# Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System
## 5 Simulation Results and Discussion
In Figure 7b, at \(M=512\), M-BPS and BD-PNC achieve a \(\Delta v\cdot T_{S}\) tolerance of \(5.6\times 10^{-4}\) and \(1.4\times 10^{-3}\) for 64-QAM 30 Gbaud signal, respectively. The studies focus on the investigation of the proposed BD-PNC algorithm's performance with the number of subcarriers \(M=1024\). As a comparison, the performance of the M-BD-PNC algorithm is also evaluated in the 30 Gbaud BTB CO-FBMC/OQAM systems with 1024 subcarriers. In Figure 7c, the M-BD-PNC achieves a better \(\Delta v\cdot T_{S}\) tolerance than the BD-PNC. This is because the column full-rank condition is easily satisfied in the M-BD-PNC scheme, and its performance benefits from the enhanced estimation accuracy of DCT coefficients by the LS method. Moreover, the M-BD-PNC has a lower CC than the corresponding BD-PNC algorithm, and a detailed analysis of their CC will be described at the end of the section. With a large number of subcarriers, the ICI components in PN have a huge negative impact on the performance. With the ICI effect mitigated, the proposed algorithms offer a significantly better performance compared to the M-BPS under the same QAM modulation order. In particular, the BD-PNC and M-BD-PNC achieve tolerated linewidth and symbol duration products of \(2.2\times 10^{-2}\) and \(2.6\times 10^{-3}\) for 64-QAM 30 Gbaud signal, while the M-BPS can only achieve a \(\Delta v\cdot T_{S}\) tolerance of \(10^{-3}\). Finally, we compare the CC of M-BPS, the proposed BD-PNC, and M-BD-PNC algorithms in terms of the number of real multiplications in one FBMC/OQAM block. Since the M-BD-PNC method involves several neighboring FBMC/OQAM blocks, its CC is evaluated as the average CC per block. As shown in Table 2, the CC of the proposed BD-PNC and M-BD-PNC algorithms are compared. According to the block diagram in Figure 2, the CC of the proposed BD-PNC involves the CC of its four DSP steps, including M-BPS, time-domain PNC, calculation of DCT coefficients, and final compensation. The CC of the M-BPS method is given by \(O(2 MY)\)[28]. The time-domain PNC model is described by Equation (19), and its CC is \(O(LM\text{log}_{2}M+LKM)\). For the BD-PNC, the DCT coefficients are calculated in Equation (24), and its CC is given by \(O(8L^{3}+8Z_{n}L^{2}+2Z_{n}L)\), where \(Z_{n}\) is the total number of pre-estimated transmitted signals in the \(n\)th FBMC/OQAM block, while in the M-BD-PNC, the DCT coefficients are obtained by Equations (30) and (34), and real multiplications needed in these equations are \(O(8L^{3}/3+8Z_{n}L^{2}+2 ZnL+2L^{2}/3)\). For BD-PNC and M-BD-PNC, the final PNC is completed by using Equation (22), and its CC is \(O(2 ML)\). In order to compare the CC of these algorithms directly, several simulations are carried out to investigate the average value of \(Z_{n}\) at a BER of \(3.8\times 10^{-3}\). In this case, the average value of \(Z_{n}\) is shown in Table 3. Consequently, the required real multiplication numbers per block are counted by type, as shown in Table 4. As a comparison, when all the data after CPE compensation participate in the pre-decision (\(\delta=0\)), the required real multiplication numbers of BD-PNC or M-BD-PNC is provided in parentheses. It is observed that the optimization of the parameter \(\delta\) in the pre-decision process results in a remarkable decrease in complexity. Furthermore, it is clear that the CC of proposed BD-PNC or M-BD-PNC is not significantly higher than M-BPS, and their CC is less than four times higher than that of M-BPS for 1024 subcarriers 64-QAM 30 Gbaud signals. Nevertheless, the proposed algorithms have a great advantage over M-BPS in terms of the PNC performance. The CC of M-BD-PNC is slightly lower than that of BD-PNC, and its performance is even superior to the BD-PNC algorithm. Therefore, at \(M=1024\), the proposed M-BD-PNC should be the first choice.