## 5 Numerical Results
### Results for a General Wideband Signal Detection  
To simulate the detection of a general wideband signal, we have considered a single primary transmitter whose total bandwidth was partitioned into \(K=8\) sub-bands. We have also considered: \(m=6\) single sensor (single antenna) cooperating CRs, signal-to-noise ratio \(\text{SNR}=-10\) dB, and Gaussian-distributed primary signal with unitary transmitted power. The channel between the primary transmitter and each CR was a multipath fading channel with \(L=8\) uncorrelated propagation paths having Rayleigh-distributed magnitudes, unitary second moment and uniformly-distributed phase in \((0,2\pi]\). The channel was considered static during a sensing period, changing independently and identically distributed from one period to another. It is known that the number of collected samples and the order of the sample matrix used in the computation of the covariance matrix influence the sensing performance of eigenvalue-based spectrum sensing. Then, for a fair comparison, both should be the same in all fusion schemes analyzed here. However, this is only possible in the case of the eigenvalue and decision fusion, as can be verified in Section 4; see Equations (10) and (11). For comparisons considering general wideband signals, we have chosen to make the order of the sample matrices the same. The consequence of this is that the number of collected samples in each CR had to be larger for the eigenvalue and decision fusion schemes, when compared with the decision fusion. In practice, this will not be an issue, since a larger amount of samples in a given sensing interval can be obtained by increasing the sampling rate. Nevertheless, as a counterexample, we have also carried out simulations assuming an equal number of collected samples per carrier in all fusion schemes. For the eigenvalue and decision fusion schemes, the total number of samples collected by each CR was \(n=KN=8\times 300=2,400\) (\(N=300\) samples in each frequency sub-band). To simulate the sample fusion scheme, \(n=KN=8\times 50=400\) samples (\(N=50\) in each frequency sub-band) were utilized to form the covariance matrix at the FC. In order to consider the same number of samples for all fusion schemes, we have also simulated the sample fusion with \(N=300\) samples per carrier. The order of the covariance matrix for sample fusion was \(m\times m=6\times 6\) and \(J\times J=6\times 6\) for eigenvalue and decision fusions. Figures 1-4 show ROC curves for the proposed eigenvalue fusion scheme parallel to sample and decision fusion curves. The test statistics Equations (3)-(6) were used for the sample fusion, and the tests Equations (18)-(21) were used for individual CR decisions. The test statistics Equations (14)-(17) were considered for the eigenvalue fusion. The performances with sample fusion are in close agreement with those reported in [14], which were obtained under the same system parameters adopted here. As expected, this indicates that processing the samples in the frequency domain leads to the same results as in the case of processing them in the time domain. From Figures 1-4, one can notice that the proposed eigenvalue fusion scheme outperforms all other fusion and combining methods for all test statistics considered in this paper, except in the case of \(N=300\) samples per carrier for the sample fusion. The performance of the eingenvalue fusion is closely followed by the OR decision fusion, except for MED where the performance gap is larger. For MMED and ED, the sample fusion is worse than the decision fusion with OR and majority-voting combining, overcoming only AND. For GLRT and MED, the sample fusion overcomes the AND rule significantly, showing a slightly better performance than majority-voting. The AND is the worst among all fusion rules and test statistics under analysis. These results are not meant to state that the relative performances of the decision combining rules will always be kept the same.