Performance of momentum-based frequency-domain MIMO equalizer in the presence of feedback delay

A frequency-domain multiple-input multiple-output (FD-MIMO) equalizer employing a momentum-based gradient descent update algorithm is proposed for polarization multiplexing coherent receivers. Its performance in operation with dynamically varying optical channels is investigated and the impact of filter update delays, arising from the latency of the fast Fourier transforms (FFTs) and other digital signal processing (DSP) operations in the feedback loop, is assessed. We show that the proposed momentum-based gradient descent algorithm used to control the equalizer response has significantly greater tolerance to feedback delay than the conventional gradient descent algorithm. We considered a 92 Gbaud dual-polarization 64 QAM receiver, with DSP operating at two samples per symbol, and with the equalizer operating on blocks of 512 and 1024 samples (i.e., 512/1024-point FFT). We found that at an optical signal-to-noise power ratio (OSNR) of 35 dB, the momentum-based gradient descent algorithm can successfully track state-of-polarization (SOP) rotation at frequencies of up to 50 kHz and with filter update delays of up to 14 blocks (39 ns). In comparison, using the conventional gradient descent algorithm in an otherwise identical receiver, the equalizer performance starts to deteriorate at SOP rotation frequencies above 20 kHz

Joint estimation of dynamic polarization and carrier phase with pilot-based adaptive equalizer in PDM-64 QAM transmission system

A pilot-based adaptive equalizer is investigated for high cardinality polarizationdivision-multiplexing quadrature amplitude modulation transmission systems. Pilot symbols are periodically inserted for joint estimation of the dynamic state of polarization (SOP) and carrier phase, in a least mean square (LMS) sense. Compared to decision-directed least mean square (DDLMS) equalization and radially-directed equalization, the proposed equalizer can achieve robust equalization and phase estimation, especially in low optical signal-to-noise ratio (OSNR) scenarios. In an experiment on 56 GBaud PDM-64 QAM transmission over 400 km standard single-mode fiber, we obtained at least 0.35 bit per symbol generalized mutual information (GMI) improvement compared with other training symbol-based equalization when tracking 600 krad/s dynamic SOP. With the joint estimation scheme, the equalization performance will not be compromised even if the SOP speed reaches 600 krad/s or the laser linewidth approaches 2 MHz. For the first time, it is demonstrated that the pilot-based equalizer can track dynamic SOP rotation and compensate for fiber linear impairments without any cycle slips under extreme conditions