# Testbed for Experimental Characterization of Indoor Visible Light Communication Channels
## 4 Simulation Results  
In this section, several simulation results are presented to assess the suitability of the mockup as testbed to evaluate indoor VLC systems. Table 1 includes the main simulation parameters where a cubic room (\(4.0\,\mathrm{m}\times 4.0\,\mathrm{m}\times 2.75\,\mathrm{m}\)) with four WLED array lamps is considered. For the reflection coefficient \(\rho(\lambda)\) of the room surfaces, the experimentally measured spectral reflectances given in [13] are used. The room also contains two windows similarly as illustrated for the mockup in Figure 2a. Figure 4 shows the simulated received power and illuminance at the receiver plane. The receiver has been considered pointing upward. First of all, we can observe that the minimum standard level of 400 lx at workplaces is fulfilled throughout the room. In addition, it can be seen how the LOS component contributes with more than 70% of the total received power in most of locations (approaching 80% at the center of the room) except for areas close to the walls where contribution of reflected light becomes more significant. Moreover, in areas near the windows (south face of the room), LOS component contribution grows again (with respect to those closer to other walls) due to the loss of light, which goes away through the windows. Figure 5 shows the simulated impulse responses at three locations for the receiver: under lamp 1 close to windows, at the center of the room and under lamp 4 near a corner without windows. As we can see, LOS component dominates the impulses responses although the percentage of contribution due to first and second order reflection of emitted light are significant. It can also be observed in Figure 5c,d how the \(k=2\) reflection contribution is higher than that of \(k=1\) for the receiver positioned at room center. This is because the light emitted from LEDs, which comes back to the ceiling after the first reflection on walls makes the ceiling (for \(k=2\)) a big emitting surface, this effect being more noticeable when receiver is located at central area of the room where first order reflection decreases due to the greater distance to the room walls. The delay spread \(D\) of the impulse's responses \(h(t)\) throughout the room can be computed as [18]:  
\[D=\left[\frac{\int_{-\infty}^{\infty}(t-\mu)^{2}h^{2}(t)dt}{\int_{-\infty}^{ \infty}h^{2}(t)dt}\right]^{1/2}, \tag{12}\]  
where the mean delay \(\mu\) is given by:  
\[\mu=\frac{\int_{-\infty}^{\infty}th^{2}(t)dt}{\int_{-\infty}^{\infty}h^{2}(t) dt}. \tag{13}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** \\ \hline Room size (length \(\times\) width \(\times\) height): & 4.00 m \(\times\) 4.00 m \(\times\) 2.75 m \\ Number of LED arrays (lamps): & 4 (2 \(\times\) 2) \\ Number of LEDs per array: & 25 (5 \(\times\) 5) \\ Dimensions of each LED array: & 0.1 m \(\times\) 0.1 m \\ Positions of LED arrays & array 1: (1.00, 1.00, 2.75) \\ (central point) (\(x\), \(y\), \(z\)) [m]: & array 2: (3.00, 1.00, 2.75) \\  & array 3: (1.00, 3.00, 2.75) \\  & array 4: (3.00, 3.00, 2.75) \\ LED Lambertian order (\(n\)): & 1 \\ Power of a single LED (\(P_{E}\)): & 400 mW \\ Total LED lamp power (\(P\)): & 10 W \\ Receiver plane height: & 0.75 m \\ Total detector physical area (\(A\)): & 1.00 cm\({}^{2}\) \\ \hline Surface materials parameters [13]: & \(\overline{\rho(\lambda)}\) & \(r_{d}\) & \(m\) \\ \hline Ceiling: & 0.35 & 1 & - \\ Floor: & 0.55 & 1 & - \\ Walls (plaster): & 0.69 & 1 & - \\ Windows (glass): & 0.04 & 0 & 280 \\ \hline Windows dimensions (width \(\times\) height): & 1.00 m \(\times\) 1.00 m & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of VLC Simulation Scenario. Figure 6 depicts the mean delay and delay spread throughout the room at the receiver plane. It is seen as maximum delay spread hardly achieves 2.5 ns at room corners going below 1 ns for the central area of the room, leading to a coherence bandwidth of cents of megahertz.