An adaptive Kalman filter for extreme polarization effects equalization in coherent optical communication system

Abstract The specially designed Kalman filter was proved to be competent to complete the polarization equalization in some extreme environments with the large time-varying polarization mode dispersion (PMD) and the ultrafast rotation of state of polarization (RSOP). But the performance of this kind of Kalman filter is strongly restricted by the initial noise statistics represented by the process noise covariance Q and the measurement noise covariance R which will limit its effectiveness in an actual scene. To solve this problem, this paper proposes an adaptive Kalman filter structure by an adjustable way of estimating the process noise covariance Q and the measurement noise covariance R based on the measurement residual in order to be adaptive to the time-varying environments. The performance of the proposed adaptive Kalman scheme is checked both by the simulation and experiment on the 28 Gbaud PDM-QPSK/16QAM coherent optical communication system platforms. The simulation and experiment results demonstrate that the proposed adaptive Kalman filter scheme has a stable and better performance of the equalization for large PMD combined with ultrafast RSOP, with a greater tolerance the to time-varying extreme polarization environments than that using the extended Kalman filter scheme adopted in our previous work.

[1]  C. Rizos,et al.  Improving Adaptive Kalman Estimation in GPS/INS Integration , 2007, Journal of Navigation.

[2]  Jinling Wang,et al.  Evaluating the Performances of Adaptive Kalman Filter Methods in GPS/INS Integration , 2010 .

[3]  Greg Welch,et al.  An Introduction to Kalman Filter , 1995, SIGGRAPH 2001.

[4]  Jiachuan Lin,et al.  Joint tracking and equalization scheme for multi-polarization effects in coherent optical communication systems. , 2016, Optics express.

[5]  M. Winter,et al.  Error Vector Magnitude as a Performance Measure for Advanced Modulation Formats , 2012, IEEE Photonics Technology Letters.

[6]  Simo Särkkä,et al.  Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations , 2009, IEEE Transactions on Automatic Control.

[7]  Bernhard Schmauss,et al.  Joint Tracking of Polarization State and Phase Noise Using Adaptive Cascaded Kalman Filtering , 2017, IEEE Photonics Technology Letters.

[8]  Zibo Zheng,et al.  Two-parameter-SOP and three-parameter-RSOP fiber channels: problem and solution for polarization demultiplexing using Stokes space. , 2018, Optics express.

[9]  Kwanho You,et al.  Adaptive Extended Kalman Filter Based Geolocation Using TDOA/FDOA , 2011 .

[10]  Qian Xiang,et al.  Adaptive and joint frequency offset and carrier phase estimation based on Kalman filter for 16QAM signals , 2019 .

[11]  M. Shtaif,et al.  The effect of the frequency dependence of PMD on the performance of optical communications systems , 2003, IEEE Photonics Technology Letters.

[12]  Zibo Zheng,et al.  Window-split structured frequency domain Kalman equalization scheme for large PMD and ultra-fast RSOP in an optical coherent PDM-QPSK system. , 2018, Optics express.

[13]  F. Jenau,et al.  Demanding response time requirements on coherent receivers due to fast polarization rotations caused by lightning events. , 2016, Optics express.

[14]  R. Mehra On the identification of variances and adaptive Kalman filtering , 1970 .

[15]  Kangping Zhong,et al.  Joint polarization tracking and channel equalization based on radius-directed linear Kalman filter , 2018 .

[16]  Kemalettin Erbatur,et al.  An improved real-time adaptive Kalman filter with recursive noise covariance updating rules , 2016 .

[17]  Armando N. Pinto,et al.  Extended Kalman Filter vs. Geometrical Approach for Stokes Space-Based Polarization Demultiplexing , 2015, Journal of Lightwave Technology.

[18]  Qian Xiang,et al.  Noise Adaptive Kalman Filter for Joint Polarization Tracking and Channel Equalization Using Cascaded Covariance Matching , 2018, IEEE Photonics Journal.

[19]  Sirish L. Shah,et al.  Identification of chemical processes with irregular output sampling , 2006 .

[20]  James B. Rawlings,et al.  The autocovariance least-squares method for estimating covariances: application to model-based control of chemical reactors , 2006, IEEE Transactions on Control Systems Technology.

[21]  R. Mehra Approaches to adaptive filtering , 1972 .

[22]  A. H. Mohamed,et al.  Adaptive Kalman Filtering for INS/GPS , 1999 .