# A Novel OFDM-Based Time Domain Quadrature GSM for Visible Light Communication System
## 5 Simulations
### BER Performance  
In this study, we compare the BER performance of the OFDM-based generalized MIMO schemes under different conditions, including the comparisons among the schemes with different target SEs and different modulation orders. In addition, the BER performance is evaluated when employing different detection algorithms. It is worth noting that the channel gain in a typical indoor VLC system always varies owing to the distinct distance  
Figure 4: SE performance comparison for \(N=2\).  
Figure 5: SE performance comparison for \(N=3\).  
and transmit/incidence angle for each LED/PD pair, leading to a significant difference in the received SNR.  
Figures 6 and 7 compare the BER performance of various TD-generalized MIMO schemes with the same SE. It should be noted that different QAM should be deployed in these schemes so as to achieve the same SE for fair comparison. As clearly shown in these two figures, the BER performances of TD-QGSM and TD-QGSMP are basically the same under the conditions of SE of 4 bits/s/Hz and 6 bits/s/Hz, and both of them are significantly better than TD-GSM and TD-GSMP. This fact indicates that the TD-QGSM and TD-QGSMP require less modulation order to transmit the same number of bits per unit time than TD-GSM and TD-GSMP, which not only reduces the wastage of spectral resources but also makes the system more resistant to interference, resulting in better BER performance.  
Figures 8 and 9 compare the BER performance of different OFDM-based generalized MIMO schemes under the same modulation order when \(N=2\) is employed. When \(M=64\), the BER performance of TD-QGSM is almost the same as that of FD-GSM and outperforms that of all other OFDM-based generalized MIMO schemes, while the BER performance of TD-QGSMP is similar to that of FD-GQSM. In addition, the BER advantage over TD-GSM and TD-GSMP becomes especially significant. In the case of \(M=256\), the TD-QGSM still shows the best BER performance. However, the advanta  
Figure 6: BER performance comparison for \(SE=4\,\mathrm{bits/s/Hz}\) and \(N=2\).  
Figure 7: BER performance comparison for \(SE=6\,\mathrm{bits/s/Hz}\) and \(N=2\).  
significant due to the fact that the signal stream has been divided into many groups prior to OFDM modulation, which results in reduced spacing between neighboring symbols and increases the probability of inter-symbol interference. In addition, as the modulation order increases, the constellation points will become denser and the Euclidean distance will decrease, resulting in poorer BER performance. Combined with the previous analysis of SE, compared with the other generalized MIMO schemes, TD-QGSM not only has higher SE but also has excellent BER performance. For TD-QGSMP, its BER performance is slightly inferior to that of FD-GSM and FD-GSMP but still demonstrates a great improvement over TD-GSM and TD-GSMP. Moreover, it also has a huge SE advantage.  
Figure 10 shows the BER performance comparison of the TD-generalized MIMO systems when the ML-MRC detection and the proposed IVC-based OMP detection are deployed, respectively, under the same modulation order (\(M=16\)). It can be seen that the BER performance of TD-QGSM and TD-QGSMP using the proposed IVC-based OMP detection method is significantly improved by about 62.5% as compared to the one using the ML-MRC method. As for TD-GSM, a much lower BER can also be achieved when using  
Figure 8: BER performance comparison for different generalized MIMO schemes in the case of \(M=64\).  
Figure 9: BER performance comparison for different generalized MIMO schemes in the case of \(M=256\).  
the IVC-based OMP, and the improvement is even greater than that of TD-QGSM and TD-QGSMP. In summary, the proposed IVC-based OMP algorithm can achieve computational complexity reduction as well as BER performance improvement, which is beneficial for the proposed QG-MIMO schemes.