# A Full-Duplex LED-to-LED Visible Light Communication System
## 3 Receiver Characteristics of LED  
In our experiment, we used HB10P red, yellow, green, blue, and white LEDs (Yinhui photoelectric). The size and viewing angle of the LEDs were 10 \(\varnothing\) (mm) and 30\({}^{\circ}\), respectively. To obtain more detailed characteristics of the LEDs, we measured their spectra and optical powers. The measurement results are shown in Figure 1 and the parameters are summarized in Table 1. The peak wavelengths for red, yellow, green, blue, and white LEDs were measured as 628, 587, 520, 465, and 454 nm, respectively. Note that the white LED was a phosphor-converted white LED (pc-WLED). [PERSON]'s channel capacity law is one of the powerful tools used to estimate the link performance when the channel bandwidth, average signal power, and average noise power are given. The channel capacity equation is given by:  
\[C=f_{3 dB}\cdot\log\left(1+\frac{E\left[\overline{P_{s}}\right]}{E\left[\overline {P_{n}}\right]}\right) \tag{1}\]  
where \(C\) is the capacity of the channel, \(f_{3 dB}\) is the 3 dB bandwidth of the channel, \(P_{s}\) is the signal power, and \(P_{n}\) is the noise power. For a simple low-pass resistor capacitor (RC) network, the step response of the system is given by:  
\[V(t)=V_{0}\left(1-e^{-\frac{t}{\tau}}\right) \tag{2}\]  
where \(\tau\) is an RC time constant. The time that the signal takes to achieve \(x\%\) of the voltage level can be obtained by solving Equation (2):  
\[t_{x\%}=-\tau\ln\left(1-\frac{x}{100}\right) \tag{3}\]  
Thus, the rise time \(t_{r}\) can be expressed as:  
\[t_{r}=t_{0.9}-t_{0.1}=\tau\ln 9 \tag{4}\]  
Since the 3 dB bandwidth of the low-pass RC system is given by  
\[f_{3 dB}=\frac{1}{2\pi\tau} \tag{5}\]  
using Equations (4) and (5), the 3 dB bandwidth of a system can be approximated by the rise time of the received signal as:  
\[f_{3 dB}=\frac{\ln 9}{2\pi t_{r}}\cong\frac{0.35}{t_{r}} \tag{6}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value** & **Dimension** & **Parameter** & **Value** & **Dimension** \\ \hline Viewing angle & 30 & deg. & Diameter & 10 & mm \\ \hline \multirow{4}{*}{Peak Wavelength} & Red & 628 & nm & \multirow{4}{*}{Optical power Blue} & Red & 1.168 & mW \\  & Yellow & 587 & nm & & Yellow & 0.518 & mW \\  & Green & 520 & nm & (3V applied) & Green & 3.25 & mW \\  & Blue & 465 & nm & & Blue & 4.28 & mW \\  & pc-white & 454 & nm & & pc-white & 2.15 & mW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of LEDs. Figure 1: (**a**) The spectrum and (**b**) optical power of red, yellow, green, blue, and white light-emitting diodes (LEDs). Therefore, with Equations (1) and (6), we can derive another channel capacity equation:  
\[C\cong\frac{0.35}{t_{r}}\cdot\log_{2}\left(1+\frac{E\left[\overline{P_{s}}\right] }{E\left[\overline{P_{n}}\right]}\right) \tag{7}\]  
Using Equation (7), the approximated channel capacity of each LED color set (a transmitter and receiver LED set) can be calculated by the rise time, average signal power, and average noise power of the received signal. Figure 2 shows the experimental setup for measuring the rise time and SNR for all of the possible combinations of color LED transmitters and color LED receivers. On the transmitter side, a square wave (SQW) is used to modulate the transmitter LED. A serial resistance of 15 \(\Omega\) is used in the transmitter circuit for circuit protection purposes. The frequency rate is 100 Hz and the transmission distance is 15 cm. The optical signal is accepted through a receiver LED with a reverse bias of 5 V and a load resistance of 1 M\(\Omega\). The electrical signal on the load resistance was measured by an oscilloscope (OSC). The rise time of the electrical signal is measured from 10% to 90% of the leading edge of the received signal. Table 2 shows the experimental results of the rise time and SNR according to the pairs of transmitter and receiver LEDs.