CMA-based adaptive MIMO equalization for MDM systems.

In modern optical communication systems, mode division multiplexing (MDM) faces challenges such as intermodal interference, mode coupling, and differential mode delay. Traditional multiple input multiple output (MIMO) equalization algorithms, including the constant modulus algorithm (CMA), have shown limitations in terms of convergence speed, precision, and robustness. In this work, a CMA-Adam-NAG equalization algorithm is proposed, which integrates the strengths of the adaptive learning capability of the adaptive moment estimation method (Adam) and predictive updates of the Nesterov accelerated gradient method (NAG) into CMA. The proposed equalization algorithm achieves faster convergence, reduced steady-state errors, and improved stability by addressing the shortcomings of conventional CMA, such as its tendency to get trapped in local minimum and slow convergence. An experiment is conducted on 10 km few-mode fiber (FMF) for 20 GBaud and 40 GBaud DP-QPSK 4 × 4 MDM systems, respectively. The experimental results demonstrate that the proposed CMA-Adam-NAG equalization algorithm consistently outperforms the conventional CMA in terms of convergence and symbol error rate (SER). The proposed equalization algorithm achieved faster convergence with only 100 iterations, which is much faster than that of the CMA equalization algorithm (400 iterations). Furthermore, compared with CMA, the proposed scheme achieved lower SER values and better signal quality, making it a robust and efficient solution for blind equalization in advanced optical communication systems.