Interest), the depth of discharge (DoD) remained $< 20\%$, preserving cycle life.

2.2 Thermal Analysis

Heat dissipation in vacuum is purely radiative. The Stefan-Boltzmann law dictated our surface area requirements:

$$Q_{rad} = \epsilon \sigma A (T_{surf}^4 - T_{space}^4)$$

• Heat Load ($Q_{gen}$): $\approx 75W$ peak.
• Result: The calorimetric box tests proved that while continuous operation would lead to thermal runaway ($Q_{gen} > Q_{rad}$), the thermal mass of the chassis combined with the $30\%$ duty cycle allows the system to radiate stored heat during eclipse/idle periods.

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3. The Kill Chain: Failure Analysis

3.1 Passive Interception (The "Two Bullets" Physics)

The core mission was passive interception of cross-link or downlink sidelobes from a target satellite. This failed due to geometry and Friis transmission limits.

The Geometry Problem

LEO satellites move at $v \approx 7.6 \text{ km/s}$. In a crossing orbit scenario (e.g., $90^\circ$ inclination difference), the relative velocity vector magnitude is:

$$|\vec{v}_{rel}| = \sqrt{v_{sat1}^2 + v_{sat2}^2 - 2v_{sat1}v_{sat2}\cos(\alpha)} \approx 10.7 \text{ km/s}$$

The "Dwell Time" ($T_{dwell}$) within a target's sidelobe (assuming a sidelobe beamwidth of $\theta_{sl} \approx 2^\circ$ at a distance $d = 100 \text{ km}$) is:

$$T_{dwell} \approx \frac{d \cdot \tan(\theta_{sl})}{v_{rel}} \approx \frac{100 \cdot 0.035}{10.7} \approx 0.32 \text{ seconds}$$

We have roughly 300ms to detect, lock, and demodulate.

The Link Budget Collapse

The Link Margin ($M$) was calculated using the Friis Transmission Equation, modified for sidelobe interception:

$$P_{rx} = P_{tx} + G_{tx}(\theta) + G_{rx} - L_{fspl} - L_{sys}$$

Where:

• $P_{tx}$: Target transmit power (High).
• $G_{tx}(\theta)$: The Killer Variable. We are not in the main beam ($30 \text{ dBi}$). We are in the sidelobes, where gain is often negative or zero ($G_{tx} \approx -5 \text{ to } 0 \text{ dBi}$).
• $L_{fspl}$: Free Space Path Loss. $$L_{fspl} = 20\log_{10}(d) + 20\log_{10}(f) + 92.45$$

The Energy Per Bit ($E_b/N_0$) Reality: To demodulate complex data (e.g., QPSK/16QAM), we need a specific $E_b/N_0$.

$$\frac{E_b}{N_0} = \frac{P_{rx}}{k_B \cdot T_{sys} \cdot R_{bit}}$$

• $R_{bit}$: Target data rates are high ($>100 \text{ Mbps}$), which dilutes energy per bit.
• $P_{rx}$: Extremely low due to sidelobe attenuation.

Result: The resulting $E_b/N_0$ was consistently below the Shannon Limit for the required modulation schemes. The data received was indistinguishable from the noise floor.

3.2 Uplink Asymmetry (The ML Ops Wall)

We determined that "Static AI" is useless. Models must be updated.

Data Transfer vs. Orbital Mechanics

• Model Size ($S_{model}$): A quantized YOLO model + weights $\approx 300 \text{ MB} = 2.4 \times 10^9 \text{ bits}$.
• S-Band Uplink Rate ($R_{up}$): Realistically limited to $\approx 256 \text{ kbps}$ for robust uplink.
• Pass Duration ($T_{pass}$): Average visible pass $\approx 600 \text{ seconds}$.

Total Data per Pass:

$$D_{pass} = R_{up} \times T_{pass} = 256 \times 10^3 \times 600 \approx 153 \text{ Mb}$$

Passes required for ONE update:

$$N_{passes} = \frac{S_{model}}{D_{pass}} = \frac{2400 \text{ Mb}}{153 \text{ Mb}} \approx 15.6 \text{ passes}$$

Conclusion: It would take 16 perfect passes (approx. 2-3 days of operations) to update a single model. This assumes 0% packet loss. Given the bit error rates in S-Band tumbling, the probability of a corrupted model file is near $100\%$.

Since commercial X-Band uplink is not available, we cannot sustain the "Continuous Learning" requirement of the mission.

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4. Final Verdict

The Compute Payload is viable. The RF Payload is physically impossible with current antenna sizes (SWaP constrained). The ConOps is logistically impossible without Optical Inter-Satellite Links (OISL).

Action: Terminate. Archive "Truck" designs. Wait for OISL commoditization.

5. Whitepaper

The following is the white paper of the Pathfinder Mission:

https://us-west-2.graphassets.com/cmea76jmo0qmr07my8kv3domu/cml83fuu80agl07lixvqv25ez