HLOS for Air VLC
Let’s carefully go through HLOS for air VLC. This is the line-of-sight channel gain, the main factor that determines how much optical power from an LED reaches a photodetector.
1. Definition of HLOS
For air (clear indoor VLC), $H_{\text{LOS}}$ accounts for:
- Distance between the LED and the photodetector.
- Radiation pattern of the LED (how the LED spreads light).
- Photodetector area and orientation.
- Incidence angle at the receiver.
Mathematically:
\[ H_{\text{LOS}} = \frac{(m+1) A_r}{2 \pi d^2} \cos^m(\phi)\, T_s(\psi)\, g(\psi)\, \cos(\psi) \]Where:
| Symbol | Meaning |
|---|---|
| $m$ | Lambertian order of LED emission (controls beam spread) |
| $A_r$ | Receiver area $(\text{m}^2)$ |
| $d$ | Distance between LED and receiver (m) |
| $\phi$ | Irradiance angle (angle between LED axis and line to receiver) |
| $\psi$ | Incidence angle at the receiver (angle between receiver normal and incoming light) |
| $T_s(\psi)$ | Optical filter gain (often $1$ if no filter) |
| $g(\psi)$ | Concentrator gain (e.g., lens or optical concentrator) |
2. Lambertian LED Radiation
The LED usually follows a Lambertian pattern:
\[ I(\phi) \propto \cos^m(\phi) \] \[ m = -\frac{\ln 2}{\ln \left( \cos(\Phi_{1/2}) \right)} \]$\Phi_{1/2}$ is the LED semi-angle at half power.
This describes how light intensity decreases as you move away from the LED axis.
3. Concentrator Gain $g(\psi)$
If the photodetector uses a lens:
\[ g(\psi) = \begin{cases} \dfrac{n^2}{\sin^2 \Psi_c}, & 0 \le \psi \le \Psi_c \\ 0, & \psi > \Psi_c \end{cases} \]- $n$ = refractive index of lens
- $\Psi_c$ = receiver field of view (FOV)
If no lens is used, $g(\psi) = 1$.
4. Simplified Indoor VLC (No Filter, No Lens)
For a basic setup:
\[ H_{\text{LOS}} = \frac{(m+1) A_r}{2 \pi d^2} \cos^m(\phi)\, \cos(\psi) \]- Only depends on distance, LED beam, and receiver area/orientation.
- There is no absorption or scattering for clear air.
5. Key Points
- $H_{\text{LOS}}$ is unitless. It represents the fraction of transmitted optical power received.
- Decreases with $d^2$ (inverse-square law) and angles $\phi$, $\psi$.
- For indoor VLC, this is usually the dominant factor; absorption and scattering are negligible unless there is fog or smoke.