Closed-Form Statistics and Design of Mode-Division-Multiplexing Systems Employing Group-Delay Compensation and Mode Permutation
Anirudh Vijay, Nika Zahedi, Oleksiy Krutko, Rebecca Refaee, Joseph M. Kahn · Journal of Lightwave Technology · 2025
Excessive accumulation of group-delay 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 multi-mode fiber. Group-delay compensation, which involves periodically exchanging propagating signals between modes with lower and higher group delays, can potentially reduce group-delay spread. In this work, we investigate two group-delay compensation schemes: conventional compensation, which alternates fiber types with opposite group delay orderings, and self-compensation, which employs a single fiber type with periodically inserted mode permuters. We provide analytical expressions for group-delay statistics in compensated systems with arbitrary multi-mode fiber types and mode permuters, accounting for random inter-group coupling, mode scrambling, and refractive index errors. To enhance the effectiveness of group-delay compensation over the C-band, we propose optimized graded-index depressed-cladding multi-mode fibers 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 group-delay characterization and sorting. Design examples and numerical simulations demonstrate improved system performance, highlighting the trade-offs between compensation effectiveness, system complexity, and transmission losses. For a 5000 km multi-mode fiber link, the design examples achieve a group-delay standard deviation of 438$~\textrm {ps}$(effectively 6.2$~\textrm {ps}/\sqrt{\textrm {km}}$) and 257$~\textrm {ps}$(effectively 3.6$~\textrm {ps}/\sqrt{\textrm {km}}$) for conventional and self-compensation schemes, respectively, under ideal conditions. In the presence of random inter-group coupling (characteristic coupling length = 500km), the group-delay standard deviation increases to 803$~\textrm {ps}$(11.4$~\textrm {ps}/\sqrt{\textrm {km}}$) and 575$~\textrm {ps}$(8.1$~\textrm {ps}/\sqrt{\textrm {km}}$), respectively. Additionally, with refractive-index errors (error STD =$10^{-5}$), the group-delay standard deviation further increases to 1.28$~\textrm {ns}$(18.1$~\textrm {ps}/\sqrt{\textrm {km}}$) for both schemes.