# Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System
## 5 Simulation Results and Discussion
When the value of \(\delta\) is changed from 0 to 1.8, it can be seen that the BER performance does not degrade significantly due to the reduction in decision error probability. Moreover, with the increase in the value of \(\delta\), the participation of a low number of data benefits greatly to complexity reduction in the proposed algorithm. Hence, \(\delta=1.8\) is adopted in the remainder of this paper. \(L\) denotes the length of the DCT basis. Generally, under a large value of \(L\), we can obtain a more accurate approximation of the PN by the DCT in Equation (14). Figure 5b displays the BER performance as a function of \(L\) at the linewidth and symbol duration product \(\Delta v\cdot T_{S}=10^{-2}\) with 12 dB optical signal-to-noise ratio (OSNR) and 256/512/1024 subcarriers when using the proposed BD-PNC algorithm and its modified version. The modified algorithm is developed by considering the overlapped symbol structure, which is called the M-BD-PNC scheme. For the BD-PNC, with the increase in \(L\), the BER performance makes a small improvement, and is even deteriorated for the 256/512 subcarrier FBMC/OQAM systems. While using the M-BD-PNC method, there is a significant improvement for its BER performance as the value of \(L\) is increased. The PN estimation precision depends on the accuracy of the DCT coefficients estimated by the LS method. In Equation (24) or Equation (34), if the matrix \(\mathbf{S}_{n}\mathbf{P}_{n}\) or \(\mathbf{\overline{S}}_{n}\mathbf{\overline{P}}_{n}\) does not meet the column full-rank condition, its LS solution could produce a large error. With the increase in the number of subcarriers, more rows in the matrix allow it to meet the column full-rank condition more easily. Hence, when \(L\) is increased, the proposed BD-PNC algorithm achieves better performance under a large number of subcarriers; its performance becomes worse in the system with a low number of subcarriers, while in the M-BD-PNC method, \(\mathbf{\overline{P}}_{n}\) is the extended version of \(\mathbf{P}_{n}\) so that it is easier for the matrix \(\mathbf{\overline{S}}_{n}\mathbf{\overline{P}}_{n}\) to satisfy a column full-rank term. In this case, the PN estimation precision is almost not negatively influenced by the LS method, and a large value of \(L\) contributes to the improvement of the PN estimation precision. Therefore, for the M-BD-PNC, the BER performance exhibits a better result at a large \(L\). The optimized values of \(L\) in the BD-PNC and M-BD-PNC are selected as 2 and 10, respectively. The CO-FBMC/OQAM system with a large number of subcarriers is robust against fiber CD [12]. However, the PN becomes strong with the increase in the number of subcarriers. It is always a challenge for the existing PNC algorithm to achieve good performance under a large number of subcarriers [18; 25; 26; 27; 28; 29]. So the performance of the proposed algorithm is evaluated in the BTB system with a large number of subcarriers. In Figure 5c, the influence of the number of subcarriers on the performance of the method is investigated at \(L=2\) and \(\delta=1.8\) using M-BPS and BD-PNC for the CO-FBMC 4/16/64 QAM systems with several different values of \(\Delta v\cdot T_{S}\) and OSNR. When the number of subcarriers becomes larger, on one hand, the effect of AWGN is better averaged so that their performance is improved rapidly; on the other hand, the FBMC/OQAM symbol duration increases, and the PN has a larger variance and becomes stronger. As a result, it can be seen that the BER using M-BPS starts to deteriorate at \(M=1024\). Note that the performance using BD-PNC remains almost unchanged when the number of subcarriers is increased from 128 to 1024 for 4/16/64-QAM modulation order. The simulation results prove that its performance is not sensitive to the number of subcarriers in the CO-FBMC/OQAM systems. Under the large number of subcarriers, the proposed algorithm is far superior to the M-BPS.