# Design of Novel Laser Crosslink Systems Using Nanosatellites in Formation Flying: The VISION
## 3 Concept of the Laser Crosslink Systems
### Optical Link Budget
#### 3.2.2 Signal-to-Noise Ratio Margin  
When the beam is propagated in free space, the signal power is reduced inversely proportional to the square of the inter-satellite distance, as shown in Figure 8. Given the aforementioned pointing errors, the received signal power on the laser communication detector, which is the avalanche photodiode detector (APD), is not sufficient for PAT and communication. The transmitted and received laser powers on each satellite are significantly enhanced by deployable optics. Moreover, the signal must be sufficiently detectable from the background noise of each detector. For feasible on-orbit communication with novel optics, the SNR margin must exceed 10 dB within the maximum range. Figure 8: Free space path loss and received power for the laser communication detector over various inter-satellite distances. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Pointing Error**} & \multicolumn{2}{c}{**PAT\#1**} & \multicolumn{2}{c}{**PAT\#2**} & \multicolumn{2}{c}{**PAT\#3**} & \multicolumn{2}{c}{**PAT\#4 and COM\#1**} \\  & \multicolumn{2}{c}{**(\(\upmu\), \(\upsigma\)) [\(\upmu\)rad]**} & \multicolumn{2}{c}{**(\(\upmu\), \(\upsigma\)) [\(\upmu\)rad]**} & \multicolumn{2}{c}{**(\(\upmu\), \(\upsigma\)) [\(\upmu\)rad]**} \\ \hline \multicolumn{2}{c}{**Elements**} & \multicolumn{1}{c}{**50 km**} & **1000 km**} & **50 km** & **1000 km** & **50 km** & **1000 km** & **50 km** & **1000 km** \\ \hline \multirow{4}{*}{**Point-Ahead**} & Body & (386.76, & (310.61, & (384.79, & (307.86, & (0.33, & (6.67, & \\) & Pointing & 171.67) & 109.99) & 171.67) & 109.99) & 2.42) & 2.43) & \\  & Alignment & (223.21, & (223.21, & (223.21, & (0.00, & (0.00, & \\  & & 173.40) & 173.40) & 173.37) & 173.37) & 173.21) & 173.21) & \\  & Sensor & & & (0.00, & (0.00, & (0.00, & (0.00, & (0.00, \\  & Noise & & & 0.40) & 8.00) & 0.40) & 8.00) & 0.10) & 0.60) \\  & Residual & & & (0.00, & (0.00, & (0.10, & (0.10, & (0.10, \\  & Jitter & & & 4.00) & 4.00) & 4.06) & 4.06) & 0.76) & 0.76) \\ \hline \multicolumn{2}{c}{**Total**} & \multicolumn{1}{c}{(609.96, & (533.82, & (608.00, & (531.06, & (0.43, & (6.77, & (0.10, & (0.10, \\  & & 244.00) & 205.34) & 244.02) & 205.51) & 173.27) & 173.45) & 0.77)} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pointing errors elements and values for each PAT sequence. Table 4 presents the optical link budget analysis results for the maximum range. The transmitted power is 1 W and split for the PAT and communication. For the PAT cases, the SNR margin is estimated for the CAM and QC detectors, following the pointing stages. Communication modulation is applied to on-off keying (OOK), which is primarily utilized in spaceborne laser communication systems. The required SNR was calculated according to a target BER of \(1\times 10^{-3}\). Although the beam power for each PAT sequence is weak compared with the communication, the SNR margin meets the system requirements, achieving approximately 11 dB for the CPS and 22 dB for the FPS. The narrow beam divergence angle for PAT#4 and COM#1 significantly contributed to increasing the received power and enhancing the optical link performance.