Kalman filter polarization demultiplexing algorithm based on diagonalized matrix treatment

Abstract

When we implement the equalizations of polarization effects using a Kalman filter (KF) in a coherent optical fiber communication system, we will require to multiply many matrices. If the state vector describing the system has a dimension of n, the state error covariance matrix P will have the dimension of n × n, and other matrices used in the Kalman filter will also have the dimension of n × l (l is the dimension of the measurement vector). If n is very large, the KF-based algorithm will suffer from significant complexity, which results in an impractical KF-based polarization demultiplexing algorithm. In this paper, we propose a new structured KF-based polarization demultiplexing algorithm in which the state error covariance matrix P is diagonalized, which we call the diagonalized Kalman filter (DKF). We theoretically analyze the rationality of the DKF, and the validity of the DKF was verified in both 64 Gbaud polarization-division multiplexed (PDM) QPSK and 16QAM Nyquist coherent optical simulation systems. Compared with the conventional KF, simulation results proved that under a rotation of state of polarization from 1 to 10 Mrad/s for QPSK and 1 to 5 Mrad/s for 16QAM, a differential group delay from 15 to 75 ps, and a residual chromatic dispersion of 100 ps/nm, the OSNR penalties for the DKF are only within 0.5 dB for QPSK at the threshold BER = 3.8 × 10−3, and within 2 dB for 16-QAM at the threshold BER = 2 × 10−2, respectively, compare to the case of no impairment. In the meantime, for the proposed DKF, a computational complexity reduction of over 30% is achieved, compared with conventional KF, at the expense of about no more than 50 symbols convergence delay.