# Extended Spatial-Index LED Modulation for Optical MIMO-OFDM Wireless Communication
## 3 Simulation Results and Computational Complexity
### Average Bit Error Rate (ABER) Performance  
In this subsection, the average bit error rate (ABER) of the proposed ESI is examined and compared with both the GLIM [31] and the FGIS [33]. Herein, the same simulation parameters and the same three physical channels that were used in [31; 33] are used, whereas the parameters (channel matrices) of the three physical channels were estimated based on the geometric configuration of LEDs and PD locations shown in Figure 2. Actually, in our simulations, we followed the same configuration setup given in [31; 32; 33]. Thus, the proposed ESI modulation scheme is tested and compared to the GLIM system [31; 32], under the same configuration setup (i.e., Figure 2) with the same three channels given in [31; 32], whereas the three channel models are estimated from this configuration setup and they are named physical channels A, B, and C. In general, the resultant three indoor VLC channels can be classified into three categories: first, the weakest correlation \(H_{A}^{P}\) that is far from being a diagonal  
Figure 3: The proposed ESI, the GLIM [31], and the FGIS [33] achievable data rates at very high \(SNR\). matrix; second, the modest correlation \(H_{B}^{P}\); third, \(H_{\mathcal{C}}^{P}\) that is considered to have the strongest diagonal structure (weak correlated channels) [31]. In other words, the configuration setup was chosen to cover many of the channel correlation cases (high, medium, and low correlation) as it was reported in [31], which was refracted on proposed ESI and the GLIM performances. The complete information about the aforementioned configuration setup is given in [31]. Although the distance between PDs seems to not be practical for some applications (i.e., \(d_{PDs}\) = 0.1 m), but with the state-of-the-art current and future micro/nano electronics LED/PD technologies [38; 39], the distance between PDs could be shrunk to be practical (with a little effect on the channel correction). However, two various scenarios with several MIMO-LED configuration are presumed. In the first scenario, the same order of modulation (\(M\)) is presumed to be utilized with the ESI, GLIM, and FGIS, whilst various MIMO-LED number (configuration) are utilized to fulfill the same SE. In the second scenario, the proposed ESI, GLIM, and FGIS are presumed to apply the same transmit MIMO-LED configuration, whilst various \(M\) are used to fulfill the same SE. _Scenario 1:_ The same modulation order with different MIMO-LED configuration. In this scenario, the proposed ESI and the GLIM systems are tested with their row version i.e., the ESI is tested with \(3\times 3\) LED configuration without any spatial data and the GLIM is tested with \(4\times 4\) LED configuration. In both systems, modulation orders of \(M=4\), \(M=8\), and \(M=16\) are used to fulfill a spectral efficiency of 2, 3, and 4 bpcu, respectively. Since it was reported in [33] that the \(3\times 3\) FGIS captured the same ABER performance of the \(4\times 4\) GLIM, the ABER performances of the proposed ESI and the GLIM are considered only in this scenario. Figure 4a-c show the ABER of the both ESI and the GLIM for the physical channels, A, B, and C [31; 33]. With each channel, 2, 3, and 4 bpcu, SEs are examined using the aforementioned MIMO-LED configurations. As it can be noticed from Figure 4, the SNR that needed to achieve the same ABER for the channels A, B, and C is varied, this owing to the correlation nature of the three channels, whereas channel A is the most correlated channel and channel B is the modest correlated one, while channel C is the most diagonal channel (less correlated). To achieve the aforementioned SEs, MIMO-LEDs of \(4\times 4\) are needed with the GLIM while only \(3\times 3\) are used with ESI.