## 3 Simulation Results and Discussions
Notice that in this case, \(\varphi_{l,u}^{2}\in[(1-\xi)\sigma_{l,u}^{2},(1+\xi)\sigma_{l,u}^{2}]=[0.2,1.8]\), in which \(\sigma_{l,u}^{2}=1\). According to Figures 3 and 4, one can easily notice that the benefits of having \(0.2\leq\varphi_{l,u}^{2}<1\) in a given sensing instant, which results in an instantaneous SNR \(P_{l,u}/\sigma_{l,u}^{2}\) larger than the average SNR \(P_{l,u}/\sigma_{l,u}^{2}\) of the received signal at the \(l\)-th antenna of \(u\)-th SU, i.e., \(P_{l,u}/\sigma_{l,u}^{2}>P_{l,u}/\sigma_{l,u}^{2}\), is larger than the penalties of having \(1<\varphi_{l,u}^{2}\leq 1.8\) in a given sensing instant, which  
Figure 2: AUCs versus the correlation coefficient for \(U=2\) SUs and \(L=9\) antennas. (a) \(\xi=0\), absence of DN; (b) \(\xi=1\), presence of DN. This figure is better viewed in color. results in an instantaneous SNR smaller than the average SNR of the received signal at the \(l\)-th antenna of \(u\)-th SU, i.e., \(P_{l,u}/\sigma_{l,u}^{2}<P_{l,u}/\sigma_{l,u}^{2}\). The aforementioned performance is in accordance with the results shown in Figure 2b when compared to Figure 2a. Notice from Figures 3 and 4 that the GLRT-DF, -EF, and -WEF are more sensitive to the number of antennas per SU than the CFCPSC, since increasing or decreasing \(L\) may considerably increase or decrease the detection performances of the GLRT in these cases, especially for larger values of \(\xi\) and independently of \(\rho\). Figure 4, for instance, depicts the worst cases where some detectors have the AUCs below or equal to 0.5, meaning that they are useless for larger values of \(\xi\), independently of \(\rho\). The increased or decreased detection performances of the GLRT-based approaches, in these cases, are consequences of the larger or smaller number of eigenvalues of the sample covariance matrices of SUs. In other words, increasing the number of eigenvalues of the sample covariance matrices increases the accuracy of GLRT statistics for distinguishing between \(\mathcal{H}_{0}\) and \(\mathcal{H}_{1}\). From these results, one can conclude that the GLRT-DF, -EF, and -WEF perform better when using smaller numbers of SUs with larger numbers of antennas per SU than larger numbers of SUs with smaller numbers of antennas per SU in the adopted SS scenarios. However, although the CFCPSC has, in general, more detection power than the GLRT; the GLRT-SF and -WSF perform better than CFCPSC for smaller values of \(\xi\), independently of \(U\), \(L\), and \(\rho\), which means that the GLRT-SF is a better choice in terms of detection performances for multiantenna-CR-based centralized CSS with calibrated antenna arrays in this case. The weighting schemes for WSF and WEF were effective in [20], but cannot bring any performance improvements here. On the contrary, results show that they are practically irrelevant in Figure 3 for \(L=9,6\) and \(0\leq\xi\leq 1\) and may degrade or severely degrade the detection performances of the GLRT in Figure 4 with \(L=3,2\) for larger values of \(\xi\)  
Figure 3: AUCs versus DN factor, \(\xi\), for \(U=2\) SUs and \(L=9\) antennas (graphs (**a**,**b**)) and \(U=3\) SUs and \(L=6\) antennas (graphs (**c**,**d**)). This figure is better viewed in color. compared to their corresponding unweighted versions, independently of \(\rho\), respectively. Notice that smaller values of \(L\) reduce the accuracy in the computation of the weights, which represent the maximum likelihood estimate of noise power, or its square root, of each SU, and, consequently, the detection performances of the GLRT, especially for larger values of \(\xi\). A comparison between graphs (a), (b) and (c), (d) for \(\rho=0\) and \(\rho=1\) in Figures 3 and 4 unveils that the GLRT and the CFCPSC suffer performance degradation with SF while GLRT-DF and -EF and CFCPSC-DF have performance improvements under correlated received signals for the majority of numerical results.