## 5 Numerical Results
### Results for an OFDMA Signal Detection  
To simulate the application of the eigenvalue fusion technique for detecting subchannels of a single OFDMA signal, we have considered a primary network with \(P=4\) subchannels. The number of cooperating CRs was \(m=6\). An OFDMA channel with \(K=20\) subcarriers was adopted. The subchannels were created by forming \(P=4\) sets with \(K^{\prime}=K/P=5\) subcarriers randomly selected. We also considered unitary primary signal power and \(\text{SNR}=-10\) dB. The wireless channel was modeled as a 20-path slow frequency-selective fading channel whose frequency response was kept constant during a sensing period, being varied from one sensing period to another. As in the case of general wideband signals, the second moment of the channel gains were normalized so as to keep the average received signal power equal to the average transmitted signal power. The number of samples collected in each subcarrier frequency was \(N=60\) for all fusion schemes. The test statistics Equations (31)-(34) were used for the sample fusion (using concatenation and MRC) and for individual CR decisions. The test statistics Equations (24)-(27) were considered for the eigenvalue fusion. Figures 5-8 show the ROCs for the eigenvalue fusion, the sample fusion and the decision fusion schemes for the detection of the OFDMA signal previously considered, for all test statistics considered in this paper. It is in order to remember that the aim of the spectrum sensing in this case is to determine the status of an entire subchannel occupation, differing from the sub-band occupation in the case of a general wideband signal. As in the case of a general wideband signal, the eigenvalue fusion scheme delivered the best performance among all fusion methods under analysis, for all test statistics, closely followed by the sample fusion using the concatenation approach for constructing the sample matrices. The performance of the sample fusion using the MRC approach produced a worse performance than the concatenation approach, also having the drawback of needing to know the channel gains. The better performance of the concatenation approach can be accredited to the large number of columns in the matrices used to compute the sample covariance matrices, as shown by Equation (28). We conjecture that the poor performance of the sample fusion for sensing OFDMA signals can be accredited to the different channel gains affecting each row of the sample matrices used for covariance matrices computations: notice in Equation (28) that the concatenated matrices come from different CRs and, thus, result from different channel gains. Thisis in contrast with the model presented in Section 2, which assumes that the channel gain present in the elements of each row of the sample matrix is the same. The test statistics Equations (3)-(6) considered as references for all test statistics proposed in this paper subsumes this invariant gain. Then, when the gains vary within a given row, performance degradation is expected. Figure 5: ROCs for sample fusion, decision fusion and eigenvalue fusion using GLRT for sensing OFDMA subchannels. Figure 6: ROCs for sample fusion, decision fusion and eigenvalue fusion using MMED for sensing OFDMA subchannels. The ranking of the performances considering different test statistics still has ED in the first position, followed by MED, GLRT and MMED. Again it is observed the inversion of the behaviors of ED and MED when comparing with traditional eigenvalue detection of narrowband signals via Equations (3)-(6). Figure 8: ROCs for sample fusion, decision fusion and eigenvalue fusion using ED for sensing OFDMA subchannels. Figure 7: ROCs for sample fusion, decision fusion and eigenvalue fusion using MED for sensing OFDMA subchannels. This indicates that the empirical test statistics Equations (27) and (34) have more statistical power than Equations (26) and (33), which means that Equations (26) and (33) have margin for improvements in their definitions.