A Variable Step-Size Unconstrained Adaptive FD-LMS Algorithm for MDM Transmission

Mode-division multiplexing (MDM) over few-mode fibers has been proposed to break through the Shannon limit of the single-mode fiber. Mode coupling and differential mode group delay are two major drawbacks, which limit the performance of the system. In this paper, a variable step-size unconstrained adaptive frequency-domain least mean square (FD-LMS) algorithm is proposed for demultiplexing in a 6 × 6 MDM transmission. In an 80 km link, at the 7% FEC threshold, the least required optical signal noise ratio (OSNR) for the proposed algorithm is about 13.5 dB, which is the same as the constrained FD-LMS algorithm and the unconstrained FD-LMS algorithm. Besides, the proposed algorithm can improve the convergence speed by 45.1% and 56.9% in comparison with the constrained FD-LMS algorithm and the unconstrained FD-LMS algorithm. For the distance of 2000 km, the computational complexity of the proposed algorithm is 52.8% lower than that of the constrained FD-LMS algorithm. The effect of mode-dependent loss (MDL) on the proposed algorithm is also explored. The result shows that the MDL tolerance of the proposed algorithm is similar to the constrained FD-LMS algorithm, and the OSNR penalty of the proposed algorithm is 0.5 dB higher than that of the constrained FD-LMS algorithm at a transmission distance of 800 km.