MIMO carrier phase recovery for carrier-asynchronous SDM-MIMO reception based on the extended Kalman filter.

We propose a novel phase recovery scheme designed for coherent space division multiplexing (SDM) systems with independently-operated asynchronous light sources. The proposed scheme is based on the approach of the extended Kalman filter and is referred to as multiple-input multiple-output carrier phase recovery (MIMO-CPR). In the minimum mean squared error (MMSE) sense, it simultaneously and optimally obtains estimates of the multiple phase errors arising from phase-unlocked asynchronous light sources. To ensure the scheme's application for SDM fibers with a time-varying property, we also describe a modification to incorporate a MIMO equalization scheme and analyze the computational complexity. The performance of the proposed MIMO-CPR scheme is investigated through numerical simulation, which shows that it has a tolerance for the sum linewidth symbol duration product of up to 3.4 × 10, 1.0 × 10 and 2.2 × 10 for QPSK, 16QAM, and 64QAM signals, respectively, if 1-dB optical signal-to-noise ratio (OSNR) penalty is allowable to achieve BER of 10. Transmission experimental results using three spatial modes in a 51-km-long few-mode fiber (FMF) also verify the applicability of the MIMO-CPR scheme to carrier-asynchronous coherent SDM-MIMO systems.