## 4 Results and Discussion
### Results
It is also found in Figure 14 that for the small phase noise variance (or effective phase noise variance), the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms, while for the large phase noise variance (or effective phase noise variance), the one-tap normalized LMS algorithm shows a better performance than the other two algorithms in the carrier phase recovery. Figure 5:0 BER floors versus laser linewidths in the Viterbi-Viterbi carrier phase recovery in the coherent optical transmission systems using different modulation formats. The block length is 11, and the indicated linewidth value is the 3-dB linewidth for both the Tx and the LO lasers. Figure 5:1 BER floors versus transmission distances in the Viterbi-Viterbi carrier phase recovery in the coherent optical transmission systems using different modulation formats. The block length is 11, and the linewidth of both the Tx and the LO lasers are 1 MHz. As shown in Figures 15 and 16, the comparison of the one-tap normalized LMS, the block-wise average, and the Viterbi-Viterbi carrier phase recovery algorithms has also been investigated in terms of different modulation formats. Here a block length of \(11\) is used in the block-wise average and the Viterbi-Viterbi algorithms. It can be found in Figure 15 that the BER floors in all the three algorithms are increased with the increment of modulation formats, but the variation in the one-tap normalized LMS CPR algorithm is larger than in the other two algorithms. Therefore, the one-tap normalized LMS algorithm is more sensitive to the level of the modulation formats. Figure 5:2 BER floors versus different phase noise variances in the three carrier phase recovery algorithms in the 8-PSK optical fiber communication systems. (**a**) Block length of the BWA and VV algorithms is 5; (**b**) block length of the BWA and VV algorithms is 11; (**c**) block length of the BWA and VV algorithms is 17. Figure 16 shows the performance of BER floors versus transmission distances in the three carrier phase recovery methods under different modulation formats, where the linewidths of both the transmitter and the LO lasers are set as 1 MHz and the transmission distance are set from 0 km to 5000 km. It can also be found in Figure 16 that, similar to Figure 15, the one-tap normalized LMS algorithm is more sensitive to the level of the modulation formats than the block-wise average and the Viterbi-Viterbi CPR algorithms. In addition, the Viterbi-Viterbi algorithm outperforms the other two carrier phase recovery approaches when the transmission distance varies from 0 km to 5000 km,  
Figure 5:3 BER floors versus different transmission distances in the three carrier phase recovery algorithms in the optical fiber communication systems using different modulation formats. Linewidths of the transmitter and LO lasers are both 1 MHz, and block lengths of the BWA and VV CPR algorithms are both 11. **(a)** QPSK system; **(b)** 8-PSK system; **(c)** 16-PSK system; **(d)** 32-PSK system. Figure 5:4 BER floors versus different phase noise variances in the three carrier phase recovery algorithms in the optical fiber communication systems using different modulation formats. Block lengths of the BWA and VV algorithms are both 11. **(a)** QPSK system; **(b)** 8-PSK system; **(c)** 16-PSK system; **(d)** 32-PSK system. while the differences between the three carrier phase recovery algorithms become smaller with the increment of modulation formats.