# Optical Wireless Communications Using Signal Space Diversity with Spatial Modulation
## 1 Introduction
If transmitter diversity is provided in an open-loop for OWC links, transmit signals must be further designed. In RF transmission, open-loop transmitter diversity incorporated with SM can be achieved by exploiting a signal constellation dimension [15; 16], such as a complex interleaved orthogonal design, or by exploiting the time dimension in SM [15] with space-time shift keying modulation or space-time coding, etc. Particularly, the signal space diversity (SSD) scheme [16] provides a good option to be adapted for indoor OWC transmission. The SSD scheme uses the inherent orthogonal signal constellation to realize the in-phase and quadrature components of the interleaved constellation symbol pairs transmitted over independent wireless channels [17]. It is easy to incorporate with SM to improve the BER performance without an uplink or extra RF chain and has low signal processing complexity. The SSD scheme has been investigated in various RF wireless channels. The results indicate that the BER performance with the optimum signal constellation rotation angles in the SSD scheme depends on the wireless channel conditions [18; 19]. Unlike complex RF channel models, for the IM/DD-based indoor OWC system, optical signal intensities are transmitted rather than signal fields [4]. Thus, the SSD scheme must be adapted to achieve real-valued signal constellation transmission. The corresponding OWC channel gain characteristics should be re-evaluated for their transmitter diversity performance when the SSD scheme is incorporated with SM. Our previous experimental study has shown the capability of the adapted SSD scheme for achieving transmitter diversity in the \(2\times 1\) MISO OWC links [20]. In this paper, the BER expressions of the SSD scheme in such \(2\times 1\) MISO OWC links were further theoretically investigated for the first time. In Section 2, after introducing the \(2\times 1\) MISO OWC system configuration and the SM implementation, the principle of the SSD scheme incorporated with SM is described. The theoretical expressions of the SSD scheme are then proposed based on the distance of neighboring constellation symbols. In Section 3, the theoretical results from the BER expressions are compared with numerical simulation results to show that a high accuracy of BER expressions can be achieved for most scenarios. In addition, the SSD scheme is theoretically evaluated using different channel gain distributions together with different signal constellation rotation angles to show its capability of offering transmitter diversity under partial beam obstructions. The results showed that the SSD scheme can achieve a significantly improved BER by two orders of magnitude with a reasonably high channel-gain ratio and with a larger rotation angle. Finally, the conclusions are given in Section 4. Principle and Theoretical BER Expressions of the SSD Scheme Incorporated with SM in a 2 \(\times\) 1 MISO OWC System  
This section presents the principle of the SSD scheme incorporated with SM and shows the derivation of the theoretical BER expressions. The configuration of the proposed 2 \(\times\) 1 MISO OWC system and the implementation of SM are introduced in Section 2.1 as the background information, followed by the principle of the SSD scheme incorporated with SM proposed in Section 2.2. The theoretical expressions of this SSD scheme are further investigated in Section 2.3.