A Sparsity Managed Adaptive MIMO Equalization for Few-Mode Fiber Transmission With Various Differential Mode Delays

Abstract

It is often observed that various differential mode delays (DMDs) coexist in single multi-core fiber (MCF) and/or few-mode fiber (FMF) transmission. From a multi-input and multi-output (MIMO) equalization perspective, this indicates optimum equalization tap length for each multi-core and/or multi-mode signal varies according to its DMD. Correspondingly, complex calculation of finding each optimum tap length is necessary to obtain satisfactory performance. This paper presents a new adaptive MIMO equalization method to deal with various DMDs while avoiding such complex calculation. The method uses the same tap length for all multi-core and/or multi-mode signals according to the maximum DMD to reduce the calculation cost. To rectify negative effects such as noise enhancement due to the non-optimum tap length setting, the method applies the improved proportionate normalized least mean square (IPNLMS) with leveraged equalization coefficients update on the basis of the overall sparsity of coefficients. IPNLMS inherently updates equalization coefficients by proportionately promoting the previous coefficients in order that the coefficients of signal part are promoted while those of noise part are suppressed. To determine the IPNLMS parameters that govern the amount of the promotion, the presented method uses a simple sparsity metric that calculates the overall sparsity of coefficients. Then, the sparsity metric is mapped to IPNLMS parameters in a manner that the overall sparsity of coefficients is progressively facilitated as adaptation. Evaluations using experimental data of FMF transmission over 527 km end-to-end with 33.2 ns maximum DMD show the presented method effectively deals with various DMDs to suppress the noise and obtains 0.7 dB of Q-factor performance enhancement comparing to the conventional method.