# Time-Domain Blind ICI Compensation in Coherent Optical FBMC/OQAM System
## 5 Simulation Results and Discussion  
A 30 Gbaud BTB CO-FBMC/OQAM transmission system is simulated to evaluate the performance of the proposed blind PNC scheme, which is built by Optisystem 17.0 and MATLAB. Firstly, a pseudo-random bit sequence with a word length of \(2^{17}\) is mapped into m-QAM and the symbol rate is set to 30 Gbaud/s. All the complex-valued QAM symbols are converted into the real-valued PAM symbols through QAM to PAM module. The base-band time-domain FBMC/OQAM symbols are generated after all PAM data sequences through IFFT and FBS-PPN. The pulse length of the square root raised cosine filter is chosen as \(L_{g}\) = 4\(M\), and its roll-off coefficent \(\alpha=1\). Then, the base-band FBMC/OQAM signals are modulated onto an optical carrier at 1550 nm using a Mach-Zehnder modulator with a pair of independently controllable branches. At the receiver, the optical signal is coherently detected in a 90\({}^{\circ}\) optical hybrid, and the received analog signals are converted into digital signals by analog-to-digital converters with two samples per symbol. Subsequently, the obtained digital symbols are fed into the offline DSP module. With time synchronization being perfectly implemented, all the time-domain symbols are converted to the frequency domain by the PPN for filter bank analysis and FFT. In this paper, perfect channel equalization is considered, and specifically, we suppose that the channel response is flat and time-invariant on each carrier [27]. Next, the blind discrete-cosine-transform-based phase noise compensation (BD-PNC) is implemented, including CPE and ICI compensation. In the related M-BPS algorithm, the total numbers of test phases for 4/16/64-QAM are chosen as 16/32/64, respectively [28]. The original binary bits can be recovered after m-OQAM and m-QAM de-mapping, and the bit error rate (BER) is estimated by comparing them with the transmitted bits. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviation** & **Full Name** \\ \hline CO-FBMC/OQAM & Coherent optical offset-quadrature amplitude modulation-based filter-bank multicarrier \\ MCM & multicarrier modulation \\ OFDM & orthogonal frequency division multiplexing \\ CO-OFDM & coherent optical OFDM \\ PN & phase noise \\ CPE & common phase error \\ ICI & inter-carrier interference \\ PNC & Phase noise compensation \\ IMI & intrinsic imaginary interference \\ SE & spectral efficiency \\ IFFT & inverse fast Fourier transform \\ FFT & fast Fourier transform \\ CC & computational complexity \\ BPS & blind phase search \\ M-BPS & modified BPS \\ BD-PNC & blind discrete-cosine-transform-based phase noise compensation \\ M-BD-PNC & modified BD-PNC \\ CD & chromatic dispersion \\ OBE & orthogonal-basis-expansion \\ DCT & discrete cosine transform \\ BTB & back to back \\ LS & least square \\ OSNR & optical signal-to-noise ratio \\ HD-FEC & hard-decision forward error correction \\ PPN & poly-phase network \\ DSP & digital signal processing \\ AWGN & additive Gaussian white noise \\ BER & bit error rate \\ \(EVM_{RMS}\) & root-mean-square error vector magnitude \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of abbreviation. The effects of two parameters of \(\delta\) and \(L\) on the performance of the algorithm are investigated in Figure 5a,b. \(\delta\) is the width of shadow rectangle in a high decision error probability region, which determines how many signals after CPE compensation join the pre-decision process. As mentioned in Section 3, \(\delta=0\) means that all the data are used to perform the pre-decision while \(\delta=2\) implies that only the leftmost and rightmost data in the I-Q plane participate in the process in Figure 3. The decision error increases with the participation of more data after the CPE compensation. In Figure 5a, \(\delta\) is optimized at the length of DCT basis \(L=2\) for the CO-FBMC 4/16/64-QAM BTB system with 512 subcarriers.