## 4 Results  
This section presents the results obtained by the simulations. Table 3 summarize the performed simulations, highlighting the main parameters for each case. The simulations were divided into three main groups: (i) a single modulated band, (ii) all 10 bands being modulated, and (iii) only the odd bands being modulated (as shown in Figure 2). For each group, two Rx filters, \(g(t)\), were evaluated: Bessel and Butterworth. In each case, two Tx filters were evaluated: (i) a raised cosine filter, including different \(\beta\) values, and (ii) a matched filter. Figure 9: Matched filter generation: (**a**) impulse response of a third-order Bessel filter, \(g(t)\), sampled at \(F_{s}\); (**b**) matched filter, \(p(t)\), consisting of the flipped impulse response of (**a**), with zero padding at the end; (**c**) normalized impulse response of the in-phase filter and the correspondent carrier (first band). Previously, Figure 7 presented the frequency spectrum for \(y_{d}(t)\) when \(p(t)\) was a raised cosine filter. Figure 10 shows the output signal normalized frequency spectrum, however using the generated matched Bessel and matched Butterworth filters as \(p(t)\). As seen, the energy was more spread in the case of the Bessel when compared with the Butterworth. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Simulation Number** & **Modulated Bands** & \(\mathbf{Rx\,}g(t)\)**Type** & \(\mathbf{Tx\,}p(t)\)**Type** \\ \hline
1 & 1 & Bessel & Raised cosine \\
2 & 1 & & Matched Bessel \\ \hline
3 & 1 & Butterworth & Raised cosine \\
4 & 1 & Matched Butterworth \\ \hline
5 & 10 & Bessel & Raised cosine \\
6 & 10 & Matched Bessel \\ \hline
7 & 10 & Butterworth & Raised cosine \\
8 & 10 & Matched Butterworth \\ \hline
9 & 5 (odd) & Bessel & Raised cosine \\
10 & 5 (odd) & & Matched Bessel \\ \hline
11 & 5 (odd) & Butterworth & Raised cosine \\
12 & 5 (odd) & & Matched Butterworth \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation scenarios. Figure 10: Normalized frequency spectrum considering a matched filter (third order): (**a**) Bessel and (**b**) Butterworth. The first presented results evaluated the performance with only one modulated band, in particular the first band. Therefore, inter-band interference was not present in these results. Figure 11 presents the simulation results considering \(g(t)\) as a third-order Bessel filter, for various \(p(t)\) (Simulation Numbers 1 and 2 of Table 3). Regarding the raised cosine filter, there was a BER degradation as \(\beta\) decreased. This was mainly due to the raised cosine impulse response change as \(\beta\) changed: lower roll-off factors had a higher ripple in the impulse response, thus resulting in higher ISI in non-ideal scenarios, in particular when \(g(t)\) was not a matched filter and did not guarantee ISI-free communication. The matched filter in the receiver presented an improved BER when compared to the raised cosine filter, as expected. The simulated BER curve of the matched filter was almost coincident with the theoretical QAM BER curve for the same Eb/No, showing a remarkable improvement when compared with the RC-Bessel setup. The same scenarios were simulated for the Butterworth filter as \(g(t)\), which are presented in Figure 12 (Simulation Numbers 3 and 4). Identical performance was observed for the raised cosine filter as \(p(t)\), when compared with Figure 11's results. However, there was an \(Eb/No\)degradation, in particular for lower \(\beta\) values. Regarding the matched Butterworth filter as \(p(t)\), it presented a better performance than the raised cosine filter. Nevertheless, the matched Bessel filter showed the best performance for scenarios without inter-band interference. Since every parameter was identical, except for the filter type, it can be concluded that the group delay characteristics of Bessel filters were essential for improving the demodulation performance.