# Indoor MIMO-VLC Using Angle Diversity Transmitters
## 4 Simulation Results
Figure 6 shows the average achievable rate versus the number of LEDs in each transmitter for different types of transmitters, where the transmitted SNR is 150 dB. As we can see, the average achievable rates are all gradually increased when there are more LEDs in each transmitter for all types of transmitters, which suggests the advantage to design the transmitter with more LEDs under the conditions of increased complexity and cost. Particularly, the improvement of average achievable rate is much more significant for the optimized ADT in comparison to the conventional NADT when increasing the number of LEDs in each transmitter. For example, the average achievable rate using NADT with  
Figure 5: Contour plot of the average achievable rate (bit/s/Hz) vs. inclination angle \(\theta\) and ADT spacing \(2d\) for **(a)**\(N=4\), **(b)**\(N=5\), **(c)**\(N=6\) and **(d)**\(N=7\). \(2d=2.5\) m, and \(\theta=0^{\circ}\) is improved from 6.2 to 7.1 bits/s/Hz when the number of LEDs in each transmitter is increased from \(N=4\) to 7, which corresponds to an average achievable rate improvement of about 14.5%. In contrast, a significant 49.5% average achievable rate improvement can be achieved by using the optimized ADT, when the number of LEDs in each transmitter is increased from \(N=4\) to 7. Moreover, for the same number of LEDs in each transmitter, the 4 \(\times\) 4 MIMO-VLC system using ADT can generally obtain a higher average achievable rate than that using conventional NADT, while the 4 \(\times\) 4 MIMO-VLC system using optimized ADT can always achieve the highest average achievable rate. More specifically, for the case that each transmitter consists of \(N=\) five LEDs, the average achievable rates using NADT with \(2d=2.5\) m and \(\theta=0^{\circ}\), non-optimized ADT with \(2d=2.5\) m and \(\theta=9^{\circ}\) and optimized ADT are 6.6, 8.4 and 12.0 bits/s/Hz, respectively. Hence, an average achievable rate improvement of 27.3% is obtained by the non-optimized ADT with \(2d=2.5\) m and \(\theta=9^{\circ}\) in comparison to NADT with \(2d=2.5\) m and \(\theta=0^{\circ}\), while the optimized ADT outperforms the NADT with \(2d=2.5\) m and \(\theta=0^{\circ}\) by an average achievable rate improvement of up to 42.9%. We further investigate the impact of transmitted SNR and the PD spacing on the average achievable rate of the 4 \(\times\) 4 MIMO-VLC system using different types of transmitters. Figure 7a-d shows the average achievable rate versus the transmitted SNR using different types of transmitters for \(N=4\), 5, 6 and 7, respectively. It can be clearly observed that the average achievable rates are all gradually increased with the increase of the transmitted SNR for all types of transmitters. Moreover, to reach the same average achievable rate, the 4 \(\times\) 4 MIMO-VLC system using optimized ADT always requires the smallest transmitted SNR in comparison to other benchmark schemes. For example, for the case of \(N=5\), the required transmitted SNRs to reach an average achievable rate of 8 bits/s/Hz for NADT with \(2d=2.5\) m and \(\theta=0^{\circ}\), non-optimized ADT with \(2d=2.5\) m and \(\theta=9^{\circ}\) and optimized ADT are about 155, 149 and 144 dB, respectively. Hence, transmitted SNR reductions of 11 and 5 dB are obtained by using optimized ADT in comparison to that using NADT with \(2d=2.5\) m and \(\theta=0^{\circ}\) and non-optimized ADT with \(2d=2.5\) m, respectively. Figure 8a-d shows the average achievable rate versus the PD spacing using different types of transmitters for \(N=4\), 5, 6 and 7, respectively. Similarly, we found that the average achievable rates are all gradually increased with the increase of the PD spacing for all types of transmitters, and the 4 \(\times\) 4 MIMO-VLC system using optimized ADT always requires the smallest transmitted SNR to reach the same average achievable rate in comparison to other benchmark schemes. Figure 6: Average achievable rate vs. the number of LEDs in each transmitter.