# A Full-Duplex LED-to-LED Visible Light Communication System
## 4 Full-Duplex LED-to-LED VLC
The experimental conditions are summarized in Table 4.  
Figure 4a shows the interference path and signal path in the experimental setup, while Figure 4b shows the bit error rate (BER) results of the half-duplex and the full-duplex LED-to-LED VLC. The received 32-QAM constellations are also shown in Figure 4b. At data rates of 4.9, 12.25, and 24.5 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Dimension** \\ \hline Modulation & DCO-OFDM & - \\ Tx offset & 2.9 & V \\ Tx amplitude & 0.3 & V \\ FFT size & 100 & - \\ QAM level & 32 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental conditions in the full-duplex LED-to-LED VLC experiment. Figure 3: **(a)** Block diagram, **(b)** picture, and **(c)** detailed block diagram of the experimental setup for the full-duplex LED-to-LED VLC. Note that P/S and S/P stands for parallel-to-serial and serial-to-parallel, respectively. kbps, the BER results are under \(10^{-5}\) for both the half- and full-duplex systems. When the data rate is 49 kbps, the BERs of the half- and full-duplex systems are \(6.25\times 10^{-5}\) and \(2.5\times 10^{-4}\), respectively. When the data rate is 122.5 kbps, the BERs of the half- and full-duplex systems are 0.1604 and 0.1621, respectively. Note that the reason why we only considered a few bit rates (i.e., 4.9, 12.25, 24.5, 49, and 122.5 kbps) in the experiment is that those bit rates showed the optimum sample rates in the experimental equipment. These experimental results show that both half- and full-duplex LED-to-LED VLC systems with a data rate of 49 kbps can be implemented, assuming the maximum allowable BER threshold is \(10^{-3}\). Additionally, our system shows a channel capacity value similar to that of Shannon's channel capacity. The results also show that the performance of the half-duplex case is slightly better than the full-duplex case. We think that the reason for the performance difference is that the light emitted from the Tx2 LED is reflected at the surface of the Tx1 and Rx1 LED, then the Rx2 receives the reflected signal, as shown in Figure 4a. Based on this, we analyzed the interference effect mathematically. The luminous intensity of a transmitter LED at an irradiance angle of \((\theta,\ \varnothing)\) is given by:  
\[I(\theta,\ \varnothing)=I(0,0)\cos^{m}(\theta,\ \varnothing) \tag{10}\]  
where \(I(0,0)\) is the center luminous intensity of the LED and \(m\) is the Lambertian radiation pattern [18]. Analytic expression for the SNR of the half-duplex system is derived as:  
\[SNR_{H}=\frac{R_{p}\Big{(}1-R_{f}\Big{)}\int_{0}^{2\pi}\int_{0}^{\tan^{-1}{( \frac{\beta}{2})}}I(\theta,\ \varnothing)d\theta d\varnothing}{P_{n}} \tag{11}\]  
Figure 4: (a) Interference path (noise path 1 and noise path 2) and signal path in the experimental setup. (b) BER results and received constellations of the half-duplex and full-duplex LED-to-LED VLC systems. where \(R_{p}\) is the responsivity of the receiver LED, \(d\) is the transmit distance, \(r\) is the radius of the LED, \(R_{f}\) is the reflectance of the fused silica (pure glass) at a wavelength of 589 nm, and \(P_{n}\) is the measured average ambient noise power in the receiver LED. The analytic expression for the SNR of the full-duplex system is derived as:  
\[SNR_{F}=\frac{R_{p}\Big{(}1-R_{f}\Big{)}\int_{0}^{2\pi}\int_{0}^{ \tan^{-1}\left(\frac{r}{2}\right)}I(\theta,\ \varnothing)d\theta d\varnothing\Big{(}1+2R_{f}\sin\!\left(2\tan^{-1}\frac{d_{ tr}}{d}\right)\cos\!\left(\cos^{-1}\frac{d_{tr}}{d}\right)\Big{)}}{P_{n}+2R_{p}R _{f}\Big{(}1-R_{f}\Big{)}\int_{0}^{2\pi}\int_{0}^{\tan^{-1}\left(\frac{r}{2} \right)}I(\theta,\ \varnothing)d\theta d\varnothing\cos^{2}\!\left(\cos^{-1}\frac{d_{ tr}}{d}\right)} \tag{12}\]  
where \(d_{tr}\) is the distance between Rx 1 and Tx 1 LEDs and for Rx 2 and Tx2 LEDs. The values for each parameter are listed in Table 5. As shown in Figure 5, the analytic results and experimental results give similar curves.