Low-complexity robust baud-rate clock recovery for probabilistically shaped Nyquist signals in short-reach coherent transmission systems

Probabilistic shaping (PS) has emerged as a promising technique in enhancing the capacity and adaptability of coherent transmission systems. However, it is reported that the impact of the PS on clock recovery may be detrimental and lead to the malfunction of coherent receivers. The joint clock recovery and adaptive equalization (JCA) scheme proposed by us recently is a comprehensive and hardware efficient solution for short-reach coherent transmission systems. It can realize clock recovery, as well as chromatic dispersion (CD) and receiver IQ skew compensation, and can accommodate Nyquist signals with small roll-off factors (ROFs). In this letter, we investigate the impact of the PS on the clock recovery performance of the JCA scheme, focusing specifically on its core the baud-rate modified Mueller and Müller timing phase error detector (3M-TPED). Its performance is compared with the other PS compatible clock recovery techniques with both numerical simulations and experiments. It has been proved that the proposed scheme is more robust for the PS, CD and local oscillator frequency offsets.