Sparse Adaptive Frequency Domain Equalizers for Mode-Group Division Multiplexing

In this paper, we develop low complexity sparse frequency domain equalizers (FDEs) that exploit the sparsity that we observe in the graded index multimode fiber multiple-input multiple-output channel. The sparse channel impulse response is caused by the strong crosstalk at the mode MUX/DEMUX and weak coupling in the fiber between different mode groups. Two sparse FDE designs are proposed in order to compensate the crosstalk with relatively low computational complexity. The first method is based on a priori knowledge of the channel impulse response, which is used to generate a mask of taps with significant magnitudes. The second method is based on the improved proportionate normalized least-mean-square algorithm, where the active and inactive taps are adjusted at different rates of convergence. The computational complexity and the system performance of the proposed algorithms are analyzed. It is shown that the sparse FDEs offer low complexity relative to the sparse equalizers that use delay buffers, while maintaining improved performance over non-sparse equalizers in the presence of noise.