Closed-Form Statistics and Design of Mode-Division-Multiplexing Systems Employing Group-Delay Compensation and Mode Permutation

Excessive accumulation of group-delay (GD) spread increases computational complexity and affects tracking of receiver-based multi-input multi-output signal processing, posing challenges to long-haul mode-division multiplexing in multimode fiber (MMF). GD compensation, which involves periodically exchanging propagating signals between modes with lower and higher GDs, can potentially reduce GD spread. In this work, we investigate two GD compensation schemes: conventional compensation, which alternates fiber types with opposite GD orderings, and self-compensation, which employs a single fiber type with periodically inserted mode permuters. We provide analytical expressions for GD statistics in compensated systems with arbitrary MMF types and mode permuters, accounting for random inter-group coupling, mode scrambling, and refractive index errors. To enhance the effectiveness of GD compensation over the C-band, we propose optimized graded-index depressed-cladding MMFs with index profiles tailored to control mode-dependent chromatic dispersion. We also analyze the impact of fiber fabrication errors and explore mitigation strategies based on GD characterization and sorting. Design examples and numerical simulations demonstrate improved system performance, highlighting the trade-offs between compensation effectiveness, system complexity, and transmission losses.