## 5 Simulation Results
### Performance Comparison of GBD, MGBD and Proposed Scheme  
The BER and normalized throughput performances of the GBD, MGBD and the proposed scheme are shown in Figures 6-8. When \(N_{T}=N_{R}=8\) and \(N_{T}=N_{R}=16\), the numbers of data streams from 6 to 8 and from 12 to 16 are considered, respectively. The cases with the number of the data streams which are less than the \(\frac{2}{3}\) of the number of receive antennas are inefficient since the loss of the data rate is serious compared to the transmit diversity gain. Therefore, the cases with the number of the data streams which are more than the \(\frac{2}{3}\) of the number of receive antennas are considered. Figure 5: Normalized throughput performance comparison between the RBD and the proposed scheme with \(N_{T}=N_{R}=8\). The BER performances of GBD, MGBD and the proposed scheme are shown in Figure 6 with \(N_{T}=N_{R}=8\) and Figure 7 with \(N_{T}=N_{R}=16\). The performance of each scheme with 16 QAM is better than the performance of each scheme with 64 QAM. When the number of data streams is same as the number of transmit antennas in Figures 5(a) and 6(a), MGBD and the proposed scheme cannot obtain the diversity gain. In addition, the precoder of the MGBD and the proposed scheme is same as the precoder of the RBD. Therefore, the BER performances with full data streams of the MGBD and the proposed scheme are exactly same in Figures 5(a) and 6(a). When the number of data streams is reduced,  
Figure 8: Normalized throughput performance of GBD, MGBD and proposed scheme. Figure 7: BER performance of GBD, MGBD and proposed scheme with \(N_{T}=N_{R}=16\). The normalized throughput performances of GBD, MGBD and the proposed scheme are shown in Figure 8 with \(N_{T}=N_{R}=8\) and \(N_{T}=N_{R}=16\). When the numbers of the transmit and receive antennas are 8 at Figure 8a,b, the throughput performances are normalized according to maximum data rate which is achieved with 8 data streams. When the numbers of the transmit and receive antennas are 16 at Figure 8c,d, the throughput performances are normalized according to maximum data rate which is achieved with 16 data streams. When GBD, MGBD and the proposed scheme utilize full data streams and 16 QAM, the maximum data rate with full data streams cannot be achieved due to insufficient BER performance. When the number of data streams is reduced and the 16 QAM is used, the data rate can be achieved due to the diversity gain. However, when the 64 QAM is used in Figure 8b,d, the data rate cannot be achieved regardless of the number of the data streams. Since the Modulation level is too high, the BER performances become low. Therefore, even though the number of data streams is reduced, the data rate is not achieved. The conventional schemes and the proposed scheme are inappropriate schemes to be used with high level modulation. When the number of data streams is same with the number of the transmit antennas, the proposed scheme and MGBD has same precoder with RBD. Therefore, the throughput performances of MGBD and the proposed scheme with full data streams are exactly same. When the number of data streams is 7 in Figure 8a and 14 in Figure 8c, the proposed scheme achieves the data rate which is accomplished with 7 data streams and 14 data streams by obtaining diversity gain. The MGBD also achieves the data rate which is accomplished with 7 and 14 data streams. However, MGBD needs more transmit power to achieve the data rate with 7 and 14 data streams. In the case with the smallest data streams in Figure 8a,c, all schemes achieve the data rate which is accomplished with the smallest data streams by getting more sufficient diversity gain. In Figures 6c and 7c, the MGBD with 6 and 12 data streams has better BER performance than the proposed scheme at the high transmit power. However, Figure 8a,c show that the throughput performances of MGBD and the proposed scheme at the high transmit power are same.