## 8 Results
### Ergodic Capacity Results
Taking an average SNR of 10 dB as a reference, the results in Figure 5 indicate that the spectral efficiency of 2.74 bit/s/Hz in the single carrier scenario can be improved to around 4 bit/s/Hz with the use of CA as a diversity technique (in all cases, namely, 4G LTE, 5G NR and unconstrained CA), which represents a 55% increase in the system capacity without increasing the available bandwidth. The results presented above indicate that CA can provide a slightly better performance in the heterogeneous SNR scenario than in the homogeneous SNR scenario as a result of a higher level of diversity. To illustrate this aspect more clearly, Figure 6 shows the impact of the spread parameter \(\varepsilon\), which determines the width of the interval of SNR values in each individual CC, on the capacity as a function of the number of CCs. The results show that the capacity gain of using CA increases with the spread of SNR values over the different CCs. This means that for the same average SNR across the different CCs, the higher the standard deviation of the SNR in the individual CCs, the higher the capacity gain obtained by using CA (with respect to the single carrier scenario). A higher SNR spread can somehow be seen as an additional form of channel diversity that benefits the use of CA as a diversity technique. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{\(\boldsymbol{\alpha=10^{-3}}\)} & \multicolumn{2}{c}{\(\boldsymbol{\alpha=10^{-2}}\)} \\ \hline
**Scenario** & **Capacity** & **Improvement** & **Capacity** & **Improvement** \\ \hline No CA & 2.90 bit/s/Hz & — & 2.88 bit/s/Hz & — \\ \hline
4G LTE CA & 5.64 bit/s/Hz & 94\% & 5.41 bit/s/Hz & 88\% \\ \hline
5G NR CA & 7.29 bit/s/Hz & 151\% & 6.34 bit/s/Hz & 120\% \\ \hline Unconst. CA & 9.28 bit/s/Hz & 220\% & 6.45 bit/s/Hz & 124\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Best attainable ergodic capacity for various scenarios and levels of bandwidth penalty (\(\boldsymbol{\alpha}\)) according to Figure 3.  
The results presented so far have been obtained based on the ideal model of effective SNR presented in Section 5.1. As discussed at the beginning of Section 8, this choice is preferred because the numerical results obtained from such a model show more pronounced trends that illustrate more clearly the impact of different relevant parameters on the performance of CA as a diversity technique. However, the ideal model for effective SNR assumes an optimistic best-case scenario and the results obtained from that model should be interpreted as performance upper bounds. The reader may naturally wonder whether the main conclusions obtained from the results presented in this section are also valid under a more realistic SNR model. To corroborate this, some illustrative results based on the average model of effective SNR proposed in Section 5.2 are presented here as well. Figures 7 and 8 show the counterparts to Figures 2 and 4, respectively, based on the average model of effective SNR. Taking into account that the average effective SNR model is more conservative and provides a scaled version of the ideal effective SNR model, the effective SNR value obtained under the former model will always be lower than the latter. This explains the lower numerical values of capacity obtained in Figures 7 and 8 (average model) compared to Figures 2 and 4 (ideal model). However, besides the mere  
Figure 4: Ergodic capacity as a function of the number of CCs for various values of the average SNR (\(\alpha=0.05\), \(\varepsilon=3\) dB). Figure 5: Optimum number of component carriers as a function of the average SNR (**left**) and the resulting ergodic capacity (**right**). numerical differences between both models, it can be seen that the qualitative performance trends are preserved when the average model of effective SNR is considered and that the main conclusions derived from the analysis presented in this section for the ideal model of effective SNR are still valid.