## 4 Performance Assessment
### Comparison between the Proposed Method and the Method without ECC  
Performance comparison is measured using the output bit-error-rate (BER) of each subband decoder of the proposed method and the output BER of each subband equalizer of the method without ECC. The simulation results without additional noise are shown in Table 3, and the results at input SNR of 10 dB acquired by adding white Gaussian noise to the signal passing through each subband are shown in Figure 8. The noise variance \(\sigma_{m}^{2}\) is determined according to the \(SNR=\sum\left|h_{\beta}^{\mathrm{a},m}(n)\right|^{2}/2\sigma_{m}^{2}\)QR.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **The Proposed Method** & **The Method without ECC** & **The Method Based on Hard Decision** \\ \hline Number of information bits for & 20,000 & 20,000 & 20,000 \\ each user & & & \\ \hline ECC & The rate \(1/2\) RSC with & & The rate \(1/2\) RSC with generator \\ generator polynomial [5; 7] & none & polynomial [5; 7] \\ \hline Constellation & QPSK & BPSK & QPSK \\ \hline Number of mapped symbols for & & & \\ each user & 20,000 & 20,000 & 20,000 \\ \hline Total information rate of each user & 16,000/3 & 16,000/3 & 16,000/3 \\ \hline Feedforward filter taps of each & & & \\ DFE & 23 & 23 & 23 \\ \hline Feedback filter taps of each DFE & 8 & 8 & 8 \\ \hline Adaptive equalization algorithm & RISE & RLS & RLS \\ \hline Decoding algorithm & Log-MAP & None & Viterbi \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the proposed method and two methods for comparison.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Subband** & **The 1 st Iteration** & **The 2 nd Iteration** & **The 3 rd Iteration** & **The 4 th–8 th Iterations** \\  & **Index** & **(User1/User2)** & **(User1/User2)** & **(User1/User2)** & **(User1/User2)** \\ \hline \multirow{4}{*}{The method without ECC} & 1 & \(2.0\times 10^{-2}/7.6\times 10^{-5}\) & 0/0 & 0/0 & 0/0 \\  & 2 & \(7.8\times 10^{-2}/1.3\times 10^{-3}\) & \(2.2\times 10^{-4}/6.1\times 10^{-4}\) & \(1.5\times 10^{-4}/4\times 10^{-4}\) & \(1.3\times 10^{-4}/4\times 10^{-4}\) \\ \cline{1-1}  & 3 & \(4.1\times 10^{-3}/0\) & 0/0 & 0/0 & 0/0 \\ \cline{1-1}  & 4 & \(1.8\times 10^{-3}/4\times 10^{-3}\) & 0/6.8\(\times 10^{-4}\) & 0/6.5\(\times 10^{-4}\) & 0/6.5\(\times 10^{-4}\) \\ \hline \multirow{4}{*}{The proposed method} & 1 & \(4.4\times 10^{-2}/0\) & 0/0 & 0/0 & 0/0 \\  & 2 & \(7.4\times 10^{-2}/0\) & \(5\times 10^{-4}/0\) & 0/0 & 0/0 \\ \cline{1-1}  & 3 & \(3\times 10^{-4}/0\) & 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 3: BERs for the proposed method and the method without ECC in the case of no added noise.  
It can be observed from Table 3 that after three iterations, the BERs of two users in the proposed method all reach zero, but the BERs of the 2 nd subband of two users and the 4 th subband of user 2 in the method without ECC still remain at the order of magnitudes \(10^{-4}\). The observations indicate when the residual ISI and CCI are the main factors degrading communication performance and noise is ignored, the proposed method can obtain better performance than the method without ECC due to its superior residual ISI and CCI suppression. Figure 8 shows that at input SNR of 10 dB, when the performance of two methods reaches stability, the BERs of the proposed method are obviously lower than those of the method without ECC. This implies that when noise, residual ISI and CCI are the main factors injuring communication performance, the advantage of the proposed method shows a more pronounced benefit from the use of ECC.