## 2 Theoretical Background  
The color and optical characteristics of the light source are described by tristimulus values X, Y, and Z, given by Equation (1). \[ \begin{array}{l}\mathrm{X}=\mathrm{K}_{\mathrm{m}}\int_{380}^{780}\mathrm{S} (\lambda)\overline{\mathrm{x}}(\lambda)\mathrm{d}\lambda\\ \mathrm{Y}=\mathrm{K}_{\mathrm{m}}\int_{380}^{780}\mathrm{S}(\lambda)\overline {\mathrm{y}}(\lambda)\mathrm{d}\lambda\\ \mathrm{Z}=\mathrm{K}_{\mathrm{m}}\int_{380}^{780}\mathrm{S}(\lambda)\overline {\mathrm{z}}(\lambda)\mathrm{d}\lambda\end{array}  \tag{1}\]  
where \(\mathrm{K}_{\mathrm{m}}=683\)\(\mathrm{Im}/\mathrm{W}\) at \(\lambda=555\) nm; \(\mathrm{S}(\lambda)\) is the relative spectral power distribution, and \(\overline{\mathrm{x}}\), \(\overline{\mathrm{y}}\), and \(\overline{\mathrm{z}}\) are the color matching functions, which are the average data of the CIE 1931 standard [28; 29] observer. From these chromaticity coordinates, the color temperature can be given by the following expression: a physical quantity to define the chromaticity quality of the source [30]. \[\text{CCT}=-437\text{n}^{3}+360\text{ln}^{2}-686\text{ln}+5514 \tag{2}\]  
where \(\text{n}=\frac{\text{x}-0.3320}{\text{y}-0.1889}\), x, and y are the CIE 1931 color coordinates obtained by normalizing tristimulus values. CRI describes the color fidelity of the light source, which helps identify minute color variations. The average CRI of the light source for color samples 1 to 8 is denoted by \(R_{a}\). \[R_{a}=\frac{1}{8}\sum_{i=1}^{8}R_{i} \tag{3}\]  
where  
\[R_{i}=100-4.6\Delta E_{i} \tag{4}\]  
\(\Delta E_{i}\) is the color difference between the sample under the reference and test sources, and \(R_{i}\) is the special CRI. The parameters mentioned above from Equation (1) to Equation (4) are essential for characterizing the quality of the white light source. The VLC performance of DL, jitter, eye diagram, SNR, PSD, and coherence bandwidth is presented in this section. OOK (On-Off Keying) modulation is widespread because it does not require receiver phase synchronization, so a square-law-based device can be utilized for direct detection [31; 32]. The intersymbol interference (ISI) is introduced when data are transmitted at symbol rates approaching the Nyquist rate [33; 34]. According to Equation (5), \(\sigma_{t}\) is the RMS delay spread, which is the minimal interval between symbol transmissions to prevent interference from multipath propagation [35]. \[\sigma_{t}=\sqrt{\pi^{2}-\left(\tau_{\text{mean}}\right)^{2}} \tag{5}\]  
where  
\[\pi^{2}=\frac{\sum_{k}\text{P}(\tau_{k})\tau_{k}{}^{2}}{\sum\text{P}(\tau_{k}) },\ \tau_{\text{mean}}=\frac{\sum_{k}\text{P}(\tau_{k}).\tau_{k}}{\sum\text{P}( \tau_{k})}\]  
\(\tau_{\text{mean}}\) is the mean excess delay, i.e., the first moment of the power profile, and P is the power received with corresponding time delay \(\tau\). RMS delay spread estimates coherence bandwidth \(\text{B}_{\text{c}}\), mathematically expressed using Equation (6), where k can vary depending on the power delay profile, i.e., 50 when the correlation between frequencies is greater than 90% and 5 when greater than 50%. Coherence bandwidth determines channel dynamics such as flat or frequency-selective fading [35; 36]. \[\text{B}_{\text{c}}=\frac{1}{\text{k}\cdot\sigma_{t}} \tag{6}\]  
The central limit theorem states that adding multiple independent random variables produces a Gaussian profile [37]. However, other noise sources, such as thermal, shot, and flicker noise, affect the Gaussian response [38]. Flicker noise is the \"trap and release\" theory in which impurities, defects, and spaces in phosphor octahedral and tetrahedral sites trap charge carriers [39]. The colored channels induce crosstalk at the receiver, quantified by jitter in the time domain. Clock time interval error (TIE) is the digital signal reference-to-received edge time interval. This error occurs between all binary bits of signal (\(2^{11}-1\) bits of random ones and zeros).