## 8 Results
### Secrecy Capacity Results  
The performance of CA as a diversity technique in terms of secrecy capacity was also evaluated as part of this study. It is worth noting that the secrecy capacity was observed to follow the same qualitative trends as the ergodic capacity, being affected in the same way by variations in the bandwidth overhead parameter, number of CCs, and average SNR. This is in line with the observation pointed out in Remark 3, which highlights the fact that the numerical value of the secrecy capacity is a reduced version of the ergodic capacity as a result of the presence of an eavesdropper. This means that the figures shown in Section 8.1 for the ergodic capacity would look very similar when calculated for the secrecy capacity, except for the fact that numerical values in the case of the secrecy capacity would be slightly lower. The analysis presented in this section focuses on the impact of the eavesdropper on the secrecy capacity, which is the main aspect that determines the difference between ergodic and secrecy capacities. As explained in Section 7, the eavesdropper needs to use the same configuration as the main link (i.e., same \(B\), \(N\), and \(\alpha\)); however, they may experience a different average SNR depending on their relative location with respect to the transmitter and receiver in the main link. Therefore, the impact of the eavesdropper can be analysed and quantified in terms of their average SNR with respect to the average SNR in the main link. Figure 9 shows the secrecy capacity of a system with CA as a diversity technique as a function of the number of CCs for various values of the bandwidth overhead parameter \(\alpha\), when both the main and eavesdropper links experience the same average SNR of 10 dB \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & \multicolumn{2}{c}{**No CA**} & \multicolumn{2}{c}{**CA with Homogeneous SNR**} & \multicolumn{2}{c}{**CA with Heterogeneous SNR**} \\ \hline \(\boldsymbol{\alpha}\) & **Capacity** & **Capacity** & **Improvement** & **Capacity** & **Improvement** \\ \hline
0.001 & 2.90 bit/s/Hz & 3.37 bit/s/Hz & 16.2\% & 3.48 bit/s/Hz & 20.0\% \\ \hline
0.01 & 2.88 bit/s/Hz & 3.18 bit/s/Hz & 10.4\% & 3.31 bit/s/Hz & 14.9\% \\ \hline
0.02 & 2.85 bit/s/Hz & 3.07 bit/s/Hz & 7.7\% & 3.24 bit/s/Hz & 13.7\% \\ \hline
0.03 & 2.82 bit/s/Hz & 2.98 bit/s/Hz & 5.7\% & 3.17 bit/s/Hz & 12.4\% \\ \hline
0.04 & 2.79 bit/s/Hz & 2.91 bit/s/Hz & 4.3\% & 3.10 bit/s/Hz & 11.1\% \\ \hline
0.05 & 2.76 bit/s/Hz & 2.85 bit/s/Hz & 3.3\% & 3.03 bit/s/Hz & 9.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Best attainable ergodic capacity for various scenarios and levels of bandwidth penalty (\(\alpha\)) according to Figure 7.  
Figure 8: Ergodic capacity as a function of the number of CCs for various values of the average SNR (\(\alpha=0.05\), \(\varepsilon=3\) dB) (counterpart to Figure 4 based on the average model of effective SNR). (based on the ideal model of effective SNR). These results suggest that the use of CA as a diversity technique, while improving the ergodic capacity with respect to the single carrier scenario (see Section 8.1), may actually lead to a lower secrecy capacity compared to the case of single-carrier transmission. In other words, while CA allows the system to transmit a higher quantity of bits per second in the same bandwidth (ergodic capacity), it reduces the level of confidentiality of the link at the physical layer (secrecy capacity). This means that the use of CA not only benefits the transmission of data in the main link, but also the transmission of data in the (undesired) link between the same transmitter and the eavesdropper, thus potentially reducing the level of confidentiality between the transmitter and the legitimate receiver. However, it is worth noting that this is due to the rather favourable propagation conditions in the eavesdropper link, which in the example of Figure 9 enjoys the same average SNR as the main link.