# Precoded Generalized Spatial Modulation for Downlink MIMO Transmissions in Beyond 5G Networks
## 4 Numerical Results
### System Level Simulations  
Using the BLER results described previously, several system level simulations were performed. The signal-to-noise ratio in dB used in the system level simulations is obtained using  
Figure 6: Block error rate (BLER) vs. \(E_{s}/N_{0}\) for \(N_{a}=2\), \(N_{sc}=256\), \(N_{u}=15\), \(N_{tx}=17\) antennas/user, and \(N_{rx}=16\) antennas/user. Figure 7: Perfect and imperfect estimation of BLER vs. \(E_{s}/N_{0}\) for \(N_{a}=3\), \(N_{sc}=256\), \(N_{u}=15\), \(N_{tx}=17\) antennas/user, and \(N_{rx}=16\) antennas/user. \(10\log(R_{s}/B)\) dB, where \(R_{s}\) is the total transmitted symbol rate per antenna and user, \(B\) is the total bandwidth (we considered 20 MHz), and \(E_{s}/N_{0}\) is the ratio of symbol energy to noise spectral density in dB. Values of \(E_{s}/N_{0}\) are obtained from the link level BLER results. In Figure 8, we have chosen \(N_{a}=2\) with perfect estimation, and computed the SNR values corresponding to the BLER \(=10^{-1}\) so as to obtain the coverage results vs. the percentage of transmitted carrier power. Based on the parameters \(N_{u}=15\), \(N_{tx}=17\) transmit antennas/user and \(N_{rx}=16\) receive antennas/user there are a total of 255 active antennas at each TRP. The coverage of each of the five different M-QAM constellations and the arithmetic average of the coverage of all constellations (labelled as AllQAM) is presented for two different clusterings. In the present cellular topology, RRUs correspond to base stations, and each user is served by one RRU while the other RRUs generate inter-interference when transmitting towards their users. The label 1C means that the cluster contains one RRU. According to BLER performance results of Figure 6, it is expected that the 1024-QAM constellation has the minimum coverage due to more demanding signal-to-noise ratio, while 4-QAM has the maximum coverage for 100% of the transmitted carrier power. Only users close to RRUs are able to decode correctly 1024-QAM symbols, whereas 4-QAM symbols are decoded everywhere. We can check in Figure 8 that only for 100% of transmitted carrier power, the average coverage of all constellations reaches 71.5% of the area. The remaining coverage curves correspond to clustering where the network is partitioned into three adjacent RRU sets and each user is served by three RRUs (labelled as 3C). It is clear that there is an improved coverage obtained for all constellations, which is due to a much lower inter-interference between RRUs. Now, the average coverage of all constellations for 100% of carrier power is 99.6%, which corresponds to a coverage gain of 139%. In Figure 9, the average throughput results corresponding to the coverage results of the previous figure are presented. Considering the impact of clustering in which only one RRU (1C) is transmitting, the constellation with the lowest throughput is 1024-QAM and the highest result is achieved for 64-QAM. The latter presents a better tradeoff of coverage and spectral efficiency when compared to  
Figure 8: Coverage 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. the use of 16-QAM and 4-QAM constellations. For 15 users and 100% of transmitted carrier power, the average throughput obtained with all constellations is 1306.5 Mbps (87.1 Mbps/user). For the clustering where three RRUs (3C) transmit to each user, the constellation with the highest throughput is 1024-QAM, followed by 256-QAM, 64-QAM, 16-QAM, and 4-QAM. There is a match between the spectral efficiency (bpcu) of each constellation and the corresponding average throughput achieved at C-RAN system level. In fact, the same type of match is also observed for the curve of all constellations with spectral efficiency of 19 bpcu and the average throughput achieved at RAN. Notice that the spectral efficiency of 19 bpcu corresponds to a 64-QAM constellation and is equal to the average spectral efficiency of all constellations.