# Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System
## 5 Simulation Results and Discussion
For the 4-QAM modulation at \(M=1024\) with \(\Delta v\cdot T_{S}=5\times 10^{-2}\) and 11 dB OSNR, the BER performance of BD-PNC is improved by more than one order of magnitude compared to the M-BPS. Figure 6a depicts one realization of the real PN and its estimation within six consecutive FBMC/OQAM blocks at the linewidth and symbol duration product \(\Delta v\cdot T_{S}=1.5\times 10^{-2}\) and an OSNR of 20 dB for 1024 sub-carrier 16-QAM CO-FBMC systems using the BD-PNC and M-BPS. For these time-domain overlapped symbols, the CPE estimated by the M-BPS is only a rough estimate of the PN, which is far from the real PN. The proposed method shows a better phase tracking capability due to the ICI compensation in time-domain. Figure 6b shows the illustration of ICI influence and the necessity of PN estimation in time domain for CO-FBMC/OQAM systems. The constellation diagrams before and after PNC are separately displayed using M-BPS and BD-PNC with an OSNR of 27 dB and combined laser linewidth of 150 kHz. The PN in time domain, including CPE and ICI, is compensated by using BD-PNC, while only CPE is compensated by using M-BPS. It is clear that the PN in time domain is compensated by the proposed BD-PNC method resulting in an improvement of about 125 times in terms of BER over the M-BPS. Moreover, the BD-PNC achieves a root-mean-square error vector magnitude (\(EVM_{RMS}\)) of 4.7%, which is much lower than the \(EVM_{RMS}\) of 7% by the M-BPS. Supposing that the pre-forward error correction BER should be lower than \(3.8\times 10^{-3}\) for hard-decision forward error correction (HD-FEC) [43], the performance of these PNC algorithms is investigated at the BER target limit. Figure 7a-c show the OSNR penalty as a function of the linewidth and symbol duration product \(\Delta v\cdot T_{S}\) using M-BPS and the proposed algorithms for CO-FBMC/OQAM BTB transmission system with 256, 512, and 1024 subcarriers, respectively. The optimal numbers of test phases in the related M-BPS scheme are chosen as 16/32/64 for 4/16/64-QAM modulation order, respectively [28]. When the number of subcarriers is 256 or 512, the length \(L\) of DCT basis is set to 2. The length of DCT basis \(L\) is selected as 10 with total number of subcarriers \(M=1024\). The parameter \(\delta\) is set to 1.8 in this paper. The OSNR penalty is defined as the difference between the required OSNR for a BER of \(3.8\times 10^{-3}\) at a current laser linewidth and zero laser linewidth in CO-FBMC/OQAM systems, where the PNC algorithm is used in the former, and none of the PNC methods is applied in the PN free system in the latter. When no PN exists in the system, the reference OSNRs for 4/16/64-QAM  
Figure 5: **(a) BER versus the width of shadow rectangle in a high decision error probability region, \(\delta\). (b) BER versus the length of DCT coefficient, \(L\). (c) BER versus the number of subcarriers, \(M\). **  
30 Gbaud signal at the HD-FEC threshold are \(\sim\)4.4, \(\sim\)10, and\(\sim\)16.8 dB, respectively. For comparison, an acceptable maximum of 1 dB OSNR penalty is regarded as a threshold value [27]. On the whole, the proposed algorithm provides significantly better performance than M-BPS. In Figure 7a, at 1 dB OSNR penalty threshold, with the number of subcarriers \(M=256\), the M-BPS achieves a \(\Delta v\cdot T_{S}\) tolerance of \(3.5\times 10^{-2}\), \(7\times 10^{-3}\), and \(10^{-3}\) for 4/16/64-QAM 30 Gbaud signal, respectively. While using the proposed BD-PNC method, under 1 dB OSNR penalty constraint, the maximum \(\Delta v\cdot T_{S}\) that can be achieved for 4/16/64-QAM are \(5\times 10^{-2}\), \(10^{-2}\), and \(1.8\times 10^{-3}\), respectively. With the increase in the QAM modulation order, the difference between the performance of the two methods is more remarkable. At higher order modulation format, the ICI effect becomes stronger, and the BD-PNC scheme achieves more significant results than M-BPS.