## 3 Simulation Results
The behavior of the interpolators remains consistent when the linewidth is increased to \(\Delta\
u=400\times 2\,\mathrm{kHz}\) at the given symbol rate, as illustrated in Figure 11. A significant modification to the frequency interpolator was made by expanding its bandwidth to \(450\,\mathrm{MHz}\), resulting in better performance. However, issues previously observed at the bandwidth edges reappeared despite this adjustment. Therefore, it can be concluded that the interpolator that combines the cosine and RLOWESS filters consistently outperforms the others. In Figure 12, the parameters are set as follows: \(\Delta\
u=800\times 2\,\mathrm{kHz}\), a symbol rate of \(50\,\mathrm{Gbaud}\), and a modulation order of \(16\,\mathrm{QAM}\). On the basis of previous results, the Cosine-RLOWESS technique has been established as the reference interpolator. Here, its performance is compared to a blind phase search (BPS) algorithm using 32 phases, which is suitable for improved performance with 16 QAM. The Cosine-RLOWESS interpolator demonstrates stable performance across the entire SNR range, consistently outperforming the BPS algorithm. Figure 11: Comparison of various CPR algorithms for BER versus SNR for 64 QAM modulation, \(\Delta\
u=400\,\mathrm{kHz}\times 2\), \(\mathrm{Rs}=50\,\mathrm{Gbaud}\). Figure 10: Comparison of various CPR algorithms for BER versus SNR for 64 QAM modulation, \(\Delta\
u=100\,\mathrm{kHz}\times 2\), \(\mathrm{Rs}=50\,\mathrm{Gbaud}\). At approximately 16 dB SNR, the Cosine-RLOWESS interpolator shows a gain of 0.5 dB over the BPS algorithm. A key advantage of the Cosine-RLOWESS method is its ease of reconfiguration. In contrast, as will be discussed later, changing the modulation scheme with the BPS algorithm requires reconfiguring its differential encoding. In Figure 13, the modulation order is increased to 64 QAM, and the phase search is expanded to 64 phases, meeting the minimum requirements for this modulation type, which typically requires at least 32 phases [1]. These results align with previous observations for the 16 QAM constellation. At an SNR of 23 dB, the Cosine-RLOWESS interpolator achieves a gain of 0.2 dB over the BPS algorithm at a BER of \(1\times 10^{-3}\). However, as the SNR increases and \(\Delta\
u T_{s}\) grows, the performance gap between algorithms diminishes. However, the Cosine-RLOWESS method continues to demonstrate stability across the entire SNR range, underscoring its robustness. In Figure 14, the parameters are set as follows: \(\Delta\
u=200\,\mathrm{kHz}\times 2\), a symbol rate of 50 Gbaud, and a modulation order of 256 QAM. These values are consistent with the requirements of the modulation format. Although there are visible differences compared to  
Figure 5:0 Comparative analysis of Cosine-RLOWESS and BPS algorithms in BER performance vs. SNR for 16 QAM modulation at a linewidth of \(\Delta\
u=800\,\mathrm{kHz}\times 2\). Figure 5:1 Comparative analysis of Cosine-RLOWESS and BPS algorithms in BER performance vs. SNR for 64 QAM modulation at a linewidth of \(\Delta\
u=800\,\mathrm{kHz}\times 2\). the theoretical curve, the Cosine-RLOWESS interpolator achieves results comparable to those of the BPS algorithm. These findings suggest that the Cosine-RLOWESS interpolator performs optimally with lower modulation orders and smaller linewidths. However, with higher modulation orders such as 256 QAM and significant linewidth effects, its performance converges with that of the BPS algorithm. Figure 15 illustrates the sensitivity penalty at a BER of \(10^{-3}\) for different modulation formats when compensating for phase noise using the BPS and Cosine-RLOWESS algorithms. The Cosine-RLOWESS algorithm demonstrates strong robustness against low values of \(\Delta vT_{s}\). Specifically, for the QPSK, 16 QAM, and 64 QAM modulation formats, the sensitivity penalty in dB is consistently lower compared to BPS [1; 32; 39], particularly when \(\Delta vT_{s}\) is below \(10^{-5}\).