A fast MIMO frequency domain equalization for MDM systems

In mode division multiplexing (MDM) systems, mechanical or acoustic disturbances can cause modal coupling changes on timescales as short as tens of microseconds, which requires multi-input multi-output (MIMO) frequency-domain equalization (FDE) be able to adapt quickly. Based on the least mean squares Newton (LMS-Newton) algorithm, the LMS-Newton–Nesterov accelerated gradient (LMS-Newton–Nesterov) algorithm is proposed for six-mode MDM transmission systems. The Nesterov accelerated gradient method accelerates convergence by adding a correction factor, subtracting the momentum term from the loss function to adjust the current direction, and then updating the parameters based on this gradient. Simulation results suggest that the LMS-Newton–Nesterov algorithm converges faster to a lower asymptotic mean-square error (MSE) than the LMS and LMS-Newton algorithms, and the convergence rate would be correspondingly enhanced by 83.3% and 66.7%, respectively. After the LMS-Newton–Nesterov algorithm, the equalized signal is more ideal than the LMS and LMS-Newton algorithm. In six-mode MDM systems with QPSK, the LMS-Newton–Nesterov algorithm outperforms LMS and LMS-Newton algorithms by $1.8dB$ and $0.8dB$ at a symbol error rate (SER) of $10^{-3}$, respectively. The research results have guiding significance for improving the performance of MIMO FDE.