# Experimental Demonstration of 3 \(\times\) 3 MIMO LED-to-LED Communication Using RGB Colors
## 2 Digital Signal Processing Model of the 3 \(\times\) 3 MIMO LED-to-LED System  
Orthogonal frequency division multiplexing (OFDM) modulation ensures strong resistance to inter-symbol interference (ISI) and high spectral efficiency by simultaneously transmitting data via orthogonally located subcarriers. Therefore, the OFDM modulation scheme is often employed in a wireless communication system to improve channel capacity. On the other hand, MIMO simultaneously transmits data via different propagation paths to achieve great spectral efficiency and high data rates. In [19], the performance comparison of spatial multiplexing (SMP), repetition coding (RC), and spatial modulation (SM) MIMO algorithms for indoor OWC was studied. When sufficiently low channel correlation and signal-to-noise ratio (SNR) are guaranteed, SMP achieved better BER performance and higher spectral efficiency compared to RC and SM. Thereby, MIMO together with OFDM modulation are widely used in wireless communication systems to maximize the spectral efficiency. The LED-to-LED communication system has a limited channel capacity and noise vulnerability due to the low responsivity of the receiver LED. To overcome such disadvantages, we apply the OFDM modulation together with the SMP MIMO algorithm to our 3 \(\times\) 3 LED-to-LED communication scheme. Since OFDM for RF communication cannot be applied to intensity modulation and direct detection (IM/DD)-based OWC systems, several optical OFDM techniques, such as direct current biased optical OFDM (DCO-OFDM), asymmetric clipped optical OFDM (ACO-OFDM), and asymmetrically clipped direct current biased OFDM (ADO-OFDM), were developed [20]. In our system, DCO-OFDM is applied since it is simple and has a high spectral efficiency compared to ACO-OFDM and ADO-OFDM. Figure 2 shows the block diagram of the 3 \(\times\) 3 MIMO LED-to-LED communication system using RGB LEDs. Information bitstreams for each red, green, and blue transmitter are converted from serial-to-parallel (S/P) and mapped onto the complex-valued symbols according to quadrature amplitude modulation (QAM). Generated QAM symbols are then extended to have Hermitian symmetry for real-valued OFDM signals. The resulting frequency-domain symbols for the \(q\)th transmitter, \(\mathbf{d}_{q}=\left[ \begin{array}{cc}d_{q,0}&d_{q,1}&\ldots&d_{q,N-1}\\ \end{array} \right]\), meet the following conditions:  
\[\left\{ \begin{array}{cc}d_{q,0}=d_{q,\frac{N}{N}-1}=0\\ d_{q,k}=d_{q,N-k}^{*}\\ \end{array} \right.,\;\;k=1,\ldots,\frac{N}{2}-1 \tag{1}\]  
Afterwards, frequency-domain symbols are transformed into the discrete \(n\)th time-domain OFDM signal, \(x_{q,n}\), by the inverse fast Fourier transform (IFFT) process:  
\[x_{q,n}=\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}d_{q,k}\exp\left(\frac{i2\pi nk}{N} \right)=\frac{1}{\sqrt{N}}\sum_{k=0}^{\frac{N}{2}-1}\biggl{\{}d_{q,k}\exp\left( \frac{i2\pi nk}{N}\right)+d_{q,k}^{*}\exp\left(-\frac{i2\pi nk}{N}\right) \biggr{\}} \tag{2}\]  
where \(N\) is the size of fast Fourier transform (FFT), \(j\) is the imaginary unit, and \((. )^{*}\) is the conjugate operator. After parallel-to-serial (P/S) conversion and zero padding (ZP) insertion, the resulting signals are fed into an arbitrary function generator (AFG) to drive  
Figure 2: Block diagram of the 3 \(\times\) 3 MIMO LED-to-LED communication system. each red, green, and blue LED with direct current (DC) bias. The optical power at the \(n\)th time can be provided as:  
\[P_{q,n}=\big{(}x_{q,n}+DC_{q}\big{)}\cdot C_{E/O_{\mathcal{A}}} \tag{3}\]  
where \(DC_{q}\) denotes DC bias at the \(q\)th transmitter, and \(C_{E/O_{\mathcal{A}}}\) is electrical current-to-optical power (E/O) conversion gain at the \(q\)th transmitter. Assuming transmitter LEDs are Lambertian radiators, the generalized luminous intensity can be expressed as:  
\[I\big{(}\phi_{q}\big{)}=\frac{m+1}{2\pi}cos^{m}\big{(}\phi_{q}\big{)} \tag{4}\]  
where \(m=-\frac{\ln 2}{\ln\big{(}\cos\phi_{q,1/2}\big{)}}\) is the order of Lambertian emission, and \(\phi_{q}\) is the \(q\)th LED's angle of irradiance.