# Extended Spatial-Index LED Modulation for Optical MIMO-OFDM Wireless Communication
## 1 Introduction
However, SE of the U-OFDM is still low (i.e., half of the conventional OFDM data rate). Since multiple LEDs are basically installed in a single room to provide sufficient illumination, the MIMO-VLC system was introduced in [16; 17; 18]. The parallel utilization of multiple LEDs and PDs offers high data rates [19]. The utilization of different optical sources and receivers gives different spatially discrete optical wireless channels, and those various channels improve the system capacity and data rates. Spatial multiplexing approaches were highlighted as a potential solution to enhance the channel capacity shortage of indoor OWC systems. Thus, different LEDs were utilized to transmit independent data streams over a short distance in [20]. Moreover, a multiplexing MIMO-LED system was considered in [21], where a zero-forcing (ZF) equalizer was used at its RX to mitigate the effect of channel interference. However, two assumptions were presumed in [21]. Firstly, the type of connection between the transmitters and receivers was assumed to be a direct line of sight (LOS). Secondly, the cross-talk is limited between the various sources since they assumed the spacing between sources up to 3 m. Moreover, a 4-channel MIMO system was depicted in [22], where the white light LEDs were utilized for data conveyance over a short distance in a diffuse environment. When the MIMO-OFDM system with four LEDs (channels) was demonstrated in [23], a data rate of 1 Gbit/s was achieved with an average bit error rate (ABER) of \(10^{-3}\) over a distance of 1 m. In [24], the SE of the OWC system was enhanced by exploring different wavelengths in the visible light band. Recently, spatial modulation (SM) [25; 26; 27; 28] techniques were integrated with the optical MIMO-OFDM to improve the VLC system spectral and power efficiency [29; 30; 31; 32; 33], where the indices of transmit LEDs (spatial LEDs positions) were exploited to convey additional bits or to handle the complex OFDM time-domain shaping problem. For example, the need for a DC bias was eliminated in [30] by using \(2\times 2\) MIMO-LED SM. The OPE of the aforesaid system was significantly improved at the same SE, where the positive and negative OFDM time-domain signals transmitted at the same time over different LED indices. In [31], a four MIMO-LEDs were split into two different transmit groups to separately convey the real and the imaginary parts of the complex OFDM signal, and the scheme was teamed as MIMO-OFDM generalized LED index modulation (GLIM-OFDM). Based on each OFDM component sign information in the GLIM-OFDM, only one LED was activated in each group to convey the absolute value of that component over the VLC channel. In other words, two out of four LED indices would be inactive while the other two LEDs were exploited to convey the data. The GLIM-OFDM achieved a significant improvement in OPE and SE when it was compared to other optical OFDM systems [31]. Even so, there is a strict restriction on the number of LEDs at the GLIM TX. As it was reported in [32; 33], the GLIM LED number must be \(2^{m}\) where \(m\) is any integer \(\geq\)2. Therefore, in [32], a LED grouping scheme was proposed to handle the GLIM-OFDM aforesaid restriction, where the LED number became any even number \(\geq 4\). Nevertheless, both [31; 32] still have a constraint on TX LED number (\(n_{t}\)) without giving a clear link between their data rates (\(R\)) and \(n_{t}\). As far as we know, there were no systematic studies considering the aforesaid constraints in literature until the authors introduced the fully generalized index-spatial (FGIS) LED modulation in [33]. The FGIS relaxed the aforementioned LEDs number constraint and improved the optical communication system SE by providing an extra spatial domain (SD). Unfortunately, the complex OFDM signal signs barrier in FGIS minimized the effectiveness of the extra SD in improving the system SE. Moreover, it restricted the LED number to be greater than 3.