# Extended Spatial-Index LED Modulation for Optical MIMO-OFDM Wireless Communication
## 3 Simulation Results and Computational Complexity
### Average Bit Error Rate (ABER) Performance
Despite this, the results show that the proposed ESI captures almost the same ABER performances GLIM as shown in Figure 4.  
Note that the three \(3\times 3\) MIMO physical channels that are used with the proposed ESI are just \(3\times 3\) sub-matrices of three \(4\times 4\) physical channels A, B, and C given in [31; 33], and each \(3\times 3\) sub-matrix is chosen randomly from its corresponding \(4\times 4\) channel matrix. _Scenario 2:_ The same MIMO-LED configuration with different modulation orders to achieve the same SE. In this scenario, two different tests are conducted, where the first test MIMO-LED configuration of \(5\times 5\) is used with the proposed ESI, the GLIM, and the FGIS systems, to achieve SE of 4 and 6 bpcu. Likewise, the same three physical channels A, B, and C are used in this scenario as shown in Figure 5a-c, respectively. However, a modulation order of \(M=16\) and \(M=4\) is exploited with the GLIM and the FGIS system, respectively, to fulfill an SE of 4 bpcu, while the ESI needs no modulation to fulfill the same SE. The SD was only exploited in the proposed ESI to convey data. In other words, the space shift keying (SSK) modulation concept [40] is used, whereas a predefined fixed dummy signal \(\delta\) was transmitted on the active LED indices as a label to distinguish between the active and non-active LED indices. Therefore, a simple maximum likelihood estimator (MLE) is used with the proposed ESI in this scenario instead of the MAP (10). However, the MLE with the fixed dummy signal \(\delta\) is given by  
\[\bar{\ell}_{\delta}=\arg\min_{\ell_{\delta}}\left\|y-\delta\sum_{i=1}^{N_{\ell _{\delta}}}\mathbf{h}_{ii}\right\|^{2}, \tag{23}\]  
where \(\ell_{\delta}\) is the active LED indices and \(\mathbf{N}_{\ell_{\delta}}=1,\ldots,\lfloor\frac{n_{\ell}}{2}\rfloor\). Figure 4: Scenario 1: The ABER of the proposed ESI compared to GLIM [31] at the same modulation orders, but with different MIMO-LED configurations for three physical channels, A, B, and C.  
dB saving compared to the FGIS as shown in Figure 5a-c, respectively. To achieve an SE of 6 bpcu in the same test (i.e., with LED configuration of \(5\times 5\)), a modulation order of \(M=64\) and \(M=16\) are used with the GLIM and the FGIS, respectively, while a modulation order of \(M=4\) is used with the proposed ESI to fulfill the same SE (\(log_{2}(M)+4\)). However, the simulation results furtherly manifest the superiority of the proposed ESI compared to the GLIM and the FGIS systems as it provides about 4.5 dB average saving compared to the GLIM while it introduced 3.75 dB average saving compared to the FGIS as shown in Figure 5.  
In the second test in this scenario, \(8\times 8\) LEDs configuration is applied on the proposed ESI, the conventional GLIM system, and the FGIS system to achieve an SE of 7 bpcu. Therefore, a modulation order of \(M=64\) QAM is used with the GLIM to satisfy the 7 bpcu spectral efficiency (\(log_{2}(64)+1\) spatial bit). Furthermore, a modulation order of \(M=4\) QAM is used with the FGIS (\(log_{2}(4)+5\)), while the proposed ESI used no modulation information just the spatial bits (2) by applying the SSK concept [40]. Likewise, the same aforementioned MLE decoder (23) is used with the proposed ESI. Therefore, the proposed ESI introduces about 5.2 and 3.7 dB saving over the GLIM and the FGIS, respectively, for the three physical channels A, B, and C as shown in Figure 6a-c. The above-mentioned result exhibits the flexibility and the practicability of the ESI. Moreover, this scenario concludes that the ESI achieves significantly better ABER performance than GLIM and the FGIS systems. This is owing to the use of a lower modulation order and the SSK concept with MLE decoder (23) with the proposed ESI compared to all the considered schemes. Figure 6: \(Cont\).