Low-complexity carrier synchronization for PS 64-QAM based on kernel RLS and zero-averaging blind phase search

With the exponentially increasing demand for high-speed information transfer, the role of probabilistic shaping has become increasingly important; however, it necessitates modifications to existing digital signal processing architectures to ensure error-free transmission. In this work, we propose a two-stage carrier synchronization method combining a kernel recursive least-squares (KRLS) filter with zero-averaging blind phase search (BPS). The method jointly synchronizes phase and frequency at the receiver while also compensating for any nonlinear phase noise present in the data. Simulation results on a probabilistically shaped 64-QAM constellation at a symbol rate of 33.33 GBaud per polarization demonstrate a significant improvement in generalized mutual information (GMI) compared to other widely used algorithms under various channel conditions. At high shaping factors, where fast Fourier transform (FFT)-based frequency estimators typically fail, the proposed method maintains accurate carrier synchronization and delivers consistently high GMI. When the optical signal-to-noise ratio (OSNR) is varied by adjusting the incident optical power, our method achieves an optimal OSNR gain of 4 dB compared to the commonly used FFT + BPS combination, thereby enhancing nonlinear tolerance and also shown to extend the transmission reach to 8000 km under a normalized GMI threshold. The computational load is substantially reduced compared to traditional BPS and FFT, making the approach well-suited for real-time digital signal processing in long-haul coherent systems.