## 3 Results  
In this work, we study the influence of both h\({}_{\text{LOS}}\)(t) and h\({}_{\text{NLOS}}\)(t) on the chaotic carrier frequency by considering the Rx's positions, for which LOS is the dominant path. We show how this influence is due to the excess delay between the beams, which increases gradually with the carrier frequency of the chaotic signal; where this mean excess delay between each of the LOS paths being collected at the Rx becomes comparable to the period of the Tx signal. This is because all LED spotlights transmit the same signal, which when placing the Rx on the floor, we obtain LOS paths with the speed of the signal matching the delay spread more closely. The proposed MISO system described in the previous section is numerically simulated. For this, the carrier's frequency is gradually increased in steps of 1 MHz until the cross-correlation coefficient is lower than 0.8--where it is considered that complete chaotic synchronization is lost. Accordingly, we steadily increased the frequency of the Colpitts carrier, establishing 12 scenarios, detailed in Table 1 with their corresponding correlation coefficient. For each scenario we have analyzed the correlation factor for each of the three Rx positions. Since the dimensions of the floor are squared (5 by 5 m), if we consider the geometrical center to be the coordinate \((0,0)\) testing the positions of the first quadrant (2, 2) and (2.5, 2.5) are equivalent for the remaining three quadrants due to the symmetry constraint. Table 2 presents the correlation values for the chaotic carrier V\({}_{\text{BE\_TX}}\)(t) and its respective synchronized state V\({}_{\text{BE\_RX}}\)(t) for every corresponding position and frequency. This has been calculated using the standard cross-correlation equation between the transmitted signal and the corresponding generated signal for every position and the multipath model outlined in Section 2 given in [31; 34]. Note that the scaling factor \(T\) is an arbitrary, proportional parameter with no units. Figure 10 shows the correlation values graphically against the normalized carrier frequency for the range of Rx's positions. The correlation coefficient drops progressively as the carrier frequency is increased due to the multipath effect. In this case, synchronization is lost when the carrier frequency is higher than 12 MHz, where the correlation coefficient is in the order of 0.8. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Carrier Frequency**} & **Position 1** & **Position 2** & **Position 3** \\  & **(0, 0)** & **(2, 2)** & **(2.5, 2.5)** \\ \hline \(T=1\), \(\omega=100\) kHz & 0.9987 & 0.9992 & 0.9992 \\ \(T=30\), \(\omega_{\text{norm}}=3\) MHz & 0.9814 & 0.9829 & 0.9848 \\ \(T=40\), \(\omega_{\text{norm}}=4\) MHz & 0.9721 & 0.9749 & 0.9749 \\ \(T=50\), \(\omega_{\text{norm}}=5\) MHz & 0.9577 & 0.9618 & 0.9669 \\ \(T=60\), \(\omega_{\text{norm}}=6\) MHz & 0.9373 & 0.9417 & 0.9480 \\ \(T=70\), \(\omega_{\text{norm}}=7\) MHz & 0.9183 & 0.9277 & 0.9371 \\ \(T=80\), \(\omega_{\text{norm}}=8\) MHz & 0.8985 & 0.9088 & 0.9192 \\ \(T=90\), \(\omega_{\text{norm}}=9\) MHz & 0.8770 & 0.8862 & 0.9106 \\ \(T=100\), \(\omega_{\text{norm}}=10\) MHz & 0.8703 & 0.8780 & 0.9000 \\ \(T=110\), \(\omega_{\text{norm}}=11\) MHz & 0.8275 & 0.8479 & 0.8701 \\ \(T=120\), \(\omega_{\text{norm}}=12\) MHz & 0.7986 & 0.8168 & 0.8440 \\ \(T=130\), \(\omega_{\text{norm}}=13\) MHz & 0.7510 & 0.7789 & 0.8050 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients between V\({}_{\text{BE\_TX}}\)(t) and V\({}_{\text{BE\_RX}}\)(t). This study showed that the strongest impact on the synchronization quality is when the Rx is at the center of the room in contrast to the corners of the room where the correlation is higher. An explanation to this trend is because at the corners of the room the transmission mode is mostly LOS with very little non-LOS components.