Adaptive Frequency-Domain Equalization in Mode-Division Multiplexing Systems

Long-haul mode-division multiplexing (MDM) employs adaptive multi-input multi-output (MIMO) equalization to compensate for modal crosstalk and modal dispersion. MDM systems must typically use MIMO frequency-domain equalization (FDE) to minimize computational complexity, in contrast to polarization-division-multiplexed systems in single-mode fiber, where time-domain equalization (TDE) has low complexity and is often employed to compensate for polarization effects. We study two adaptive algorithms for MIMO FDE: least mean squares (LMS) and recursive least squares (RLS). We analyze tradeoffs between computational complexity, cyclic prefix efficiency, adaptation time and output symbol-error ratio (SER), and the impact of channel group delay spread and fast Fourier transform (FFT) block length on these. Using FDE, computational complexity increases sublinearly with the number of modes, in contrast to TDE. Adaptation to an initially unknown fiber can be achieved in ~3-5 μs using RLS or ~15-25 μs using LMS in fibers supporting 6-30 modes. As compared to LMS, RLS achieves faster adaptation, higher cyclic prefix efficiency, lower SER, and greater tolerance to mode-dependent loss, but at the cost of higher complexity per FFT block. To ensure low computational complexity and fast adaptation in an MDM system, a low overall group delay spread is required. This is achieved here by a family of graded-index graded depressed-cladding fibers in which the uncoupled group delay spread decreases with an increasing number of modes, in concert with strong mode coupling.