## 5 Simulation Results and Discussion
In this sense, Figure 5(a) demonstrates that BER vs. SNR improves when the LDPC decoder performs ten iterations at each of the two iterations of the iterative receiver. The role of the Log-MAP equalizer is better seen in Figure 5(b). In this case, two scenarios were considered. The first scenario makes two iterations (it0 and it1) within the iterative process of equalization and decoding, as the LDPC decoder makes 20 iterations at each of the two iterations of the iterative receiver. The second one makes a single iteration (test) within the iterative receiver, as the number of iterations in the decoder (40) is the sum of the cumulative iterations of the first scenario (20 by 20). In this case, it was considered the same h1 = [0.18 0.85 0.32]. In Figure 5(b) it can be seen that at an SNR of 5 dB, the BER related to the test is located at \(10^{-4}\) while the BER related to it1 decreases, being situated between \(10^{-4}\) and \(10^{-5}\). \begin{table}
\begin{tabular}{c c c} \hline
**C. The proposed system was analyzed by comparing its performance in terms of BER vs. SNR with two other equalization and decoding systems.** \\ \hline
**C1. The BER vs. SNR performance of the first system using classic turbo equalization, considering different h’s** \\ \hline
**Graphic** & **Turbo equalization process** & **h** \\ \hline Figure 5(a) & 5 iterations & h1 = [0.18 0.85 0.32] \\ Figure 5(b) & 5 iterations & h2 = [0.302 0.725 0.456] \\ Figure 5(c) & 5 iterations & h3 = [0.407 0.815 0.407] \\ \hline
**C2. The BER vs. SNR performance of the second system in which the equalization was performed separately before the decoding process using MMSE equalizer and LDPC decoder, considering different h’s** \\ \hline
**Graphic** & **LDPC decoder** & **h** \\ \hline Figure 5(a) & 40 iterations & h1 = [0.18 0.85 0.32] \\ Figure 5(b) & 80 iterations & h1 = [0.18 0.85 0.32] \\ \hline Figure 5(a) & 40 iterations & h2 = [0.302 0.725 0.456] \\ Figure 5(b) & 80 iterations & h2 = [0.302 0.725 0.456] \\ \hline
**Graphic** & **LDPC decoder** & **h** \\ \hline Figure 5(a) & 40 iterations & h3 = [0.407 0.815 0.407] \\ Figure 5(b) & 80 iterations & h3 = [0.407 0.815 0.407] \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. Next, taking the three impulse responses h1 = [0.18 0.85 0.32], h2 = [0.302 0.725 0.456], and h3 = [0.407 0.815 0.407] as mentioned in Section 4.3, the performances in terms of BER vs. SNR of the proposed system were compared, these differing on the h function used, as it could be observed in Figure 7a-c.  
At each iteration in the iterative process of equalization and decoding, 10,000 sequences were generated, and 10 iterations took place in the LDPC decoder. At the same time, it is observed that these performances, using the same type of channel with ISI, also differed depending on h, the best performance being obtained in the case of h1. For instance, when the signal-to-noise ratio (SNR) is at 5 dB, the bit error rate (BER) ranges between \(10^{-4}\) and \(10^{-5}\), as shown in Figure 7a. On the other hand, for a channel with h2 at the SNR of 5 dB, the BER is approximately \(10^{-1}\), Figure 7b. Similarly, in the case of an ISI channel with h3, the BER is positioned between \(10^{-1}\) and \(10^{-2}\) when the SNR is at 5 dB, Figure 7c. The previous scenario was reconsidered in the case that the LDPC decoder achieves 20 iterations. This is reflected in Figure 8a-c. If the decoder makes 20 iterations inside itself (within the decoding process), the performance increases, the most visible being for the channel characterized by h1. After the SNR of 4 dB, the proposed system no longer finds any errors. Table 2 summarizes the BER vs. SNR performances of the proposed system while considering h1, h2, and h3 in two scenarios: when the LDPC decoder executes 10 or 20 iterations at each iteration of the iterative process of equalization and decoding. To analyze the performance of the proposed system, it was compared with two other equalization and decoding systems, for the same conditions of the transmission channel.