# Experimental Demonstration of 3 \(\times\) 3 MIMO LED-to-LED Communication Using RGB Colors
## 3 MIMO LED-to-LED Communication Using RGB Colors  
All experiments conducted in this paper used off-the-shelf red, green, and blue LEDs. The diameter of the LED is 10 mm, and the emission angle is 30 degrees. Note that the emission angle was measured with respect to the LED's light emission center line, at which the radiant intensity falls to half of its maximum value. Figure 3 shows the wavelength spectrum of the (a) red, (b) green, and (c) blue LEDs. The peak wavelengths of red, green, and blue LEDs were measured at 629, 521, and 466 nm, respectively. Figure 4 shows the optical power and E/O conversion efficiency of the (a) red, (b) green, and (c) blue LEDs with respect to input current. Figure 5 illustrates the geometry of the MIMO LED-to-LED communication system. Transmitter LEDs were located 1.5 cm apart from each other. The distance between the transmitter plane and the receiver plane was set to 10 cm. All MIMO experiments were performed under the geometry condition shown in Figure 5.  
Figure 4: Optical power and E/O efficiency of the (a) red, (b) green, and (c) blue LEDs with respect to the input current. Figure 3: Emission spectra of the (a) red, (b) green, and (c) blue LEDs. The responsivity and frequency response of the optical receiver varies depending on the applied wavelength of the light. Therefore, we measured the channel DC gain and frequency response in all possible color combinations to observe the channel characteristics of the LED-to-LED system. Figure 6 shows the output current and E/E conversion efficiency at the red, green, and blue receivers with respect to the transmitter input current when the transmitter LED color is (a) red, (b) green, and (c) blue. The results show that the receiver LED cannot generate optical current when its wavelength is shorter than the transmitter wavelength. Thus, the MIMO LED-to-LED communication system forms a unique channel condition, as follows:  
\[\left[ \begin{array}{c}r_{r,n}\\ r_{g,n}\\ r_{b,n}\end{array} \right] = \left[ \begin{array}{ccc}h_{r,r}^{DC}&h_{r,g}^{DC}&h_{r,b}^{DC}\\ h_{g,r}^{DC}&h_{g,g}^{DC}&h_{g,b}^{DC}\\ h_{b,r}^{DC}&h_{b,g}^{DC}&h_{b,b}^{DC}\end{array} \right]\left[ \begin{array}[ ]{c}x_{r,n}\\ x_{g,n}\\ 0&h_{g,g}^{DC}&h_{g,b}^{DC}\\ 0&0&h_{b,b}^{DC}\end{array} \right]\left[ \begin{array}{c}x_{r,n}\\ x_{g,n}\\ x_{g,n}\\ x_{b,n}\end{array} \right] \tag{11}\]  
By solving Equation (11), the transmitted signal can be recovered ensuring sufficiently low channel correlation between each channel. ZF-based MIMO systems are known to cause noise amplification effects at receivers [22]. Therefore, different amounts of power were applied to red, green, and blue transmitter LEDs to ensure sufficient levels of SNR. The blue-to-blue channel had no channel interference from the green and red transmitter LEDs, which resulted in a minimum signal power allocation to the blue transmitter LED. Since the green-to-green channel was interfered by a blue transmission signal, a higher signal power than the blue signal was applied to the green transmitter LED. Finally, the red-to-red channel was interfered by green and blue signals. Thus, we allotted the highest power to the red transmitter LED. The rest of the experiments were carried out by applying 0.94 to 2.75 mA for the blue LED, 9.4 to 25 mA for the green LED, and 0.27 to 36.4 mA for the red LED. Under such current allocations onto each color of the LED, Figure 7 shows the frequency response results when the transmitter LED is (a) red, (b) green, and (c) blue. The red-to-red, green-to-green, and blue-to-blue channel 3 dB bandwidths were measured as 6, 3, and 3 kHz, respectively. Figure 5: The geometry of the 3 \(\times\) 3 MIMO LED-to-LED communication system. Figure 8 illustrates the experimental setup of a 3 \(\times\) 3 MIMO LED-to-LED communication system using RGB colors, where 160-bit pseudo-random binary sequence (PRBS) bit streams for each channel are mapped to a QAM symbol. The complex-valued QAM symbols were modified by adding a redundancy satisfying Hermitian symmetry, as shown in Equation (1).