# Extended Spatial-Index LED Modulation for Optical MIMO-OFDM Wireless Communication
## 3 Simulation Results and Computational Complexity  
In the following, the ESI-LED efficiency is evaluated and compared with the FGIS [33] and the GLIM [31] performances. Here, we used the same simulation parameters used with the GLIM-OFDM systems [31; 33]. Moreover, as a fair comparison, the GLIM-OFDM system architecture is adapted to support the operation of the spatial modulation along with its conventional functions.  
The conventional GLIM-OFDM was first introduced in [31] to support simultaneous transmission of the complex time-domain OFDM signal (i.e., \(\pm\ c_{n_{R}}\pm\ jc_{n_{I}}\)) over the optical channel, whereas four LEDs were used (two LEDs for the real part \(\pm\ c_{n_{R}}\) and the other two for the imaginary part \(\pm\ jc_{n_{I}}\) ) to convey both the values and the signs information of the complex OFDM signal. However, this adds restrictions on the LED number of the GLIM-OFDM transmitter side (i.e., LED number must be equal \(2^{i},i=2,3,4,\ldots\)). Then, in [32], a new LED grouping technique was introduced to relax the GLIM LED number problem to be equal to \(i\geq 4\) and \(i\) is an even number.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Dimensions of the room & 5 m \(\times\) 5 m \(\times\) 3 m \\ \hline Number of Luminaries & 4 \\ \hline Number of LED Chips per Luminary & 9 \\ \hline Model of LED Chips & Cree Xlamp MC-E White \\ \hline Power of LED Chips & 5 W \\ \hline Luminary (L) Positions (x, y, z) (m) & L1: (\(-\)1.3, \(-\)0.7, 3) L2: (\(-\)1.3, 1.3, 3) L3: (0.7, 1.3, 3) L4: (0.7, \(-\)0.7, 3) \\ \hline  & Config A: PD1: (\(-\)0.05, \(-\)0.05, 0.8) \\  & PD2: (\(-\)0.05, 0.05, 0.8) PD3: (0.05, 0.05, 0.8) \\  & PD4: (0.05, \(-\)0.05, 0.8) \\ Photo detector (PD) positions (x, y, z) (m) & Config B: PD1: (\(-\)0.4, \(-\)0.4, 0.8) PD2: (\(-\)0.4, 0.4, 0.8) PD3: (0.4, 0.4, 0.8) \\  & PD4: (0.4, \(-\)0.4, 0.8) \\  & Config C: located at center of table with \\  & equidistant 0.1 m and rotated by 45\({}^{\circ}\) \\  & in xy-plane and titled by 60\({}^{\circ}\) \\ \hline View of angle of Luminary & 120\({}^{\circ}\) \\ \hline FOV of PD & 85\({}^{\circ}\) \\ \hline Area of PD & 1 cm\({}^{2}\) \\ \hline Materials & Walls \& Ceiling: Plaster Floor \& Desk: \\  & Pine Wood \\ \hline \hline \end{tabular}
\end{table}
Table 3: The physical VLC channel parameters [31].  
Figure 2: Configuration A (PD in the center of the table), B (PD at the corners of the table) and C (PD are aligned to their correspondent LED.  
Therefore, to make the GLIM-OFDM support the SM along with its normal functionality, the GLIM-OFDM structure/functionality is adapted (without major changes in its architecture) as follows.  
All possible LED indices on the TX side of the GLIM-OFDM (\(n_{t}\)) are split into distinct sets with each set involving four unparalleled combinations to include all four potential likelihoods for OFDM\({}_{td}\) signs information (i.e., \(\pm\)\(c_{n_{R}}\pm\)\(j_{cn_{t}}\)). Thus, a \(S=\lfloor log2(n_{t}/4)\rfloor\) extra bits (group selection) will be produced, and the new rate of the GLIM-OFDM in the above case can be given by  
\[R_{GLIM}=log_{2}(M)+\left\lfloor log2\Bigg{(}\frac{n_{t}}{4}\Bigg{)}\right\rfloor. \tag{22}\]