# Indoor MIMO-VLC Using Angle Diversity Transmitters
## 4 Simulation Results  
In this section, we evaluate the average achievable rate of a typical indoor 4 \(\times\) 4 (\(N_{r}\) = \(N_{t}\) = 4) MIMO-VLC system applying the designed ADTs. As depicted in Figures 1 and 3, the room is assumed to have a dimension of 4 \(\times\) 4 \(\times\) 3 m, and the square ADT array is centered at the ceiling of the room. The height of the receiving plane is 0.85 m, and a total of \(K\) = 40,000 uniformly distributed receiver locations are considered to calculate the average achievable rate using (18). Moreover, the center LED of each ADT is assumed to have a large semi-angle at half power of 70\({}^{\circ}\) to guarantee the full coverage of the receiving plane, while the semi-angle at half power of all the side LEDs is set to 30\({}^{\circ}\). The key simulation parameters can be found in Table 1.  
First, we evaluate the average achievable rate with respect to the inclination angle \(\theta\) and the ADT spacing \(2d\) for the ADTs each consisting of \(N\) LEDs. By setting \(\theta\in[0^{\circ},60^{\circ}]\) with a step of 3\({}^{\circ}\) and \(2d\in[0.5\) m, 4 m] with a step of 0.5 m, we aim to obtain an optimal combination of \(\theta\) and \(2d\) that can maximize the average achievable rate of the 4 \(\times\) 4 MIMO-VLC system for a given \(N\) value. Figure 5a-d show the contours of the average achievable rate versus the inclination angle \(\theta\) and the ADT spacing \(2d\) with a transmitted SNR of 150 dB for \(N\) = 4, 5, 6 and 7, respectively. As we can see, the optimal combination of \(\theta\) and \(2d\) to achieve the maximum average achievable rate for each case is highlighted in the white star in Figure 5.  
For the case of \(N\) = 4, the maximum average achievable rate of about 10.1 bit/s/Hz is obtained with an optimal inclination angle of \(\theta\) = 21\({}^{\circ}\) and an optimal ADT spacing of \(2d\) = 1.5 m. Similarly, for the case of \(N\) = 5, the maximum average achievable rate of about 12.0 bit/s/Hz is achieved with the same optimal combination of \(\theta\) = 21\({}^{\circ}\) and \(2d\) = 1.5 m. However, for the case of \(N\) = 6, the optimal combination of \(\theta\) and \(2d\) is given by \(\theta\) = 18\({}^{\circ}\) \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Room dimension & 4 m \(\times\) 4 m \(\times\) 3 m \\ Height of receiving plane & 0.85 m \\ PD spacing & 10 cm \\ Semi-angle at half power of center LED & 70\({}^{\circ}\) \\ Semi-angle at half power of side LED & 30\({}^{\circ}\) \\ Half-angle FOV photodetector & 70\({}^{\circ}\) \\ Gain of optical filter & 1 \\ Refractive index of optical lens & 1.5 \\ Responsivity of the PD & 1 A/W \\ Radius of LED & 0.5 cm \\ Gap between center and side LED & 5 cm \\ Active area of PD & 1 cm\({}^{2}\) \\ Signal bandwidth & 10 MHz \\ Noise PSD & 10\({}^{-22}\)A\({}^{2}\)/Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. and \(2d=1.0\) m, and the corresponding maximum average achievable rate is increased to 13.4 bits/s/Hz. Moreover, for the case of \(N=7\), the maximum average achievable rate is about 15.2 bits/s/Hz, which is achieved with an optimal inclination angle of \(\theta=24^{\circ}\) and an optimal ADT spacing of \(2d=1.5\) m. It can be concluded from Figure 5 that it is feasible and beneficial to optimize both the inclination angle \(\theta\) and the ADT spacing \(2d\) to maximize the average achievable rate of the 4 \(\times\) 4 MIMO-VLC system applying ADTs. Moreover, the maximum average achievable rate of the system is gradually increased with an increased number of LEDs in each ADT. Next, we compare the average achievable rate of the 4 \(\times\) 4 MIMO-VLC system using different types of transmitters, including (1) conventional non-angle diversity transmitter (NADT) with \(2d=2.5\) m/3 m and \(\theta=0^{\circ}\), (2) non-optimized ADT with \(2d=2.5\) m/3 m and \(\theta=9^{\circ}/33^{\circ}\) and (3) optimized ADT with the optimal combination of \(\theta\) and \(2d\).