## 4 Performance Assessment
### Comparison between the Proposed Method and the Method Based on Hard Decision  
Performance comparison between the proposed method and the method based on hard decision is measured using the output symbol error rate (SER) of each equalizer and the output BER of each decoder. The results without additional noise are shown in Figure 9 and Table 4, and the results when input SNR is 10 dB are shown in Figures 10 and 11.  
Figure 8: BERs of the proposed method and the method without ECC at input SNR of 10 dB: **(a)** BERs of the 1 st subband; **(b)** BERs of the 2 nd subband; **(c)** BERs of the 3 rd subband; **(d)** BERs of the 4 th subband.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Subband** & \begin{tabular}{c} **The 1 st** \\ **Iteration** \\ **(User1/User2)** \\ \end{tabular} & \begin{tabular}{c} **The 2 nd** \\ **Iteration** \\ **(User1/User2)** \\ \end{tabular} & \begin{tabular}{c} **The 3 rd** \\ **Iteration** \\ **(User1/User2)** \\ \end{tabular} & \begin{tabular}{c} **The 4 th-8 th** \\ **Iteration** \\ **(User1/User2)** \\ \end{tabular} \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} The method \\ based on \\ hard decision \\ 4 \\ \end{tabular} } & 1 & \(4.4\times 10^{-2}/0\) & 0/0 & 0/0 & 0/0 \\  & 2 & \(7.4\times 10^{-2}/0\) & \(1.5\times 10^{-4}/0\) & \(1.5\times 10^{-4}/0\) & \(1.5\times 10^{-4}/0\) \\ \cline{1-1}  & 3 & \(3.0\times 10^{-4}/0\) & 0/0 & 0/0 & 0/0 \\ \cline{1-1}  & 4 & 0/0 & 0/0 & 0/0 & 0/0 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} The proposed \\ method \\ 4 \\ \end{tabular} } & 1 & \(4.4\times 10^{-2}/0\) & 0/0 & 0/0 & 0/0 \\ \cline{1-1}  & 2 & \(7.4\times 10^{-2}/0\) & \(5\times 10^{-4}/0\) & 0/0 & 0/0 \\ \cline{1-1}  & 3 & \(3.0\times 10^{-4}/0\) & 0/0 & 0/0 & 0/0 \\ \cline{1-1}  & 4 & 0/0 & 0/0 & 0/0 & 0/0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Output BERs of decoding of the proposed method and the method based on hard decision in the case of no added noise.  
Figure 9: Output SERs of equalization of the proposed method and the method based on hard decision in the case of no added noise: (**a**) SERs of the 1 st subband; (**b**) SERs of the 2 nd subband; (**c**) SERs of the 3 rd subband; (**d**) SERs of the 4 th subband.  
Several observations can be obtained from Figures 9-11 and Table 4. Firstly, in the first iteration, the two methods have the same performance after equalization and decoding. The reason is that in the first iteration, due to the lack of soft information, the equalization and decoding of the proposed method are based on hard decision. Secondly, when the equalization performance of the two methods tends to be stable after 2-3 iterations, the output SERs of the proposed method are lower than those of the method based on hard decision. The reason is that the proposed method utilizes soft information in the process of interference cancellation and equalization, so it has better residual ISI and CCI suppression performance. Thirdly, when the decoding performance of the two methods is stable, the output BERs of the proposed method are lower than those of the method based on hard decision. The reason is that the proposed method exploits the soft information in the decoding, so better error correction performance can be obtained.  
Figure 10: Output SERs of equalization of the proposed method and the method based on hard decision at input SNR of 10 dB: (**a**) SERs of the 1 st subband; (**b**) SERs of the 2 nd subband; (**c**) SERs of the 3 rd subband; (**d**) SERs of the 4 th subband.