# Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System
## 6 Conclusions  
In this paper, we have presented a blind time-domain PNC scheme for the CO-FBMC/OQAM transmission, where the PN sample is approximately expanded by DCT. In the proposed algorithms, the PN in time-domain can be compensated by obtaining their corresponding DCT coefficients. The pre-decision process is firstly performed over the selected signals after CPE compensation by M-BPS, and the decision results are used to calculate these DCT coefficients. This selective decision process reduces the CC largely. Considering the overlapped symbol structure, the modified version of the proposed algorithm is reported with its performance improvement and complexity decrease. Since the proposed algorithms are devoted to removing the ICI effect, they achieve significant performance improvement compared to M-BPS for a simulated 30 GBaud CO-FBMC/OQAM system, especially with a large number of subcarriers and high order QAM modulation format. The algorithm complexity analysis shows that its CC is slightly higher than M-BPS.  
All authors contributed extensively to the work presented in this paper. conceptualization, M.G., J.L. and H.R.; methodology, H.R., B.W. and J.L.; software, B.W. and J.L.; validation, J.L., H.R., and B.W.; formal analysis, H.R. and W.H.; investigation, H.R., Z.L., Y.Q. and S.G.; resources, W.H. and H.R.; data curation, H.R., B.W. and J.L.; writing--original draft preparation, B.W.; writing--review and editing, M.G., B.W. and H.R.; visualization, H.R. and B.W.; supervision, H.R.; project administration, H.R.; funding acquisition, W.H. All authors have read and agreed to the published version of the manuscript.  
The National Natural Science Foundation of China (NSFC) (62075147,60907032, 61675183 and 61675184); Zhejiang Provincial Natural Science Foundation of China under Grant No.LY20F050009; Open Fund of the State Key Laboratory of Advanced Optical Communication Systems and Networks, China (2020 GZKF013). General program of the Education Department of Zhejiang (Y201941823).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **M-BPS** & **BD-PNC** & **M-BD-PNC** \\ \hline \multirow{3}{*}{4-QAM} & 8192\(|M=256\) & 20464 (24640)\(|M=256\) & \multirow{3}{*}{666740 (1039000)\(|M=1024\)} \\  & 16384\(|M=512\) & 41888 (50240)\(|M=512\) & \\  & 32768\(|M=1024\) & 672008 (1044288)\(|M=1024\) & \\  & 16384\(|M=256\) & 26496 (32832)\(|M=256\) & \\ \multirow{3}{*}{16-QAM} & 32768\(|M=512\) & 53952 (66624)\(|M=512\) & 494510 (1071800)\(|M=1024\) \\  & 65536\(|M=1024\) & 499776 (1077056)\(|M=1024\) & \\ \multirow{3}{*}{64-QAM} & 32768\(|M=256\) & 41440 (49216)\(|M=256\) & \\  & 65536\(|M=512\) & 84200 (99392)\(|M=512\) & 445245 (1137300)\(|M=1024\) & \\ \cline{1-1}  & 131072\(|M=1024\) & 450512 (1142592)\(|M=1024\) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: The required real multiplication numbers per block using several algorithms.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**DSP Step** & **CC (BD-PNC)** & **CC (M-BD-PNC)** \\ \hline CPE pre-compensation (M-BPS) & \(\mathcal{O}(2M\gamma)\) & \(\mathcal{O}(2M\gamma)\) \\ Time-domain PNC model & \(\mathcal{O}(LM\text{log}_{2}M+LKM)\) & \(\mathcal{O}(LM\text{log}_{2}M+LKM)\) \\ Calculation of DCT coefficients & \(\mathcal{O}(8L^{3}+8Z_{n}L^{2}+2 ZZ_{n}L)\) & \(\mathcal{O}(8L^{3}/3+8Z_{n}L^{2}+2Z_{n}L+2L^{2}/3)\) \\ Final compensation & \(\mathcal{O}(2 ML)\) & \(\mathcal{O}(2 ML)\) \\ \hline \hline \end{tabular} Note: \(M\): number of subcarriers. \(Y\): number of test phases. \(L\): length of DCT coefficient. \(K\): overlap factor. \(Z_{n}\): total number of pre-estimated transmitted signals.  
\end{table}
Table 2: The CC of the proposed BD-PNC and M-BD-PNC algorithms.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **M = 256** & **M = 512** & **M = 1024** \\ \hline
4-QAM & 140 & 280 & 570 \\
16-QAM & 80 & 160 & 320 \\
64-QAM & 40 & 90 & 180 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The average value of \(Z_{n}\).