## 3 Simulation Results and Discussions  
We present some Monte Carlo simulation results of the GLRT-based and CFCPSC-based approaches in multiantenna-CR-based centralized CSS under the seldom adopted SS scenario of correlated received signals at the antenna arrays of SUs combined with uncalibrated antenna arrays of SUs. Results are for (i) GLRT-DF with the fusion rules AND (GLRT-DF-AND), OR (GLRT-DF-OR), and MAJ (GLRT-DF-MAJ), (ii) GLRT-SF, -WSF, -EF, and -WEF, and (iii) CFCPSC-SF and -DF. Calibration errors at each antenna branch follow the DN model proposed in (2) with \(\sigma_{l,u}^{2}=1\). Simulations consider one single-antenna PU transmitter, the number of SUs and antennas given by the pairs \((U,L)=\{(2,9),(3,6),(6,3),(9,2)\}\), and \(N=30\) samples at each SU antenna per sensing period, unless stated otherwise. The PU signal was assumed to be a baseband BPSK signal with five independent and identically distributed samples per symbol with six symbols per sensing period. Each SUhas an average SNR according to Table 1. The PU signal powers at SUs are unequal and computed as \(P_{l,u}=\sigma_{l,u}^{2}\times 10^{\text{SNR}_{u}/10}=10^{\text{SNR}_{u}/10}\) according to the corresponding desired average SNR in Table 1. Notice that the average SNR of the secondary network is always \((1/U)\sum_{u=1}^{U}\text{SNR}_{u}=-10\) dB independently of the number of SUs, \(U\), in Table 1, which is a challenging SS scenario for detecting PU signals. Each sensing channel has \(Z=6\) non-zero taps and mimics a slow-FS Rayleigh fading channel. Table 2 shows the adopted normalized power gains. Finally, the CFCPSC algorithm adopts \(S=5\) sub-bands for both SF and DF. Figure 2 depicts the AUC values as a function of the correlation coefficient \(\rho\) for fixed \(U=2\) SUs, \(L=9\) antennas, \(N=30\) samples at every single SU antenna per sensing period, (a) \(\xi=0\), i.e., the antenna array of \(u\)-th SU is assumed to be calibrated by a suitable technique and (b) \(\xi=1\), when the level of noise power variation at the front-ends of multiantenna-based SUs is in the worst case in the adopted system model. If the DN is null, i.e., \(\xi=0\), the performance ranking of adopted detectors is: GLRT-SF, closely followed by GLRT-WSF, followed by, GLRT-WEF, GLRT-EF, CFCPSC-SF, GLRT-DF-MAJ, GLRT-DF-AND, GLRT-DF-OR, and CFCPSC-DF, for all range of \(\rho\) values. In this scenario, in general, the presence of correlation, i.e., for \(\rho>0\), leads to a poorer detection performances. However, notice that the CFCPSC-based approaches have a considerable improvement performance under the presence of DN, i.e., for \(\xi=1\). The opposite occurs for the GLRT-based approaches. We postpone the discussions regarding the DN variation. Figures 3 and 4 present several numerical results according to the configurations established in the aforementioned paragraphs adopting AUC versus \(\xi\). However, the correlation model uses the correlation coefficient as \(\rho=0\) or \(\rho=1\) to simulate a sensing scenario such that the received signal samples at each antenna array are uncorrelated or have maximum correlation, respectively. The adoption of these correlation coefficients yields the maximum and minimum benefit of the spatial diversity order of antenna arrays, which leads to the best and the worst cases in terms of detection performances of each detector from the perspective of correlated and uncorrelated received signals. Simulations aim at analyzing the influence of having calibration errors combined with signal correlation on the detection performances of GLRT-based approaches compared to CFCPSC-based ones. The pairs of graphs marked as (a), (b) and (c), (d) in Figure 3 show numerical results for \(U=\{2,3\}\) and \(L=\{9,6\}\), and under uncorrelated, \(\rho=0\), and correlated, \(\rho=1\), received signal samples at each antenna array, respectively. In a similar way, the pairs of graphs marked as (a), (b) and (c), (d) in Figure 4 show numerical results for \(U=\{6,9\}\) and \(L=\{3,2\}\).