Viterbi and Viterbi Algorithm based Phase Recovery for Probabilistically Shaped Signals

Unlike the scenario in traditional high-order QAM signals, Viterbi and Viterbi (V&V) algorithm becomes more powerful for carrier phase recovery (CPR) in probabilistically shaped (PS) signals. The reason relies on that the PS signals assign much higher probability to the innermost 4 constellation points, which are qualified for V&V algorithm. In this article, we compare the performance of V&V algorithm to that of blind phase search (BPS) algorithm for PS-64 QAM and PS-256 QAM in the aspects of window size and signal to noise ratio under the constraint of different laser linewidths. Besides, the impact of signal entropy on both algorithms is investigated. The computational complexity and running time for both algorithms are also summarized. Results show that the two algorithms perform similarly for PS-64 QAM signals when the linewidth is less than 1 MHz while the running time of BPS algorithm is at least 45 times longer than that of V&V algorithm. Finally, we conduct a coherent detection based optical back-to-back experiment where the laser linewidths of both transmitter laser and local oscillator are 100 kHz. For PS-64 QAM, both V&V and BPS algorithms show negligible penalty compared to the performance of homodyne detection, verifying the feasibility of applying V&V algorithm in the CPR of PS-64 QAM.