# A Scheduling Scheme for Improving the Performance and Security of MU-MIMO Systems
## 5 Numerical Results and Discussions
### Outage Probability  
The OP is defined as the probability that the instantaneous SNR of each user is below a given threshold \(T\). Thus, Figure 3 shows the OP as a function of \(E_{b}/N_{0}\), parameterized by \(U_{t}\), and by \(e\) considering \(K=1\), \(U=4\), \(A=4\) antennas, binary phase shift keying (BPSK) modulation (\(M=2\)) and a threshold \(T=0\) dB. In the figure, it can be observed that as \(E_{b}/N_{0}\) increases, the OP decreases. Moreover, when \(U_{t}\) increases, the system performance improves, since there are more users competing to transmit and, therefore, the proposed scheduling scheme can find a better combination of UTs that maximizes the SNR, which translates into a lower OP. For a given value of \(U_{t}\), notice that when \(e\) increases, the OP also increases. This is because the error in the channel estimation increases. However, for a given value of \(e\), the system performance improves when \(U_{t}\) increases. For instance, for \(e=0.05\) and \(E_{b}/N_{0}=15\) dB, the OP with \(U_{t}=5\) is equal to \(2.05\times 10^{-3}\), and with \(U_{t}=7\), it decreases to \(1.98\times 10^{-6}\). For \(e=0.5\), \(E_{b}/N_{0}=20\) dB and \(U_{t}=5\), the OP is equal to \(4.8\times 10^{-3}\), and when \(U_{t}=7\) the OP is reduced to \(9.3\times 10^{-4}\). However, the performance improvement is greater for small values of \(e\), since there is a better channel estimation and the diversity that the proposed scheduling scheme guarantees can be better employed for the MIMO system. Specifically, high values of \(e\) may cause some users to not be properly selected by the algorithm, which has a direct impact on the performance gain. Even so, it is observed in the results that when \(U_{t}\) increases from 5 to 7, the OP is reduced even for high values of \(e\). This shows that the proposed scheduling scheme, in addition to improving the ZF detector performance, also reduces the undesirable effects of imperfect channel estimation in exchange for a slight increase in computational complexity.  
Figure 4 shows the OP as a function of \(U_{t}\), parameterized by \(K\) and \(T\) considering \(U=2\), BPSK modulation, \(A=2\), \(E_{b}/N_{0}=15\) dB, and \(e=0.1\). The results show that as \(U_{t}\) increases, the OP decreases. Thus, it is evident that the proposed scheduling scheme improves the MU-MIMO system performance even though it is fully loaded, that is, when \(A=U\). On the other hand, observe that the system performance improves when \(K\) increases. This is because the power of the LOS component between the transmitter and the receiver increases, which implies a channel with better propagation conditions. In  
particular, when \(K=0\), the Rician fading becomes a Rayleigh fading channel. In this scenario, there are no line-of-sight components between the UTs and the BS, and it is the worst operation scenario, and therefore, the highest BER appears. Finally, when \(T\) increases, it is observed that the system performance worsens, since a higher value of \(T\) implies that a higher SNR is required for the system to work properly. Hence, if the SNR is not increased, then the OP increases.