# Extended Spatial-Index LED Modulation for Optical MIMO-OFDM Wireless Communication
## 1 Introduction  
The last decade has witnessed a phenomenal growth in wireless communications data. According to [1], mobile data traffic is expected to grow to 30.6 exabytes per month by 2020 (an eight-fold increase over 2015). To fulfill the ever-growing demand for such wireless data and with the aggravating limitations of the radio frequency (RF) spectrum, communication experts are rethinking visible light communication (VLC) as it is considered one of the optimal solutions for the indoor communications. Moreover, VLC attracts considerable interest in view of the fifth-generation (5G) wireless communication requirements. With the state-of-art lighting light-emitting diode (LED) technology, VLC can also fulfill the low power requirement of the internet of things (IoT) PHY layer design [2]. Moreover, with the existing infrastructure in place for lighting in daily use and other distinct advantages such aslarge bandwidth (i.e., 30 GHz of open-license bandwidth), low cost, energy conservation, and secure communication [3; 4; 5], VLC is nominated as one of the most promising solutions for future wireless communication networks. Consequently, there is an exponential growth in the deployment of the new optoelectronic technologies that can be utilized to efficiently exploit the enormous potential bandwidth of the optical wireless communications (OWC). Thus, OWC is expected to be indispensable for wireless data transmission, especially in short-range low-mobility indoor environments [6]. In OWC, data are transferred by modulating the LED light intensity. Hence, intensity modulation and direct detection (IM/DD) have emerged as one of the promising candidates for OWC systems [7; 8]. In general, LED light intensity conveys information at the VLC systems' transmitter side (TX) while the photo detectors (PDs) or cameras [9; 10; 11] are used at the receiver side (RX) to detect the transmitted information. Considering the nature of visible light, the OWC modulated signal has to be a positive real value (unipolar) signal. This requirement adds further constraints on OWC. Therefore, modulation schemes such as on-off keying (OOK), pulse width modulation (PWM), pulse position modulation (PPM), and unipolar M-ary pulse-amplitude modulation (M-PAM) can be used in a relatively straightforward fashion with the OWC [4]. Unfortunately, owing to their spectral and power inefficiency, none of the aforementioned modulation schemes could efficiently exploit the OWC system's large bandwidth. Therefore, researchers have recently turned their attention to integrate the high spectral efficiency OFDM with OWC systems. Despite its advantages, the OFDM signal must be represented as intensity in the OWC systems, thus its signal must be in real and positive form, while the equivalent base-band of the OFDM signals is generally complex and bipolar. Hence, many adjustments and modifications must be applied on the OFDM to cope with the optical wireless communications' IM/DD requirements. In [12], the DC biased optical OFDM (DCO-OFDM) was introduced where the unipolar signal was realized by adding a positive DC biased to the OFDM time-domain output from the inverse fast Fourier transform (IFFT). While the VLC-OFDM bandwidth efficiency gained strength by adding positive DC bias, unfortunately its optical power efficiency (OPE) was reduced significantly [13; 14]. On the other hand, the asymmetrically clipped optical OFDM (ACO-OFDM) was presented in [15]. The ACO-OFDM enhanced the OPE of the optical wireless communication system at the expense of reducing its spectral efficiency (SE) and degradation of its bit error rate (BER), where its data rate was reduced to half of the conventional OFDM data rate. This dates back to the zero level clipping of the IFFT output signal and its output signals are restricted to be conveyed over the odd subcarrier only. The data error rate degradation problem of the ACO-OFDM has been handled in the unipolar-OFDM (U-OFDM) [14], where both positive and negative frames for the IFFT signal are individually transmitted.