# A Python-Based Indoor Channel Model with Multi-Wavelength Propagation for Color Shift Keying
## 6 Discussion  
According to Table 2, the received power calculated by our Python recursive algorithm presented a relative error of less than 3% for the four indoor configurations for the reference model presented in [17]. Based on these results, the recursive algorithm's performance is considered to be validated. Additionally, the Python algorithm computed the received power with more than three reflection orders due to the reduced memory compared to [17]. The simulation with ten reflection orders for Configurations A and B revealed additional  
Figure 6: SER of CSK modulation with sixteen symbols against the luminous flux emitted by the RGB-LED for three photodetector positions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Position**} & \multicolumn{3}{c}{**Lighting Parameters**} \\ \cline{2-4}  & **Illuminance [lx]** & **CRI** & **Color CIE (xy)** \\ \hline P1 & 442 & 14.5 & (0.249, 0.201) \\ P2 & 267 & 14.3 & (0.257, 0.205) \\ P3 & 148 & 14.4 & (0.277, 0.214) \\ P4 & 184 & 14.2 & (0.268, 0.210) \\ P5 & 331 & 14.4 & (0.253, 0.203) \\ P6 & 206 & 14.2 & (0.265, 0.209) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Characterization results of the indoor lighting parameters. information and features that could not be elucidated in the simulation with three orders of reflection. In the case of environments with high-reflectance walls, such as Configuration A, the received power at the detector position increased by approximately 22% of the received power computed with three reflection orders. In Configuration B, however, there was an increase of only 2%. It is essential to consider high-order reflection (\(>\)3) for high-reflectance indoor environments, as the communication and illumination characteristics are strongly dependent on high-order NLoS components. Concerning the characterization of cross-talk in the indoor Configuration A, Table 4 shows the numerical variation of the normalized cross-talk matrix when the photodetector position changes. If the cross-talk is compared between positions P1 and P3, the index \(h_{11}\) changes by roughly 30% and the index \(h_{22}\) changes by roughly 13%. The other photodetector positions also show that \(h_{11}\) and \(h_{22}\) increase if the detector is closer to the walls. Because the walls are more reflective at larger wavelengths and the received power from NLoS is greater near the walls, the photodetected current of the red and green channels increases in comparison with the blue channel. The index \(h_{33}\) is always the greater value of the cross-talk matrix, as the radiometric power emitted by the blue color LED is the greatest. This occurs because one restriction of CSK modulation is that all transmitted symbols must produce the same luminous flux. The radiometric power of the blue LED for producing 1 lm is greater than the radiometric power of the red and green LEDs. This means that the luminous efficiency of the blue LED is the lowest; thus, the photo detected current generated by the blue color detector is the greatest. The inter-channel interference represented by the \(h_{12}\), \(h_{13}\), \(h_{21}\), \(h_{23}\), \(h_{31}\), and \(h_{32}\) indexes is significantly low due to the narrow spectral responses of LEDs and effective alignment of these responses with those of the detectors. The importance of cross-talk characterization is that the optimization of the VLC must consider the cross-talk matrix in order to maximize the minimum Euclidean distance between the received symbols. The solved design of the CSK constellation depends on establishing certainty regarding the inter-channel interference and the DC channel gain. Until now, previous CSK optimizations have only considered a unique cross-talk matrix. Table 4 shows the received power for every color channel when the detector's position changes. The power reported for the receivers corresponds to a radiated power of 1 W at every color LED.