# Mobile User Connectivity in Relay-Assisted Visible Light Communications
## 4 Simulation Results  
In this section, we present the results for the performance analyses of the proposed VLC relay cooperation system. In order to provide a more accurate comparison between AF and DF modes, we have adopted a simulation model with 5 reflections based on the Monte Carlo ray tracing algorithm using the assumption of a half-duplex OOK cooperation transmission link. For simulations, we have used the key parameters shown in Table 2.  
In order to evaluate the azimuthal and angular dependency of the RN, we assessed a scenario where the relay user is located at the coordinates of 2 m \(\times\) 2 m \(\times\) 1.2 m with the transmit power of 2 W. Figure 5a,b depict a comparison of the SNR as a function of the azimuth and elevation angles for AF and DF relaying schemes. SNR \(>\) 9.8 dB corresponds to a BER of \(10^{-3}\) for the relay user transmission. Note that, the maximum SNR is achieved at the azimuth angle of -15\({}^{\circ}\). Figure 4: Comparison of average BER for different irradiance angle with constant FOV. Figure 5: SNR dependency on azimuthal orientation of relay in: **(a)** AF; and **(b)** DF. To illustrate the position of the mobile relay user within the room, see Figure 1b. We calculated the impulse response of the channel, considering that the mobile relay user can only move around within a specific region in the room, see yellow marked area in Figure 1b. As an example for the relay-assisted DF model, with the RN positioned at the coordinates of 2 m \(\times\) 2 m \(\times\) 1.2 m with azimuth and elevation angles of -20\({}^{\circ}\) and 5\({}^{\circ}\), respectively, the impulse responses for source-to-RN and RN-to-Rx are depicted in Figure 6a,b, respectively. The channel gains for the source-relay \(G_{SR}\) and the relay-user \(G_{RD}\) links against the direct source-user link are determined to be 39.1 dB and 4.4 dB, respectively. Next we considered the azimuthal orientation of the RN against its position within the yellow area of the room, see Figure 1b. In the simulation, we have assumed that the Rx is (i) at the elevation angle of 55\({}^{\circ}\); and (ii) an azimuth angle is -180\({}^{\circ}\). Figure 7 shows the borders of the room covered by the RN for a range of azimuthal angles to ensure a BER of 10\({}^{-3}\). Figure 7a is for the case when the RN is oriented more to the opposite direction from the source (negative azimuth). It can be seen that the DF mode offers improved results more specifically at positions further from the source (i.e., \(x=0\) to 0.8) and close to the wall. For the azimuth of -20\({}^{\circ}\), with the DF the coverage area is only increased by \(\sim\)0.2 m\({}^{2}\) compared to AF, therefore less complex AF would be the preferred option to adopt. A difference of 20\({}^{\circ}\) in the azimuthal plane results in changes in the coverage area by \(\sim\)30 cm and 40 cm in the \(x\)- and \(y\)-axis, respectively. Note that, RN widens the coverage area by \(\sim\)1.9 m\({}^{2}\) for the azimuth angle changed from -80\({}^{\circ}\) (orientation to the wall) to -20\({}^{\circ}\). The insets in Figure 7a depict the overall impulse responses of the VLC channel (i.e., from Tx to the Rx via the RN) for given positions and the azimuth of -20\({}^{\circ}\), where SNR is mainly affected by the ISI. The azimuthal orientation of the RN in the contra-clockwise direction (i.e., from the 0\({}^{\circ}\) to 80\({}^{\circ}\) towards the Tx) is illustrated in Figure 7b. In the case where the RN rotates in azimuth to the left, the DF cooperative mode offers an improvement of more than 10 cm for all positions in the \(y\)-axis. Note that, the relay MP azimuthal oriented in 80\({}^{\circ}\) can be used only in small fraction area. For a wider angle of rotation, the difference in the coverage area between AF and DF modes increases from 0.2 m\({}^{2}\) for 20\({}^{\circ}\) to 0.4 m\({}^{2}\) for 60\({}^{\circ}\). Whereas, the azimuthal orientations of 0\({}^{\circ}\) and 80\({}^{\circ}\) result in widening of the coverage area by 2.16 m\({}^{2}\).