## 4 Simulation Results
### CE Performance  
Firstly, as shown in Figure 4, the MSE curves of TD-CE and FD-CE schemes using non-orthogonal DBT-MC-FTN pilots over the TU6 channel are evaluated. The performance at Nyquist rate, i.e., \(\alpha=\beta=1\) is set as the performance bound. For TD-CE, it is evident that, with the increase of \(\beta\) and \(\alpha\), the MSE results are gradually reduced to approach the bound. This is because the ISI/ICI introduced by two-dimensional packing in the system gradually decreases with the increase of the packing factors. Similar results occur when FD-CE is implemented and it can be observed that TD-CE can obtain a more accurate channel estimation than FD-CE at low \(E_{b}/N_{0}\). When it comes to high \(E_{b}/N_{0}\), an error floor occurs. The reason behind this is that the ISI/ICI introduced by packing and the out-of-band emission (OOBE) caused by the filter trailing can be dealt with in the case of TD-CE, but the single-tap FD-CE only considers the diagonal elements of \(\mathbf{C}\). Thus, even in the case of no packing, the error floor still occurs due to the effects of the filter and this effect is related to the sideband shape of the filter, e.g., the roll-off of the root-raised cosine (RRC) filter.  
Next, the MSE performance of LS channel estimation using orthogonal pilots is investigated in Figure 5. The linear and DFT interpolation methods have been utilized, respectively. It can be observed that, under the condition of LS channel estimation, DFT interpolation performs better than linear interpolation although the error floor occurs in both two interpolation methods compared to that of the TD-CE in Figure 4. Thus, an improved interpolation scheme can be implemented for higher accuracy, but it is not the focus in this paper. Furthermore, slight performance loss occurs when the system is compressed. The reason is that the increment in the power of the data symbol due to the packing results in a slight deviation of the SNR, which is negligible. Therefore, we can conclude that the performance of channel estimation using orthogonal pilots is not affected by the packing of the system, as mentioned.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title 1** & **Nyquist Rate Signaling** & **DBT-MC-FTN** \\ \hline Channel model & additive white Gaussian noise (AWGN) & AWGN \\  & typical urban-6 (TU-6) & TU-6 \\ Number of occupied subcarriers (\(M\)) & 16 & 16 \\ Number of the symbols transmitted on each subcarrier (\(D\)) & 30 & 30 \\ Inverse Discrete Fourier transform (IDFT) size (\(Q\)) & 900 & 540, 720 \\ Sampling frequency (MHz) & 15.36 & 15.36 \\ Modulation scheme & Quadrature Phase Shift Keying (QPSK) & QPSK \\ Type of pulse-shaping filter & root-raised cosine (RRC) & RRC \\ Roll-off factor of filter & 0.3 & 0.3 \\ Shift-orthogonal interval (\(N_{s}\)) & 30 & 30 \\ Shift interval of the shaping filter(\(N_{f}\)) & 30 & 18, 24 \\ Frequency packing factor (FPF, \(\alpha\)) & 1 & 0.8, 0.6 \\ Time packing factor (TPF, \(\beta\)) & 1 & 0.8, 0.6 \\ Joint time-frequency packing factor (\(v\)) & 1 & 0.8, 0.6 \\ Spectral efficiency (\(\text{bps}/\text{Hz}\)) & 2 & 2.5, 3.33 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental system specifications.