Kernel adaptive filtering-based phase noise compensation for pilot-free optical phase conjugated coherent systems

In coherent optical systems, Kerr nonlinearity-induced distortions and accumulated chromatic dispersion can be simultaneously compensated using optical phase conjugation (OPC). In fiber-based OPC devices, a common approach to overcome the limitation on the launched pump power imposed by stimulated Brillouin scattering is reducing the integrated power spectral density over the Brillouin bandwidth by imparting a phase modulation to the pump source. However, the phase distortions induced by the pump phase modulation on the conjugated signal can degrade the phase-modulation signal performance. Similarly, modulating the two pumps in a dual-pump OPC system with the opposite phase modulation to suppress phase modulation transfer to the conjugated signal is difficult to perform exactly as it involves adjusting the amplitude and delays of the electrical signals driving the phase modulators.

Some residual dithering is common in practice, even when dithering settings are carefully adjusted. Most existing digital signal processing phase recovery methods for high-order signal modulation formats have been developed to estimate and compensate the phase noise induced by laser nonzero spectral width in conventional coherent optical systems. Unfortunately, these methods are unsuitable for counteracting the imperfection effects associated with dithering schemes of OPC systems.

Recently, machine learning methods have been identified as promising approaches for addressing some inherent challenges in optical communications, such as nonlinear transmission impairments. Kernel methods are a powerful framework for solving nonlinear problems in machine learning and signal processing, which use kernels (or basis functions) to map the input space of the data to a higher dimensional feature space, in which simple linear models can be applied. Specifically, kernel-based adaptive filtering (KAF) techniques can be used to recover desired signals by adapting their parameters as new data become available, typically minimizing a least-squares (LS) cost function.

Herein, Aston University researchers: Dr. Sonia Boscolo, Dr. Tu Nguyen, Dr. Abdallah Ali, Dr. Stylianos Sygletos and Professor Andrew Ellis developed a KAF method to mitigate phase noise induced by deviations from ideal pump counter-dithering in dual-pump fiber-based OPC of pilot-free quadrature-amplitude modulation (QAM) signals. In their approach, a sliding window kernel-based recursive LS (KRLS) algorithm was used to facilitate the phase noise compensation. The online algorithm was used to track the time variations of the signal phase after conventional phase noise compensation (blind phase search, BPS) based on data from the fixed-size windows and computations of the updated solution for each window. Their work is currently published in the journal, Optics Express.

The KRLS-based technique was numerically and experimentally verified using 28-Gbaud dual-polarization 16-QAM signals in an optical back-to-back OPC configuration. It exhibited 0.4 dB improvement in signal-to-noise ratio over the BPS method under fully optimized pump dithering settings. Also, it could accommodate pump-phase mismatch levels with negligible performance penalty across small to moderate mismatch values. As a result, a sufficiently higher signal-to-noise ratio of the system and a relatively small impact of the residual dithering phase noise were desired to realize the full benefits of the proposed method. This was attributed to the high sensitivity of the solution update to wrong decision symbols. The performance gain over conventional phase noise compensation under small or moderate dithering-induced phase noise was preserved in transmission, although the gain was reduced with an increase in the transmission length.

In summary, the authors developed a KRLS algorithm-based phase noise compensation method to estimate and correct the phase distortion arising from residual pump dithering in OPC-assisted pilot-free coherent systems. Unlike existing dithering compensation methods, the presented approach requires no prior knowledge of the dithering frequencies and is highly sensitive to the residual dithering. he deployed KRLS algorithm is non-parametric in nature, hence indifferent to the number of dithering frequencies used, which makes the presented method potentially applicable to cascaded OPC systems. In a statement to Advances in Engineering, first author Dr. Sonia Boscolo explained that the presented scheme would be a powerful tool for improving the performance of OPC-assisted coherent optical systems.