## 10 Simulation Results  
In this section, the performance of the proposed methods (MF-PIC and MBMF-SIC) will be evaluated in terms of BER in different scenarios. We assume a scenario with the following settings: the carrier frequency \(f_{c}=650\) MHz; the subcarrier spacing \(\Delta f=976.5\) Hz; and the OFDM symbol period is \(T_{\text{OFDM}}=1/\Delta f\approx 1\) ms. The number of subcarriers is \(N_{s}=128\). The symbols are modulated by QPSK, the extension of which to other modulation schemes is straightforward. In addition, a \(1/2\) rate convolutional code with generator polynomial \((7,5)\) is employed for the iterative interference cancellation, and the length of the code is \(2560\) bits. A wide-sense stationary uncorrelated scattering channel with a uniform power delay profile is simulated according to the Jakes model and the normalized Doppler frequency \(f_{d}T_{\text{OFDM}}=0.65\). The maximum delay of the channel is \(L=8\). Because of the band assumption, we assume \(D=\lceil f_{d}T_{\text{OFDM}}\rceil+1\) as described in [4, 5] given the time-domain window. For MSCE, the number of segments \(T=2\) is used, and the number of pilots \(N_{p}=N_{s}/4\). We also define an approximate matched filter bound (AMFB) [4] as a benchmark for ICI cancellation, which implies that the ICI inside the band \((Q=2D)\) is perfectly removed. Additionally, we use the band \begin{table}
\begin{tabular}{l l} \hline \hline
**Algorithm** & **Complex Operations** \\ \hline SBCE [16] & \(\mathcal{O}(N_{s}^{2})+\mathcal{O}(2N_{s}L)\) \\ PA-LS [36] & \(\mathcal{O}((2D^{2}-1)L^{3})+\mathcal{O}((4 DN_{s}-2)L^{2})\) \\ MSCE & \(\mathcal{O}(TL^{3})+\mathcal{O}(2N_{s}L)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Complexity comparison between different channel estimation techniques for the \(p\)-th iteration. Figure 5: BER performance against SNR (dB) of MF-PIC, GSG-based MBMF-SIC, ordering GSG-based MBMF (OGMBMF)-SIC, TSG-based MBMF (TMBMF)-SIC, ordering TMBMF (OTMBMF)-SIC, MF-SIC, banded MMSE-SIC and approximate matched filter bound (AMFB) in the fourth iteration with \(f_{d}T_{\text{OFDM}}=0.65\). MMSE-SIC [4], MF-SIC [16] and MBMF-SIC with and without SINR ordering, as well as AMFB for comparison. In Figure 5, we introduce several OFDM equalization techniques for comparison. The list includes the approximate MAP equalizers, namely belief propagation Ungerboeck-MAP (BP-MAP), recursive-SIC-linear-MMSE (RSL) in [3,15], the benchmark AMFB without ICI inside the band [2], the banded MMSE-SIC [4] and MF-SIC [16]. Note that the RSL we used is a modified SIC-MMSE with two taps (\(Q=4\)) in the fourth iteration. The BER performance of GSG-based MBMF-SIC (GMBMF-SIC) and TSG-based MBMF-SIC (TMBMF-SIC) with SINR ordering show performances close to the approximate MAP equalizers (BP-MAP), with only \(1\) dB loss with the BP-MAP and a fraction of 1 dB loss with the benchmark AMFB. The proposed scheme may significantly reduces the error floor compared to banded MMSE-SIC and MBMF-SIC without SINR ordering. It can be seen that the SINR ordering improves the reliability of detected symbols and makes the assumption for Equation (14) more appropriate. For a fair comparison, the SINR ordering in Section 7 is incorporated in other schemes in the later, iterations except for the first iteration. This is because serial ICI cancellation requires previous symbol estimates to improve the reliability of the remaining symbols. However, the ordering for MBMF-SIC can be employed in the initial iteration due to the use of LLR to generate multi-feedback candidates in the Steps \(3\) and \(4\) of Algoritm 1. We can also observe that the BER performance difference between GMBMF-SIC and TMBMF-SIC is negligible, but TSG performs better than GSG. This also agrees with the statements in [27] that the tree search algorithm works better than the Gibbs sampler at high SNR. For simplicity, we only consider GMBMF-SIC and TMBMF-SIC with SINR ordering in the rest of the chapter, which will be referred to as OGMBMF-SIC and OTMBMF-SIC.