## 4 Results and Discussion
### Results
It can be found that the phase noise (or effective phase noise) induced BER floor in the block-wise average carrier phase recovery algorithm is increased with the increment of block length. Generally, a smaller block length will lead to a lower phase noise induced BER floor due to a more accurate estimation of carrier phase, while a larger block length is more effective for mitigating the amplitude noise (such as the amplified spontaneous emission--ASE--noise) to improve the SNR sensitivity. In practical transmission systems, the optimal  
Figure 6: BER floors versus laser linewidths in the one-tap normalized LMS carrier phase recovery in the optical fiber transmission systems using different modulation formats. The indicated linewidth value is the 3-dB linewidth for both the Tx and the LO lasers. Figure 7: BER floors versus transmission distances in the one-tap normalized LMS carrier phase recovery in the coherent optical transmission systems using different modulation formats, considering the equalization enhanced phase noise. Both the Tx and LO lasers linewidths are 1 MHz. block length is determined by considering the trade-off between the phase noise and the amplitude noise. As an example, the block length of \(N_{BWA}=11\) is employed in all subsequent analyses, if the value is not specified. Based on Equations (12) and (13), the performance of the block-wise average carrier phase recovery in the coherent optical communication systems using different modulation formats is shown in Figure 8b, where the block length is 11. It can be found in Figure 8b that the block-wise average carrier phase recovery algorithm is also very sensitive to the phase noise variance and the modulation formats, when phase noise variance is less than 0.1. Based on the analyses in Equations (1), (12) and (13), the BER floors versus laser linewidths in the block-wise average carrier phase recovery for the back-to-back case or without considering EEPN has been studied in Figure 9, where the indicated linewidth value is the 3-dB linewidth for both the transmitter laser and the LO laser. It can be found that the BER floors in the block-wise average carrier phase recovery are also degraded with the increment of modulation format levels and laser linewidths. The degradations due to the laser phase noise (laser linewidths) are also more severe for higher-level modulation formats. Figure 8: BER floors versus phase noise variances in the block-wise average carrier phase recovery in the coherent optical transmission systems. (**a**) Different block lengths in the 8-PSK transmission system; (**b**) different modulation formats with the block length of 11. As shown in Figure 10, the BER floors of the block-wise average carrier phase recovery have been investigated for different transmission distances by considering the impact of EEPN, where the linewidths of both the Tx and the LO lasers are set to 1 MHz. It can be found that the performance of the block-wise average carrier phase recovery is degraded significantly with the increment of transmission distances, and this effect is more severe for higher-level modulation formats, since the EEPN influence will scale with the increment of transmission distances and modulation formats. From Figures 11-13, the performance of the Viterbi-Viterbi carrier phase recovery approach has been investigated in terms of the phase noise variances, the laser linewidths and the transmission distances. The BER floors versus the phase noise variances in the Viterbi-Viterbi carrier phase recovery algorithm is studied in Figure 11. In Figure 11a, the BER floors are also studied in terms of different block lengths in the Viterbi-Viterbi CPR algorithm for the 8-PSK optical transmission system. Similar to the block-wise average algorithm, a smaller block length in the Viterbi-Viterbi carrier phase recovery will generate a lower phase noise induced BER floor; in contrast, a larger block length is more tolerant to the amplitude noise and will lead to better SNR sensitivity.