## 3 Simulation Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{8}{c}{**SNR for the \(u\)-th SU, dB**} \\ \hline  & \(\mathbf{u=1}\) & \(\mathbf{u=2}\) & \(\mathbf{u=3}\) & \(\mathbf{u=4}\) & \(\mathbf{u=5}\) & \(\mathbf{u=6}\) & \(\mathbf{u=7}\) & \(\mathbf{u=8}\) & \(\mathbf{u=9}\) \\ \hline \(U=2\) & \(-12\) & \(-8\) & & & & & & \\ \(U=3\) & \(-12\) & \(-10\) & \(-8\) & & & & & \\ \(U=6\) & \(-12\) & \(-11.2\) & \(-10.4\) & \(-9.6\) & \(-8.8\) & \(-8\) & & & \\ \(U=9\) & \(-12\) & \(-11.5\) & \(-11\) & \(-10.5\) & \(-10\) & \(-9.5\) & \(-9\) & \(-8.5\) & \(-8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average SNRs at each SU according to the number of SUs, \(U\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Path Index** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Propagation delays in \(\mu\)s & \(0\) & \(3\) & \(8\) & \(11\) & \(13\) & \(21\) \\ Path gains in dB & \(0\) & \(-7\) & \(-15\) & \(-22\) & \(-24\) & \(-19\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power delay profile of the channel between primary user and secondary user. First of all, it is worth emphasizing that the adoption of the DN model proposed in (2) led to considerably different results in terms of performance ranking compared to those corresponding results presented in [20] for uncorrelated received signals and unequal signal and noise powers (remembering that [20] considers \(\rho=0\), and \(\xi=0.8\) according to (2)). For example, choosing \(U=3\), \(L=6\), \(\rho=0\), and \(\xi=0.8\), the performance ranking of adopted detectors is, in [20]: GLRT-WSF followed by CFCPSC-SF, GLRT-WEF, GLRT-DF-OR, GLRT-EF, GLRT-SF, GLRT-DF-MAJ, and GLRT-DF-AND, while in Figure 3 the performance ranking is: CFCPSC-SF followed by CFCPSC-DF, GLRT-SF, GLRT-WSF, and GLRT-EF closely followed by GLRT-WEF and GLRT-DF-AND, -MAJ, and -OR. Besides, performance gaps between detectors adopted in [20] are also, in general, considerably larger than shown in Figure 3. Yet, performance rankings of Figures 3 and 4 are consistent with those presented in [23] for FS sensing channels and \(\rho=1\) for the majority of detectors (remembering that differently from this paper, [23] considers equal signal and noise powers among SUs and antennas per SU, i.e., it adopts the same average SNR at each SU and \(\xi=0\) according to (2), which justify some few differences compared to Figures 3 and 4). The numerical analysis of Figures 3 and 4 unveils that the presence of DN at the antennas of SUs, which occurs when \(\xi>0\), may be highly detrimental to the detection performances of GLRT-based approaches, independently of the values of \(U\), \(L\), and \(\rho\). See, for example, that the AUCs for any GLRT curve decrease as \(\xi\) increases. The poorer detection performances of the GLRT, in this case, are credited to the higher levels of calibration errors for larger values of \(\xi\) that directly impact the elements of the sample covariance matrices, their eigenvalues, and consequently, the resulting test statistic for distinguishing between noise only, \(\mathcal{H}_{0}\), and noise plus PU signal, \(\mathcal{H}_{1}\), in the sensed PU band. Surprisingly, the opposite occurs with the CFCPSC-based approaches. In this case, the presence of DN is interestingly beneficial to the detection performances of the CFCPSC since its AUCs, for any curve, increase as \(\xi\) increases, independently of the values of \(U\), \(L\), and \(\rho\). These improvements in detection performances indicate that the benefits of having antennas with noise powers below the nominal noise power in a given sensing period, i.e., \(\varphi_{l,u}^{2}<\sigma_{l,u}^{2}\), outperform the penalties of having \(\varphi_{l,u}^{2}>\sigma_{l,u}^{2}\) in a given sensing period in the case of the CFCPSC, especially for large \(\xi\). For a better understanding of the above statement, let us consider, for instance, a numerical example with \(\xi=0.8\).