Null space method for tap value initialization in constant modulus algorithm for mode division multiplexing systems.

Area of Science:

• Optical communication systems
• Signal processing for optical networks

Background:

• Mode division multiplexing (MDM) systems face challenges with sparse channels and large differential mode group delay (DMGD).
• Existing constant modulus algorithms (CMAs) may struggle with convergence in such demanding conditions.

Purpose of the Study:

• To propose a novel constant modulus algorithm (CMA) for mode division multiplexing (MDM) systems with enhanced convergence performance.
• To address singularity issues and tap convergence failures in MDM systems.

Main Methods:

• The proposed CMA utilizes a variable step size, inspired by the improved proportionate normalized least-mean-square (IPNLMS) algorithm.
• It incorporates a reinitialization strategy for tap coefficients when convergence issues arise, leveraging channel matrix properties in the frequency domain.
• The approach limits initial tap values within the null space of complex conjugate vectors to avoid singularity.

Main Results:

• The algorithm effectively avoids singularity and guarantees tap convergence.
• It demonstrates resilience to mode dependent loss (MDL), with no convergence failures observed for MDL below 4 dB.
• The proposed CMA reduces to the constrained CMA for two-mode systems, similar to polarization division multiplexing (PDM) systems.

Conclusions:

• The developed CMA provides robust performance for MDM systems, particularly in challenging sparse channel environments.
• The reinitialization strategy ensures reliable convergence and overcomes limitations of standard CMAs.
• The algorithm shows practical applicability and robustness against mode dependent loss.