Free-Space Optical (FSO) Communication
Free-space optical (FSO) communication entails the transmission of modulated optical signals through an unguided medium, typically the atmosphere, from a transmitter to a receiver. Conceptually, this can be analogized to emitting a collimated optical beam over a distance and reconstructing the information at the remote receiver, with the received signal being influenced by both deterministic and stochastic propagation effects.
1. Received Power and Link Budget
The received optical power \(P_r\) can be expressed in terms of the transmitted power \(P_t\) and the cumulative link losses:
$$ P_r = P_t \cdot L_{\text{geo}} \cdot L_{\text{atm}} \cdot L_{\text{opt}} $$
Where:
- \(L_{\text{geo}}\) accounts for geometric spreading
- \(L_{\text{atm}}\) accounts for atmospheric attenuation
- \(L_{\text{opt}}\) encompasses optical coupling and alignment losses
2. Free-Space Geometric Loss
Assuming a Gaussian beam profile, the free-space path loss is approximated as:
$$ L_{\text{fs}} = \left(\frac{\lambda}{4\pi d}\right)^2 $$
- \(\lambda\) is the optical wavelength
- \(d\) is the propagation distance between transmitter and receiver
3. Beam Divergence
For a Gaussian beam:
$$ w(d) = \theta d $$
The corresponding power density:
$$ I(d) \propto \frac{1}{w(d)^2} \propto \frac{1}{(\theta d)^2} $$
4. Atmospheric Attenuation
Using the Beer–Lambert law:
$$ P(d) = P_0 e^{-\alpha d} $$
5. Composite Received Power
$$ P_r = P_t \cdot \frac{A_r}{\pi (\theta d)^2} \cdot e^{-\alpha d} $$
6. Noise Considerations
a) Shot Noise
$$ \sigma_{\text{shot}}^2 = 2 q I B $$
b) Thermal Noise
$$ \sigma_{\text{thermal}}^2 = \frac{4 k T B}{R_L} $$
7. Signal-to-Noise Ratio (SNR)
$$ \text{SNR} = \frac{(R P_r)^2}{\sigma_{\text{shot}}^2 + \sigma_{\text{thermal}}^2} $$
8. Achievable Data Rate
$$ C = B \log_2 \big( 1 + \text{SNR} \big) $$
9. Atmospheric Turbulence
$$ \sigma_I^2 \propto C_n^2 k^{7/6} d^{11/6} $$
10. Summary
$$ \boxed{ \text{FSO link performance} = \text{Geometric spreading (beam physics)} \times \text{Atmospheric attenuation (exponential decay)} \times \text{Noise processes (stochastic statistics)} } $$