# Precoded Generalized Spatial Modulation for Downlink MIMO Transmissions in Beyond 5G Networks
## 4 Numerical Results
### System Level Simulations
For 15 users and 100% of transmitted power, the average throughput of all constellations is 2031.0 Mbps (135.4 Mbps/user), which gives a throughput gain of 155%. Figure 10 presents the throughput averaged over all users uniformly distributed, for the C-RAN scenario where three RRUs (3C) transmit to each user. The parameters of the previous figures are kept the same, namely \(N_{tx}=17\) antennas/user, \(N_{rx}=16\) antennas/user, \(N_{sc}=256\), and we vary the number of users \(N_{u}\) from 1 up to 15, considering 100% of transmitted carrier power. We consider that the channel estimation is perfect. We can confirm that the BD MU precoding used at the RRUs and the ADMM receivers are operating as expected because every throughput curve is a straight line with slope dependent of the constellation but independent of \(N_{u}\). The increase in throughput depends on the spectral efficiency. We present two set of results. For \(N_{a}=2\), the minimum is 11 bpcu (4-QAM) and the maximum is 27 bpcu (1024-QAM). The second set of performance curves have \(N_{a}=3\), starting from 15 bpcu (4-QAM) up to a maximum of 39 bpcu (1024-QAM). We observe the same throughput results for 15 bpcu with 16-QAM and \(N_{a}=2\) or 4-QAM with \(N_{a}=3\). The throughput results are almost the same between the average of all constellations with \(N_{a}=2\) (19 bpcu) or \(N_{a}=3\) (27 bpcu) and the 64-QAM constellation having the same spectral efficiencies. This can be explained because the average coverage of all constellations is only slightly lower than the coverage of 64-QAM. The ratio of  
Figure 9: Average throughput vs percentage of transmitted power for \(N_{a}=2\), \(N_{sc}=256\), \(N_{u}=15\), \(N_{tx}=17\) antennas/user and \(N_{rx}=16\) antennas/user. throughput results for the average of all constellations with \(N_{a}=3\) (27 bpcu) compared to those of \(N_{a}=2\) (19 bpcu) is 2875.8/2031.0 = 1.42, the same as the expected ratio (27 bpcu/19 bpcu) = 1.42. Figure 11 considers the same parameters of Figure 10 but the channel estimation is imperfect instead of perfect. Some performance degradation due to imperfect channel estimation can be observed. The throughput results are not anymore the same between the average of all constellations with \(N_{a}=2\) (19 bpcu) or \(N_{a}=3\) (27 bpcu) and the 64-QAM constellation having the same spectral efficiencies. Indeed, the simulation results indicate that the throughput of the average of all constellations is lower than the 16-QAM constellation results with \(N_{a}=2\) (15 bpcu) or \(N_{a}=3\) (21 bpcu). For both numbers of active antennas, the throughput results for 1024-QAM become the lowest instead of the highest and for \(N_{a}=3\), the throughput is zero (does not attain a BLER of \(10^{-1}\) as observed previously). There is an obvious decrease in the simulated throughput results compared to the expected results based on the constellation bpcu. The ratio of throughput results for the average of all constellations with \(N_{a}=3\) (27 bpcu) compared to those of \(N_{a}=2\) (19 bpcu) is 2062.5/1546.5 = 1.33, lower than the expected ratio (27 bpcu/19 bpcu) = 1.42. The comparison between Figures 10 and 11 indicates that the throughput reduction due to imperfect channel estimation for \(N_{a}=2\) is (1-1546.5/2031.0) = 0.24 and for \(N_{a}=3\) is (1-2062.5/2875.8) = 0.28. Therefore, the throughput reduction due to imperfect estimation increases with the number of GSM active antennas which was expected based on the BLER results of Figures 6 and 7. Figure 12 presents the cumulative distribution function (CDF) of a RRU with three TRPs, each TRP with \(N_{tx}=255\) active antennas serving 60 users each with \(N_{rx}=16\) antennas. The CDF of this figure corresponds to the case of 100% of carrier transmission power. We consider only the C-RAN scenario with clusters of three RRUs (3C), with curves for both perfect channel estimation and imperfect channel estimation cases.