Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers.

We propose a fractionally spaced frequency-domain adaptive multi-input multi-output (MIMO) filter architecture in which the sampling rate of input signals is below 2× oversampling with a non-integer oversampling factor for mode demultiplexing in long-haul transmission over coupled multi-core fibers. The frequency-domain sampling rate conversion to the symbol rate, i.e., 1× sampling, is placed after the fractionally spaced frequency-domain MIMO filter. The filter coefficients are adaptively controlled by stochastic gradient descent and gradient calculation with back propagation through the sampling rate conversion from the output signals on the basis of deep unfolding. We evaluated the proposed filter through a long-haul transmission experiment of 16-channel wavelength-division multiplexed and 4-core space-division multiplexed 32-Gbaud polarization-division-multiplexed quadrature phase shift keying signals over coupled 4-core fibers. The fractional oversampling frequency-domain adaptive 8×8 filter with 9/8× oversampling provided little performance penalty after 6240-km transmission compared to the conventional 2× oversampling frequency-domain adaptive 8×8 filter. The computational complexity in terms of the required number of complex-valued multiplications was reduced by 40.7%.