# Mobile User Connectivity in Relay-Assisted Visible Light Communications
## 3 System Model
### Mobile User  
Research work on direct VLC links using mobile devices as Rxs has been reported e.g., in [29]. In contrast to work reported in the literature, in this paper, we investigate the use of MP acting as the Rx and an RN as a part a relay-based VLC system, see Figure 2a. Let's assume that the MP has (i) two photodetectors (PDs) on both sides, thus providing the MP with spatial diversity using a selection of the strongest received signal; and (ii) the Tx LED array placed perpendicular to the Rx planes as depicted in Figure 2b. Note that within the MP elevation plane, an azimuth angle remains the same as in the case of the Rx. The MP parameters are summarized in Table 2.  
In this work we investigate the orientation of the MP within the indoor environment. Based on 1300 observations of people using their MPs on the street, airports, on trains and buses, 49% of them used their MPs with only one hand and up to 90% held it vertically facing upwards [30]. Based on our tests, people were reading messages and surfing the Internet by holding the MP typically with the elevation angle within the range of 5\({}^{\circ}\)-65\({}^{\circ}\). Therefore, without any loss of generality, we have adopted the same elevations in this study. Note that, the download traffic (mostly data) is significantly higher  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Rx area & \(A_{r}\) & 1 cm\({}^{2}\) \\ Effective area of a photodiode & \(\Psi_{FOV}\) & 50\({}^{\circ}\) \\ Photodetector responsivity & \(\gamma\) & 0.53 A/W \\ Optical filter concentrator & \(T_{S}\) & 1 \\ Optical concentrator gain & \(g\) & 3 \\ User position & - & 0.5 \(\times\) 0.5 \(\times\) 1.2 m \\ Rx elevation & - & 50\({}^{\circ}\) \\ Rx azimuth & - & 90\({}^{\circ}\) \\ Tx\({}_{\text{RNN}}\) power per LED & - & 200 mW \\ Size of LEDs & - & \(1\times 10\), 1 \(\times\) 14 \\ Semiangle at half power & \(\theta_{1/2}\) & 60\({}^{\circ}\) \\ Background dark current & \(I_{bg}\) & 10 nA \\ Noise bandwidth factors & \(I_{2}\), \(I_{3}\) & 0.562, 0.0868 \\ Absolute temperature & \(T_{k}\) & 295 K \\ Open-loop voltage gain & \(G\) & 10 \\ Capacitance & \(\eta\) & \(112\times 10^{-8}\) F/m\({}^{2}\) \\ FET channel noise factor & \(T\) & 1.5 \\ FET transconductance & \(g_{m}\) & 0.03 S \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mobile Device Parameters.  
Figure 2: (**a**) Mobile user position in a room; and (**b**) the positions of the Rx and Tx on a mobile device.  
than the upload and other forms of traffic as reported in [31], therefore we have focused only on the download case.  
Let us have an example of a NLOS transmission when the Rx (i.e., the MP) is located near the corner of a room (i.e., the position of 0.5 m \(\times\) 0.5 m \(\times\) 1.2 m), see Figures 1b and 2b. The upper edge of the user's MP is oriented in azimuth and elevation angles of 180\({}^{\circ}\) and 50\({}^{\circ}\), respectively. The impulse responses of the link with no LOS path and using a MP-based Rx with front and rear cameras are depicted in Figure 3a,b, respectively. The impulse responses are calculated using the first five reflection components from walls. As can be seen from the figures, using the rear camera oriented to the Tx, the received power is higher and the impulse response is slightly less dispersive compared to the front photodiode.