# Optical Wireless Communications Using Signal Space Diversity with Spatial Modulation
## 4 Conclusions  
This paper proposed a signal space diversity scheme that can be incorporated with spatial modulation to offer transmitter diversity in an IM/DD-based \(2\times 1\) MISO indoor optical wireless system. Two theoretical BER expressions of the SSD scheme were established by comparing \(d_{1}\) and \(d_{3}\). The BER expressions were then verified by detailed numerical simulations. The results showed that the theoretical BER expressions agree well with numerical results for most scenarios, except for the slightly lower-accuracy performance in the scenario of comparable distances of neighboring constellation symbols, i.e., comparable \(d_{1}\), \(d_{2}\), and \(d_{3}\) with the condition of low \(\frac{E_{k}}{\mathrm{h}_{0}}\). Using such theoretical BER expressions, the SSD scheme was theoretically investigated using different channel gain distributions together with different signal constellation rotation angles. For the first channel gain setting that emulates the scenario where one channel is not obstructed while the other one is occasionally and partially obstructed, the results showed that the optimum BER improvement ranged from \(10^{-2.9}\) to \(10^{-4.9}\), which is by two orders of magnitude. Such a BER improvement can be achieved with a larger signal constellation rotation angle and a reasonably high channel-gain ratio \(\frac{\mathrm{h}_{2}}{\mathrm{h}_{1}}\) (\(\mathrm{h}_{1}>\mathrm{h}_{2}\)), as long as the channel gain difference is met for SM. For the second channel gain setting that emulates the scenario where one channel is partially obstructed at one time slot while the other one compensates for such optical loss at the adjacent time slot, the optimum BER improvement ranged from \(10^{-1.26}\) to \(10^{-3.0}\), which is inferior to the first setting due to the constraint of constant (\(\mathrm{h}_{1}+\mathrm{h}_{2}\)). The results of different channel gain settings showed the capability of the SSD scheme to offer transmitter diversity under partial beam obstructions. Compared with other conventional transmitter diversity schemes, such as the space-time coding, the SSD scheme with SM incorporated could improve the BER performance with an increased data rate in the MISO-OWC system without an uplink or extra RF chain.  
Note that the best achievable BER performance improvement in the SSD scheme in this paper was limited by the required channel gain difference for the SM implementation, as mentioned in Section 3. In the future, the impact of channel gain difference can be further experimentally investigated when SM is incorporated with the SSD scheme in a practical indoor OWC environment. In addition, inspired by the SM concept, other dimension entities with less impact of channel gain difference, such as frequency/code/index domains, can also be explored for modulation to increase the data rate together with the SSD scheme, so that the advantages of the SSD scheme can be better exploited.  
Conceptualization and methodology, T.S., C.L., A.N. and K.W.; software and validation, T.S.; writing--original draft preparation as well as review and editing, T.S., C.L., A.N. and K.W.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Australian Research Council Discovery Project Grant, DP170100268.  
The authors declare no conflict of interest.