## 3 Results
### Experimental Results  
The pilot symbol-aided AKF scheme is experimentally studied in a 10 Gbaud Dual-polarization 16 QAM system, as shown in Figure 9. In the transmitter, an arbitrary waveform generator (AWG7122C, Tektronix, Portland, Oregon, USA) is used to generate electrical signals to drive an optical I/Q modulator. The optical carrier from a 100 kHz narrow linewidth laser is divided into two parts by a 3 dB coupler. One part of the light is fed into the optical modulator. The other part is used as a local oscillator for coherent detection. The length of the signal fiber link is 10 km. In the receiver, the electrical signal after coherent detection is sampled by a digital serial analysis with 50 GSa/s (DSA72004C). Finally, the sampled data is processed by an offline digital signal processor (DSP), including timing recovery and frequency offset estimation based on maximum fast Fourier transform (Max-FFT). The dynamic polarization rotation is also digitally achieved in the DSP section by the polarization matrix, which is mentioned in Equations (2) and (3).  
Firstly, the convergence performance is described by the curves of the estimated {a,b,c,d}, as shown in Figure 10. Two data structures are used to evaluate the convergence performance of AKF: pilot symbols and non-pilot symbols. As shown in Figure 10a, AKF with pilot symbols can achieve a stable estimation within 20 symbols, which is attributed to the quick acquisition capability of AKF with pilot symbols. However, AKF without pilot symbols requires more than 800 symbol periods to achieve high accuracy and stable estimation of the state vector in AKF, as depicted in Figure 10b. The experimental results confirm that the quick tracking capability is achieved by the aid of pilot symbols in the AKF scheme.  
Figure 10: (**a**) The convergence curves of AKF with pilot symbols and (**b**) convergence curves of AKF without pilot symbols.  
Figure 9: Experimental setup of 16 QAM coherent optical communication system.  
In the following, the tracking capability of AKF with pilot symbols is investigated under dynamic polarization rotation rates. The format ratio and the dynamic polarization rotation rate are set to 1:7 and 6.1 rad/us\({}^{2}\), respectively. As shown in Figure 11a, the estimated state vector {a,b,c,d} is changed synchronously with the applied time-varying polarization rotation rate. Meanwhile, Qpol is adjusted in an adaptive manner, which ensures that the AKF scheme can track the accelerating polarization rotation rate. It can be seen in Figure 11b that after the convergence is achieved, after around 5000 symbols, the tuning parameter Qpol increases basically. This is consistent with the accelerated rotation.  
In Figure 12, the system target BER is set to \(10^{-2}\). With the increasing polarization rotation frequency drift rate, the performance of FR = 1:7 is better than pure-16 QAM. The allowable polarization rotation frequency drift rates under FR = 1:7 are 28.6 rad/us\({}^{2}\). The improvement of tracking performance by 53% is obtained compared with the pure-16 QAM case. The result shows that the improvement of tracking capability is successfully achieved by employing less pilot symbols in the proposed scheme.  
Finally, the verification of tracking the performance of AKF with pilot symbols is carried out under a fixed rotation rate, which is compared with EKF. In Figure 13, AKF and EKF with pilot  
Figure 11: (**a**) The curves of {a,b,c,d} and (**b**) adaptive parameter Qpol.  
Figure 12: BER performance of FR = 1:7 compared with pure-16 QAM of dynamic polarization rotation.  
symbols have different performance dependence on Qpol. The performance of EKF relies on Qpol. High estimation accuracy is achieved with reduced estimation range when the Qpol is small, and low estimation accuracy is achieved with high estimation range when the Qpol is large. The proposed AKF with pilot symbols with different Qpol shows the same estimation accuracy and range.