## 4 Results and Discussion
### Simulation Results
#### 4.2.2 Performance of Simplified Beamforming  
The following examines the proposed beamforming scheme in Case 3. Figure 5 shows the cumulative distribution functions (CDFs) of SINR per stream in a CSI estimation period. Case 2 exhibits high stable SINR distribution compared to Case 1 as its 2 nd, 3 rd and 4 th eigenmodes cause relatively low SINR. The proposed scheme of Case 3 can match the SINR performance of Case 2. Though the proposed scheme is based on the simplified approximate approach of 1 st eigenmode transmission, its degradation at CDF = 50% is only about 3 dB. It is still superior to Case 1 and achieves large SINR, more than 25 dB with 90% probability, where maximum MCS is available. Therefore, the 3 dB SINR degradation of the proposed scheme is negligible in terms of throughput, as shown in Figure 6. Throughput performance of multistream transmission (Case 1) is largely degraded due to the instability of the higher eigenmodes. Figure 4: Time variant characteristics within the CSI estimation period. Case 1: \(Nu=4\), \(Ns=4\); Case 2: \(Nu=16\), \(Ns=1\). (**a**) Average SINR per stream versus elapsed time. (**b**) Average throughput per stream versus elapsed time. Figure 5: Cumulative distribution functions (CDFs) of SINR per signal stream. Figure 7 shows the CDFs of UE throughput. Case 1, with multistream transmission, outperforms the other single stream transmission schemes. Though it potentially deserves to provide a higher transmission rate per UE, it sacrifices system throughput and is strongly impacted by the channel time variation. Figure 8 shows the CDFs of system throughput performance. As shown, Cases 2 and 3 provide quite large system throughput compared to Case 1. Under the constraint of total transmission stream number, multiplexing a large number of UEs to use a single stable stream is effective from the system throughput viewpoint. Figure 6: CDFs of throughput per signal stream. Figure 7: CDFs of UE throughput. Figure 9 plots the average system throughput versus UE speed, \(v\). With Case 1, system throughput is decreased as movement speed increases and is reduced by 46.9% at 60 km/h. The reductions observed in Cases 2 and 3 are 6.8% and 10.4%, respectively. The gap between them is only 3.6%. Multiuser MIMO with 1 st eigenmode transmission as well as our proposal can handle such high mobility situations, the movement speed is expected to be around 10 km/h considering the small cell use cases. It should be noted that extending the CSI feedback period \(M\) times corresponds to increasing the UE speed \(M\) times. Therefore, this evaluation is useful in understanding the impact of long CSI feedback periods from the viewpoint of control overhead savings. Finally, average system throughput in terms of multiplexed UE number, \(Nu\), is evaluated and the result is shown in Figure 10. Case 1 achieves its peak system throughput at \(Nu=16\). In addition, Case 1 provides higher system throughput than Cases 2 and 3 at \(Nu<12\). This is because the total number of signal streams for Case 1 is four times those of Cases 2 and 3 under the same spatially multiplexed UE number. However, it devours the DoF resources and results in inefficient UE throughput. The system throughput finally decreases as \(Nu\) increases further. Meanwhile, the system throughput of Cases 2 and 3 linearly increases with \(Nu\) in the plotted region and they outperform Case 1 when \(Nu>14\). There remain enough DoF resources with single stream transmission per UE and all UEs exploit the 1 st eigenmode, which provides the highest gain. Since UEs are spatially de-correlated, 1 st eigenmodes can keep their high gain and thus higher spectral efficiency is achieved even in large number of \(Nu\). Above results prove that exploiting the 1 st eigenmode can realize stable multiuser MIMO transmission in time varying channels. System throughput can be significantly enhanced by spatially multiplexing a large number of UEs.