## 4 Simulation Results
### BER Performance with SIC Equalization  
Furthermore, the BER performance of the proposed channel estimation in the DBT-MC-FTN system using orthogonal pilots have been shown in Figure 6 and Figure 7, respectively. First, to investigate the BER performance of the proposed SIC, a perfect CSI of AWGN channel is assumed to neglect the effect of the channel estimation effect. As shown in Figure 6, the performance of Nyquist rate system, i.e., \(\beta=\alpha=1\) is set as the performance bound and it can be observed that with the packing in the time or frequency domain, the BER performance performances a certain loss compared to the orthogonal system. With the increase in the number of the iteration, the BER performances will  
Figure 4: Mean squared error (MSE) performance of time-domain channel estimation (TD-CE) and frequency-domain channel estimation (FD-CE) methods using DBT-MC-FTN pilots over the TU-6 channel, where the parameters of the DBT-MC-FTN system were set to \((\alpha,\beta)\)=(0.8, 1), (0.6, 1), (1, 0.8) and (1, 0.6).  
Figure 5: MSE performance of least square (LS) channel estimation with linear and DFT interpolation methods using orthogonal pilots over the TU-6 channel, where the parameters of the DBT-MC-FTN system were set to \((\alpha,\beta)\)=(0.8, 1), (0.6, 1), (1, 0.8) and (1, 0.6).  
be improved gradually to approach the performance bound. It is observed that the BER performance with FPF \(\alpha=0.8\) can save up to 25% of bandwidth with a performance loss of less than 0.5 dB at \(P_{e}=10^{-3}\) with five iterations while there is a little performance penalty of about 1 dB in the case of the system with TPF \(\beta=0.8\). Hence, we can conclude that the proposed soft SIC has a better effect on the ICI introduced by frequency domain packing than the ISI introduced by time domain packing.  
Figure 6: BER performance of DBT-MC-FTN and orthogonal symbols over the AWGN channel, where the parameters of the DBT-MC-FTN system were set to \((\alpha,\beta)\)=(0.8, 1) and (1, 0.8), and the number of iterations were set to 0 and 5.  
Figure 7: BER performance of DBT-MC-FTN and orthogonal symbols with perfect and estimated channel impulse responses (CIRs) over the TU-6 channel, where the parameters of the DBT-MC-FTN system were set to \((\alpha,\beta)\)=(0.8, 1) and (1, 0.8), and the number of iteration was set to 5. LS channel estimation with DFT interpolation method using DBT-MC-FTN pilots over the TU6 channel, and ZF channel equalization was utilized.  
Next, to investigate the effect of the two-dimensional packing on the DBT-MC-FTN system in a fading channel, the interference introduced by a fading channel has been taken into consideration. As shown in Figure 7, the LS channel estimation with DFT interpolation method using DBT-MC-FTN pilots and ZF channel equalization have been utilized. Observe in Figure 7, in the case of the perfect CIR, there is a significant performance loss relative to the performance bound. Nevertheless, the BER performance has been improved with the increase of the iterations, as shown in Figure 6. The performance loss can be owing to the fact that the estimation error existing in the LS channel estimation algorithm with DFT interpolation will lead to bit errors in the channel-equalized signals. Furthermore, when it comes to the case of estimated CIR, the BER performance loss is around 4 dB at \(P_{e}=10^{-3}\), compared to that of the perfect CIR. The reason is that the residual interference resulting from the previous LS channel equalization step will be mixed into the ISI tackled later, which will amplify the error propagation effect of the following SIC detection. Hence, certain joint channel estimation and signal detection schemes could be explored to further improve the performance.