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Research to mode division multiplexing (MDM) systems based on few-mode or multi-mode fibers is one of the hot spots to achieve the demand for rapidly increased global user data traffic. Polar code, with a very low encoding and decoding complexity to achieve Shannon Limit, is worthwhile to apply to MDM systems into the research. Besides, the acquisition of channel state information (CSI) is of great significance for equalization and detection of coherent receivers. However, CSI is considered to be fully known at receiver in most existing research and few research discusses impact of imperfect CSI induced by channel estimation on MDM systems.This paper investigates channel estimation problem in a polar-code-encoded fiber-optic MDM (P-PC-MDM) system, and studies effect on system performance with channel estimation under impact of mode-dependent loss (MDL) using different Multiple Input Multiple Output (MIMO) detection algorithms: Maximum Likelihood (ML), Minimum Mean Square Error (MMSE) and the improved Alternating Direction Method of multipliers based Infinity-Norm (ADMIN). Simulation results demonstrate that P-PC-MDM system achieves a low bit error rate in the range of 2-3 dB SNR faster than MDM system of more than 10 dB. Besides, the addition of channel estimation error acceptably degrades system performance, and the improved ADMIN detection algorithm has a better bit error rate performance than MMSE by 0.5-2dB, and computational complexity is 13 times lower than ML.Therefore, the P-PC-MDM system is proved to be feasible, and the improved ADMIN detection algorithm can represent a good candidate in P-PC-MDM system with channel estimation and MDL.
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