We propose a two-stage equalization based on a simplified Kalman filter, which is used to solve the rapid rotation of the state of polarization (RSOP) that is caused by lightning strikes on optical cables and the extra inter symbol interference (ISI) introduced in the system. By analyzing the special expression of matrix coefficient in the Kalman filter under polarization demultiplexing, the simplified idea of a Kalman filter is provided, and its updating process is transformed into a kind of multiple-input-multiple-output (MIMO) structure algorithm. At the same time, the second stage finite impulse response filter is used to solve the ISI that is difficult to be solved by a Kalman filter. The performance of the proposed algorithm was tested in a coherent system of 28Gbaud PDM-QPSK/16QAM. The results confirm that on the basis of lower complexity than a Kalman filter, the proposed algorithm reduces its complexity by more than 30% compared to traditional MIMO equalization algorithm under the premise of linear operation, and which also can handle RSOP of 20 Mrad/s. When the system suffers from the extra ISI due to the limited device bandwidth, the optical signal to noise ratio of the proposed algorithm is about 4 dB lower than the Kalman filter at the same bit error rate.
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