Recursive Least Squares Based Low-Complexity Frequency-Domain MIMO Equalization for MDL-Tolerant Long-Haul Space Division Multiplexing Transmission

We propose a novel low-complexity, fast-converging frequency-domain multiple-input multiple-output (MIMO) equalization technique suitable for long-haul space division multiplexed (SDM) transmission. Based on the recursive least squares (RLS) method, the proposed scheme, referred to as out-of-band exclusive frequency domain equalization (OBE-FDE), provides a robust learning of MIMO filter coefficients even in the presense of accumulated mode dependent loss (MDL), while achieving reduced complexity by selectively performing computations only within the signal's bandwidth. Numerical evaluation results show that complexity reduction effect is enhanced with increased number of spatial modes in a specific roll-off factor range. Also demonstrated is an improved convergence tolerance against MDL introduced by the RLS adaptation, contrasting with the widely-used least mean squares (LMS) adaptation in scenarios involving long-haul MDL accumulation and/or high-mode-count mode division multiplexing (MDM) transmissions. We also show experimental demonstrations, proving that the proposed low-complexity RLS-adapted MIMO-FDE achieved a ten-fold faster learning of filter coefficients in 4-coupled core multi-core fiber transmission at 5528 km. Additionally, by newly applying the scheme into 10-spatial-mode transmission, a record-long signal transmission distance over 1560 km was achieved while reducing computational complexity requirements by 40%.