# True Equalization of Polarization-Dependent Loss in Presence of Fast Rotation of SOP +
## 4 Simulation and Analysis  
In order to verify the proposed method for joint equalization of PDL and RSOP, we built a simulation platform of a 112 Gbit/s PDM-QPSK coherent system in MATLAB (R2019b, MathWorks, Natick, MA, USA, 2019), as shown in Figure 6. The transmitter sends the Golden-coded signal. Subsequently, in the fiber channel, the optical signal experiences RSOP, PDL, and amplified spontaneous emission (ASE) noise. In this simulation, we assume RSOP is dynamic and PDL is a deterministic phenomenon as it varies slowly. At the receiver, after coherent detection, the signals enter the digital signal processing (DSP) module. At the DSP side, the received signal \(\mathbf{Y}\) is divided into two branches. The upper branch is applied to obtain channel state information. PDL is estimated and the power inequality is equalized by utilizing the 3D Stokes space method, and RSOP parameters are tracked with the Kalman filter. After that, the signal in the lower branch and the obtained channel information are sent to the ML decoder for symbol decision by Equation (15). Figure 6: Numerical simulation system platform. Figure 7 depicts the performance of the proposed Golden code and Kalman filter equalization method (marked as Golden code + KF). For references, we also simulate the following two methods: The first one is an uncoded signal at the transmitter with constant modulus algorithm (CMA) equalization at the receiver (marked as Uncode + CMA); and the second is a golden-coded signal at the transmitter with training sequence (TS)-assisted RSOP tracking at the receiver (marked as Golden code + TS). The idea for the TS-assisted RSOP tracking scheme is based on the assumption that the TS and the entire data block have suffered from the same RSOP. Hence, the RSOP tracking ability of TS depends on how frequent TS is inserted in the data block. Obviously, the more frequent the TS that is inserted, the more redundancy there will be. In this paper, we design to insert 10 TSs in every 400 symbols, which means 2.5% of the redundancy. Figure 7a illustrates the BER depending on the OSNR with different PDLs and speeds of variation of RSOP. We can see that using the hard decision forward-error correction (HD-FEC) threshold (BER = \(3.8\times 10^{-3}\)) as the criterion [30; 31; 32], the Golden code + KF method exhibits an apparently better performance than those of the uncode + CMA and Golden code + TS schemes under different conditions of RSOP from 300 to 600 krad/s and PDL from 3 to 6 dB. In Figure 7b, we discuss the PDL-induced OSNR penalty at BER = \(3.8\times 10^{-3}\) under the severe impairment environment of RSOP = 1 Mrad/s. Thanks to the coding gain brought by the Golden code and the excellent RSOP tracking ability of the Kalman filter, at PDL up to 7 dB, the proposed Golden code + KF scheme only needs an OSNR penalty of approximately 1.2 dB. It is worth mentioning that the proposed method wins 3 dB OSNR than the uncode + CMA scheme, and 2.1 dB OSNR than the Golden code + TS scheme. Therefore, it is obvious that the Golden code + KF method has an overwhelming advantage over the other two methods. At the same time, RSOP tracing performance of the proposed Golden code + KF method is also shown in Figure 7c. The polarization impairment is assumed to be 1 Mrad/s RSOP and 6 dB PDL under 14 dB OSNR. In Figure 7c, the black line and the red line represent the true value and tracking value of \(\gamma\), respectively, and the pink line and the black line represent the true value and tracking value of \(\delta\), respectively. We can see that the RSOP tracking curve converges quickly, and the tracking results of rotation angles \(\gamma\) and \(\delta\) agree well with the original linearly increased ones, which means the proposed Golden code + KF method is indeed effective to track ultra-fast RSOP. In Figure 7a,b, we discuss the average BER on the worst and the best polarization cases. Now, we study the worst and the best BERs of the PDM signal separately.