# Precoded Generalized Spatial Modulation for Downlink MIMO Transmissions in Beyond 5G Networks
## 4 Numerical Results
### Link Level Simulations
When we focus on the curve's behavior for a \(10^{-4}\) BER considering a 8 bpcu/user scenario, the GSM MU-MIMO shows a gain of about 10 dB over the conventional MU-MIMO. Moving on to the 12 bpcu/user scenario and maintaining the BER at \(10^{-4}\), the GSM MU-MIMO presents a gain of about 5 dB over the conventional MU-MIMO. These results suggest that GSM MU-MIMO can be a potential alternative to increase the SE of the system when compared with the adoption of higher-level modulations in conventional MU-MIMO. Figure 4: BER performance of ADMM in a MU-MIMO scenario with \(N_{tx}=255\), \(N_{rx}=10\), \(N_{u}=15\), \(N_{s}=17\) and \(N_{a}=2\), 1024-QAM. A second set of simulations were performed in order to analyze the block error rate (BLER) performance versus the energy per symbol to noise power spectral density (\(E_{s}/N_{0}\)) in dB of the proposed GSM MU-MIMO system. These results are required for the system level evaluation in the next subsection. Both perfect channel estimation and imperfect channel estimation curves are presented. For the imperfect channel estimation results we adopted the same model as in [40]. Denoting the CSI available at the transmitter as \(\overline{\mathbf{H}}\) and the CSI error as \(\mathbf{H}_{error}\) we can express the channel matrix as \(\mathbf{H}=\overline{\mathbf{H}}+\mathbf{H}_{error}\). The entries of \(\overline{\mathbf{H}}\) and \(\mathbf{H}_{error}\) are drawn assuming complex Gaussian distributions of \(\mathcal{CN}\Big{(}0,\sigma_{h}^{2}\Big{)}\) and \(\mathcal{CN}\Big{(}0,\sigma_{h}^{2}\Big{)}\), with \(\sigma_{h}^{2}+\sigma_{herror}^{2}=1\). In the presented results we considered \(\sigma_{herror}=0.03\). In our simulations, a minimum of 25,000 blocks were transmitted for computing each BLER result. In Figures 6 and 7, we have \(N_{sc}=256\) subcarriers, \(N_{tx}=17\) antennas/user, \(N_{rx}=16\) antennas/user and \(N_{u}=15\) users. The number of active antennas are \(N_{a}=2\) and \(N_{a}=3\), respectively. The case \(N_{a}=3\) and 1024-QAM corresponds to a spectral efficiency of 39 bpcu/user. The peak bit rate per user achieved assuming 5G NR numerology 1 is 279.552 Mbps. This means that 1 bpcu/user is equivalent to bit rate of 7.168 Mbps. Doubling \(N_{sc}=256\) to \(N_{sc}=512\) doubles the spectral efficiency to 78 bpcu/user use which is equivalent to a bit rate of 14.336 Mbps. In both figures, the BLER of GSM MU-MIMO is presented versus (\(E_{s}/N_{0}\)) in dB, for five uniform M-QAM constellations namely, M \(\in\) {4,16,64,256,1024}. As expected, independently of \(N_{a}\), higher values of M require higher values of \(E_{s}/N_{0}\) (dB) to reach the reference \(\mathrm{BLER}=10^{-1}\). In Figure 6, 1024-QAM with perfect estimation requires an additional 24 dB of \(E_{s}/N_{0}\) compared to 4-QAM(QPSK). With imperfect channel estimation there is an additional 15 dB penalty to reach \(\mathrm{BLER}=10^{-1}\) in the detection of 1024-QAM (it has a higher sensitivity to channel estimation errors). In Figure 7, for \(N_{a}=3\), it is clear the higher sensitivity of 1024-QAM, as one can notice that with imperfect estimation there is the emergence of a BLER floor. The other modulations only reveal small or negligible degradation. Figure 5: BER performance of a precoder based on GSM MU-MIMO and a precoder based on conventional MU-MIMO.