## 9 Discussion  
The main aim of the analysis presented in Section 8 was to determine whether the mathematical model and closed-form expressions derived in this work can correctly predict the trends observed by simulations in [22] and evaluate the impact of various relevant parameters on the system performance. The numerical results obtained by evaluating  
Figure 11: Secrecy capacity as a function of the number of CCs for various values of the bandwidth overhead parameter \(\alpha\) (average effective SNR model; 20 dB SNR in the main link and 10 dB SNR in the eavesdropper link). Figure 10: Secrecy capacity as a function of the number of CCs for various values of the bandwidth overhead parameter \(\alpha\) (ideal effective SNR model; 20 dB SNR in the main link and 10 dB SNR in the eavesdropper link). the mathematical expressions derived in this work have been shown to be in line with our previous simulation study and demonstrate that CA can be effectively exploited as a diversity technique to increase the data rate of the system without increasing the available bandwidth (owing to a higher spectral efficiency per unit bandwidth), thus improving the capacity and performance of mobile communication systems compared to the case of single-carrier transmission over the same amount of bandwidth. The performance of the considered CA-based transmission scheme has been evaluated under various SNR scenarios, namely, a homogeneous SNR scenario, where all CCs experience the same average SNR, and a heterogeneous counterpart, where the SNR values in the CCs are different and spread around a certain average SNR value. The performance has been observed to be noticeably higher in the heterogeneous SNR scenario than in the homogeneous counterpart, obtaining better performance improvements when the SNR values are spread over broader intervals. This is an indication not only of the ability of the proposed CA-based scheme to exploit and benefit from the frequency diversity existing in wireless communication channels but also the capability of the developed mathematical modelling framework to capture this phenomenon. It has been shown that several parameters can affect, to different extents, the performance of CA when exploited as a diversity technique. The two main parameters are the number of CCs into which the available spectrum is divided (\(N\)) and the overhead parameter, representing the fraction of the available bandwidth that needs to be sacrificed to accommodate for signalling traffic and guard bands between CCs (\(\alpha\)). Increasing the number of CCs initially has a beneficial effect as it enhances the diversity gain of the system. However, each new CC has an associated bandwidth penalty as a result of its required signalling traffic and guard bands, which has a negative effect on performance. If \(N\) is too low, the diversity gain may not be significant, while if \(N\) is too high, the bandwidth penalty may completely cancel out the obtained diversity gain and even reduce the performance below that of the single-carrier transmission scenario. Therefore, the existence of an optimum number of CCs that provides the best trade-off between these two conflicting aspects and maximises the overall capacity has been shown. This optimum number of CCs, which was indeed suggested by the simulation results obtained in [22], has a strong dependency on the bandwidth penalty parameter \(\alpha\). An important practical limitation in real mobile communication systems is the maximum number of CCs that may be supported in certain versions of the 3 GPP standard for mobile communication systems (e.g., up to five CCs in the case of 4G LTE systems). Even in those cases where a larger number of CCs is supported (e.g., 5G NR), mobile operators may actually implement a lower number of CCs in their real network deployments. As a result, the optimum number of CCs that provides the best capacity performance from a theoretical point of view may not be supported in some practical scenarios.