ADMM-Based MIMO Equalization Algorithm for SDM Transmission With High MDL Tolerance

In this paper, we propose a novel multiple-input multiple-output (MIMO) equalization algorithm for optical space division multiplexing (SDM) systems impaired by mode-dependent loss (MDL). The proposed algorithm is a least mean square (LMS)-like algorithm derived on the basis of the alternating direction method of multipliers (ADMM) framework and consists of an iterative filtering process and filter tap update process. The filtering process is implemented in the frequency domain using the overlap-save technique and the filter update process is a gradient descent-based algorithm which tries to minimize the mean squared error of the equalizer output. The computational complexity of the proposed algorithm increases in proportion to the number of iterations and is the same as that of conventional LMS-based MIMO equalization when the number of iterations is one. We evaluate, through simulations, the bit error rate (BER) performance of the proposed algorithm for a coupled multi-core fiber channel model with significant MDL. The simulation results show that increasing the number of iterations improves the BER performance significantly compared to the conventional LMS-based equalization algorithm. The proposed algorithm offers a good tradeoff between BER performance and computational complexity and enhances the MDL tolerance for SDM systems.