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Abstract
Since the frequency offset estimation (FOE) must be implemented before the subcarrier de-multiplexing and chromatic dispersion compensation (CDC) for digital subcarrier multiplexing (DSM) signals, traditional FOE algorithms for single carrier transmission is no longer suitable. Here, we propose a hardware-efficient blind FOE solution for the DSM signals by monitoring spectral dips in the frequency domain. With the use of a smoothing filter, the estimation accuracy of FOE can be significantly increased. Moreover, we identify that the proposed FOE method is robust to various transmission impairments, including amplified spontaneous emission (ASE) noise, optical filtering, and fiber nonlinearity. The effective function of the proposed FOE method is numerically and experimentally verified under scenarios of both back-to-back (B2B) and the 2560 km standard single-mode fiber (SSMF) transmission, leading to a FOE error less than 100 MHz with a FFT size of 1024.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical coherent detection along with digital signal processing (DSP) has become a compelling solution for the implementation of high-capacity fiber optical transmission systems by exploiting the information encoding on all dimensions of the optical field. Although linear transmission impairments including polarization mode dispersion (PMD) and chromatic dispersion (CD) can be effectively mitigated in the digital domain, fiber nonlinearity imposes a limit on the transmission performance. Thus, mitigation and compensation of fiber nonlinearity have received worldwide research attentions recently [1]. In this context, digital subcarrier multiplexing (DSM) was extensively studied, because dividing the available bandwidth of a high baud-rate single-carrier transmission into several low baud-rate subcarriers without the spectrum overlapping can significantly improve the tolerance of fiber nonlinearity [2,3]. Furthermore, DSM systems allow the flexible adaption of both bandwidth and modulation format for each subcarrier. Therefore, flexible design of the spectral efficiency (SE) and a finer granularity in various transmission reaches becomes possible [4,5]. Meanwhile, the tolerance towards optical filtering in meshed networks can be enhanced as well [6]. Another advantage of using DSM is the simplification of the digital CD compensation (CDC) as the size of the static digital equalizer scales quadratically with the symbol rate, leading to a complexity reduction, when the CDC is implemented after the subcarrier de-multiplexing [7,8].
Frequency offset (FO) between the transmitter-side (Tx) laser and the receiver-side (Rx) local oscillator (LO) causes a time-variable phase fluctuation, leading to erroneous phase decisions [9,10]. As for DSM signals, the FO estimation (FOE) and compensation (FOC) should be carried out before the subcarriers demultiplexing. Otherwise, there occurs a significant performance penalty proportional to the number of subcarriers for an aggregated symbol rate. Figure 1 shows the relationship between the residual FO before the subcarrier de-multiplexing and the required optical signal-to-noise ratio (OSNR) to achieve a target normalized generalized mutual information (NGMI) of 0.861 for the 64 Gbaud DSM signals with DP-64QAM, when 20% overhead low-density parity-check (LDPC) code is used [11]. Obviously, the required OSNR increases with the growing number of subcarriers and the increment of residual FO. Therefore, it is compulsory to implement efficient FOE algorithms with high estimation accuracy before the subcarrier de-multiplexing. However, existing blind FOE algorithms, such as Fast Fourier transform (FFT) based FOE (FFT-FOE) or differential FOE (Diff-FOE), are mainly designed for single-carrier signals and not suitable for DSM systems since these algorithms must be implemented after the CDC [10,12]. Although the pilot-tone based FOE is an alternative for DSM signals by searching the pilot-tone before the CDC at the Rx, it not only sacrifices the SE by leveraging a guard-band but also leads to a receiver sensitivity penalty [13–15]. Recently, a FOE algorithm dedicated for DSM signals is proposed by locating the spectral edges at the Rx, but it requires more hardware resources for the implementation [16]. Moreover, it fails when there exists optical filtering effect induced by reconfigurable optical add-drop multiplexers (ROADMs) [17].
Fig. 1. Required OSNR with respect to the residual FO before the subcarrier de-multiplexing for 64 Gbaud DP-64QAM DSM signals.
In this paper, we propose a blind FOE algorithm for DSM signals by searching the spectrum dips among subcarriers. By reusing the spectral information for the CDC and subcarrier de-multiplexing, our proposed FOE method is hardware-efficient with a high estimation accuracy and a wide estimation range. In particular, it is transparent to the modulation formats allocated for each subcarrier. The numerical and experimental results indicate that the proposed FOE method is tolerant towards several transmission impairments including amplified spontaneous emission (ASE) noise, optical filtering, and fiber nonlinearity.
2. Operation principle
Figure 2 shows the electrical spectra of the 64 GBuad DP-64QAM DSM signal at the Tx and Rx with/without the FO of 2 GHz, respectively. The OSNR is 20 dB to emulate the ASE impact, the roll-off factor of Nyquist shaping with a root-raised-cosine (RRC) filter is 0.1, and the sampling rate is 80 GS/s. We can observe that there exist several dips in the electrical spectra of DSM signals at the Tx, while the dip positions vary with the FO occurred at the Rx. For instance, when the FO is 2 GHz, as shown in Fig. 2, those dips at the Rx spectra are integrally shifted by 2 GHz. With the position identification of those spectral dips, we can estimate the FO as we know the exact positions of these spectral dips at the Tx spectra. If we assume the number of subcarriers is $N = 2M$, then the number of spectral dips is $2M - 1$ and those spectral dips are located at
where $j \in [{1,2M - 1} ]$ is the dip label, $\alpha $ is the roll-off factor for Nyquist shaping and $B$ is the aggregate symbol rate for DSM signals. Obviously, there always exists a dip located at 0 GHz and the other $2M - 2$ dips are located symmetrically in the frequency domain. Due to the existence of FO, the position of spectral dip varies. At the Rx, we can observe $2M - 1$ spectral dips located at ${\hat{F}_j}$. Therefore, we can estimate the FO byFig. 2. Electrical spectra of 64 GBaud DP-64QAM DSM signals with a sampling rate of 80 GS/s at the Tx at the Rx without FO, and at the Rx with the FO of 2 GHz.
$\Delta {F_j}$ denotes the FOE value from $jth$ spectral dip. Generally, one dip is enough to realize the FOE. However, the benefits with the use of multiple dips can be twofold. First, the use of multiple dips helps to increase the estimation accuracy by minimizing the ASE impact. On the other hand, the use of multiple dips is helpful to increase the FOE range. If only one dip is used for the FOE, the FOE range is limited to $[ - (1 + \alpha ) \cdot B/4M,(1 + \alpha ) \cdot B/4M]$ due to the symmetric distribution of spectral dips. The use of multiple dips may eliminate the ambiguity introduced by the symmetric distribution of dips. As a result, the FOE range is enhanced to $[ - (1 + \alpha ) \cdot B/2,(1 + \alpha ) \cdot B/2]$, once the whole spectrum of DSM signal is obtained after coherent detection.
The typical DSP flow together with our proposed FOE method for DSM signals is presented in Fig. 3(a). After the correction of the receiver imperfection, the DSM signal is first de-multiplexed to $N$ independent subcarriers and each subcarrier is introduced to the CDC module. Thereafter, the subsequent DSP for each subcarrier includes the matched filtering, the adaptive equalization, and carrier phase recovery. Generally, the CDC and the subcarrier de-multiplexing are implemented in the frequency domain [7], thus we can reuse the data after FFT operation for the FOE, in order to minimize the Rx computational complexity. Please note that the FOC can be merged into the subcarrier de-multiplexing without additional hardware complexity, and the data from two polarizations can be averaged for the ease of processing. As for the FOE, the identification of spectral dips is practically limited by the spectral resolution which is determined by the FFT size, as shown in Fig. 3(a). A larger FFT size can improve the FOE accuracy, but increases the acquisition time and computational complexity. In order to extract the dip features with reasonable FFT size, we propose to use a smoothing filter with a rectangular window to the FFT data. Figure 3(b) shows the electrical spectrum of received 8-subcarrier DSM signal without /with a smoothing filter. The FFT size is 1024. With the aid of the smoothing filter, the spectral dips can be easily identified, as shown in Fig. 3(b). Thereafter, we can implement the FOE according to Eq. (2).
Fig. 3. (a) Typical Rx DSP procedures for DSM signals with our proposed FOE method. (b) The electrical spectrum of the received 8-subcarrier DSM signal without (left)/with (right) a smoothing filter (FFT size = 1024).
3. Simulation results and discussions
As shown in Fig. 4, we carry out numerical simulations for $B = 64G\textrm{baud}$ DP-64QAM DSM signals with $N = 8$ subcarriers to investigate the performance of our proposed FOE scheme. At the Tx, the roll-off factor for Nyquist shaping is 0.1 and no guard-band is reserved among subcarriers, indicating the aggregate bandwidth of the DSM signal is 70.4 GHz. To emulate an overall implementation signal-to-noise ratio (SNR) of 21 dB from the transceiver, additive white Gaussian noise (AWGN) is equally loaded at the Tx and Rx. Laser phase noise, the FO, and the CD are considered in our simulations. Specifically, the combined linewidth is 200 kHz, the FO is set to be 2 GHz, and the accumulated CD of each standard single mode fiber (SSMF) span is 5440 ps/nm at 1554 nm and 8 SSMF spans is under investigation. During the transmission, AWGN is loaded after each ROADM, in order to emulate the ASE noise from the gain-controlled erbium doped fiber amplifiers (EDFAs). The noise variance after each ROADM is assumed to be identical, and the total noise accumulated over the SSMF link is quantified by the OSNR. The ROADM model is based on Eq. (3) with a BOTF of 12 GHz [18]
We first investigate the impact of smoothing filter on the proposed FOE method and different filter responses are also taken into account for the ease of performance comparison. The relationship between the smoothing filter length and the estimated FO is illustrated in Fig. 5 under conditions of ONSR of 20 dB and 30 dB, respectively. It is clearly indicated, the increment of smoothing filter length is helpful to improve the FOE accuracy for all smoothing filters, due to the mitigation of ASE especially when the FFT size is small. When the smoothing filter length reaches to 5, the FOE accuracy becomes stable. However, when the smoothing filter length is further enlarged, the FOE accuracy gradually decreases. We owe this phenomenon to the fact that spectral lines out of the spectral dips are included and the spectral dips vanish after the digital filtering. Form the view of both the implementation complexity and the FOE accuracy, the rectangular filter with 5 taps is finally chosen for our next investigation. In particular, the rectangular filter with 5 taps is also identified to be the optimal value for DSM signals with different subcarrier numbers.
Fig. 5. Relationship between the estimated FO and the smoothing filter length under the OSNR of (a) 20 dB and (b) 30 dB.
Next, we investigate the performance of proposed FOE method with respect to various FO values under conditions of OSNR of 20 dB and 30 dB, respectively, as shown in Fig. 6. DSM signals with different number of subcarriers are also considered, and the FOE error is referred with the theoretical FO setting. Please note that the selected FO range of [-3 GHz, 3 GHz] covers maximal FO value of commercial transceivers mainly induced by temperature variation [14]. As shown in Fig. 6, all FOE curves almost overlap, indicating that the proposed FOE method ensures high estimation accuracy for various DSM signals. The FOE error is also presented in the inset and we find the FOE error is less than 100 MHz under both low and high OSNR scenarios. The NGMI curve with respect to the OSNR for DSM signals with different number of subcarriers and modulation formats is presented in Fig. 7. We allocate the same modulation format among all subcarriers and the reference represents the single-carrier case without the FO. Obviously, the proposed FOE scheme is insensitive to the used modulation formats, even when both the non-rectangular constellation such as 32/128-QAM and the probabilistic shaped (PS) constellation such as PS-16QAM are chosen, because the selection of modulation format will not change the electrical frequency spectrum shape of DSM signals. In addition, no performance penalty is observed for the DSM signals even with 16 subcarriers in comparison with the reference case without the FO, indicating of a high estimation accuracy for the proposed FOE method.
Fig. 6. Performance of the proposed FOE method under different OSNR conditions. (a) OSNR = 20 dB, (b) OSNR = 30 dB. Insets are the FOE error of the proposed method
Fig. 7. NGMI calculation as a function of OSNR for the 64 GBaud DSM signals with various modulation formats.
We further examine the performance of the proposed FOE method with respect to the FFT size, which determines the spectral resolution. The OSNR is set to be 20 dB for the evaluation of severe ASE impact. As shown in Fig. 8(a), we can observe that the estimation accuracy increases with the growing FFT size for all cases, and finally becomes saturated. Moreover, larger FFT size is generally required for DSM signals with more subcarrier numbers, because more spectral details are helpful to extract all dips. For the DSM signal with 2 to 16 subcarriers, the FFT size of 1024 is enough to realize an accurate FOE, indicating of a low computation complexity for the proposed FOE method. Then, we investigate the impact of RRC roll-off factor on the proposed FOC performance, when the roll-off factor varies from 0.01 to 0.25. As shown in Fig. 8(b), with the reduction of the roll-off factor, the estimation accuracy degrades. When the roll-off-factor is as small as 0.01, the proposed FOE method does not function well especially for the case with larger number of subcarriers, because the spectral dips disappear. However, this is not the usual case with such a low roll-off factor for practical implementation, because it will not only increase the implementation complexity of the RRC filter but also impose a big challenge for the timing recovery [20]. One possible solution to above issue is to allocate one subcarrier with a roll-off factor more than 0.01 and other subcarriers with a roll-off less than 0.01, in order to ensure the unchanged bandwidth occupancy of total DSM signals. Thereafter, we can detect the dedicated spectral dip created by the subcarrier with larger roll-off factor for the purpose of FOE. On the other hand, a better FOE accuracy is generally secured for the case with less subcarrier numbers, when small RRC roll-off factor is applied. We owe this phenomenon to the fact that those spectral dips especially located at the spectrum edge are more easily to disappear, due to the superposition of subcarrier spectra. Moreover, we also observe that the FOE accuracy slightly decreases when larger roll-off factor such as 0.25 is used, as those dips generated by the RRC shaping with large roll-off factor are not steep and the FOE error is likely to occur. We can conclude that the performance of proposed FOE method is related to the RRC shaping factor and we should carefully design the RRC roll-off factor for DSM signals to obtain a better FOE accuracy. Generally, roll-off factor of 0.1 is a good choice.
Fig. 8. (a) Tolerance of FFT size, and (b) tolerance of RRC roll-off factor for our proposed FOE method.
Finally, we investigate the proposed FOE performance with respect to the optical filtering induced by cascaded ROADMs in meshed network. We vary the 6-dB bandwidth of ROADM from 90 GHz to 60 GHz and strong optical filtering effect occurs after 8-loop SSMF transmission. Figure 9(a) shows the received spectrum after the use of smoothing filter for DSM signals with 8 and 12 subcarriers, given the 6-dB bandwidth of ROADM of 60 GHz. The spectral components above 25 GHz are completely filter out, resulting in the disappearance of dips at the spectrum edge. Fortunately, the spectral dips at the vicinity of 0 GHz still remain and we can use those spectral dips for the purpose of FOE. Practically, we utilize the spectral dips within 20 GHz for realizing the FOE under the condition of strong filtering, and the performance of our proposed FOE method is shown in Fig. 9(b) with respect to various ROADM 6-dB bandwidth. When the 6-dB bandwidth varies from 90-GHz to 60-GHz, our proposed FOE method secures a high FOE accuracy with an estimation error of less than 100 MHz. Therefore, our proposed FOE method is robust towards the optical filtering. Please note that the FOE scheme relying on the identification of the spectral edge at the Rx [16] fails at the presence of strong filtering effect, because the spectral edge vanishes. Our proposed FOE scheme guarantees higher FOE accuracy and lower implementation complexity in comparison with that in [16].
Fig. 9. (a) Received 64 GBaud DSM signal spectrum after passing through 8 cascaded ROADMs with 6-dB bandwidth of 60 GHz (FFT size = 1024). (b) Tolerance of optical filtering for the proposed FOE method.
4. Experimental results and discussions
The experimental setup is shown in Fig. 10. At the Tx, the electrical DSM signal with 4 subcarriers is offline generated and filtered by a RRC filter with a roll-off factor of 0.1, and then loaded into an arbitrary waveform generator (AWG) operated at 40 GS/s sampling rate with 6-bit resolution. The aggregate baud rate of DP-16QAM DSM signal is 35 GBaud. The output of an external cavity laser (ECL) with operation wavelength of 1554.54 nm and linewidth of less than 100 kHz is modulated by a dual-polarization I/Q modulator driven by the AWG. The output of the transmitter is firstly boosted by an EDFA. A variable optical attenuator (VOA) is then used to manage the launch power before the signal enters the re-circulating fiber loop. The fiber loop includes four sections of 80 km SSMF and EDFAs to compensate the transmission attenuation. When we evaluate the transmission performance against the optical filtering, a Finisar wave-shaper (WS) is inserted after the second EDFA. After fiber loop transmission, the signal is filtered, pre-amplified and filtered again. At the Rx, a coherent receiver is used to realize the polarization and phase diversity detection and four electrical outputs are recorded by an 80 GS/s real-time oscilloscope, for the offline verification of our proposed FOE scheme. The Tx and Rx DSP are the same as that in the simulation, except that a timing recovery module is added before the adaptive equalizer [21].
The estimated FO under the conditions of various OSNRs under the back-to-back (B2B) scenario is presented in Fig. 11(a). For the ease of performance comparison, a two-stage FOE implementation based on our proposed FOE method together with the FFT-FOE [9] is also under investigation. Note that FFT-FOE is implemented after CDC. To ensure fine FOE accuracy for the FFT-FOE, 16192 samples are used for the FFT-FOE. The transmission performance in terms of NGMI is also provided in Fig. 11 (a). As we can see, the estimated FO value keeps almost constant under various OSNRs. Additionally, our proposed FOE method ensures a high estimation accuracy so that the additional use of FFT-FOE is unnecessary for improving the estimation accuracy. Meanwhile, the FOE difference between our proposed FOE scheme and the two-stage FOE scheme is within 40 MHz. As a result, the NGMI curves for two schemes are almost the same, indicating of no performance penalty due to the used of our proposed FOE method solely. Next, we investigate the proposed FOE performance after the SSMF transmission. Figure 11(b) shows the estimated FO and NGMI as a function of launch power over 2560 km SSMF transmission. As the launch power varies from -5 dBm to 4 dBm, the estimated FO keeps almost unchanged, revealing of high tolerance towards the fiber nonlinearity for proposed FOE method. Moreover, the NGMI achieved by the proposed FOE method and two-stage FOE method are approximately the same. Therefore, we can conclude that the proposed FOE method secures a high estimation accuracy, without the performance penalty.
Fig. 11. (a) Estimated FO and the calculated NGMI as a function of OSNR under the B2B transmission. (b) Estimated FO and the calculated NGMI as a function of launch power after 2560 km SSMF transmission without the WS.
To investigate the tolerance of optical filtering, we insert a WS in the SSMF transmission loop with variable bandwidth. As for the 4-subcarrier DSM signal, we use all 3 dips for the purpose of FOE and the estimated FO/the calculated GMI with respect to the 3-dB bandwidth variation after 2560 km SSMF transmission is presented in Fig. 12(a). To eliminate the impact of fiber nonlinearity, the launch power is set to be -5 dBm. As we can see, the estimated FO using our proposed FOE method keeps almost unchanged with the variation of 3-dB bandwidth, revealing of its high tolerance towards the optical filtering. The DSM spectrum after the smoothing filter is also provided under the condition of 3-dB bandwidth of 36 GHz. Although the DSM signal is severely filtered, 3 dips can aid us realize the FOE. Again, the NGMI curves for two used FOE schemes overlap, indicating that additional FFT-FOE is unnecessary. Finally, we investigate the performance of our proposed FOE scheme after the SSMF transmission, by taking the optical filtering, the fiber nonlinearity as well as ASE noise into account. The relationship between the estimated FO/the calculated GMI and the SSMF transmission distance is shown in Fig. 12(b), when the launch power is 0 dBm and the WS 3-dB bandwidth is 36 GHz. As we can see, the estimated FO slightly increases with the growing SSMF length, because the fiber loop controller typically introduces a small frequency shift proportional to the loop number. In addition, the estimated FO from the FFT-FOE is quite small because our proposed FOE method achieves a high estimation accuracy already. As a result, there is no NGMI gain by the additional use of the FFT-FOE.
Fig. 12. (a) Estimated FO and the calculated NGMI as a function of WS 3-dB bandwidth after 2560 km SSMF transmission with a launch power of -5 dBm. Inset: the received DSM signal spectrum after passing through 8 cascaded WSs with 3-dB bandwidth of 36 GHz. (b) Estimated FO and the calculated NGMI as a function of SSMF transmission distance with the WS 3-dB bandwidth of 36 GHz and the launch power of 0 dBm.
5. Computational complexity analysis
Since computational complexity of DSP algorithm is critical for practical hardware implementation, it is essential to analyze the computational complexity of our proposed FOE method. If we assume the FFT size for the CDC is ${N_{FFT}}$, the computational complexity for our proposed FOE method can be summarized as follows,
- i. For the averaging process among X/Y polarizations, ${N_{FFT}}$ real adders are in need.
- ii. The smoothing filter length is ${L_{SF}}$, applying the rectangular filter over ${N_{FFT}}$ points generally requires $({L_{SF}} - 1){N_{FFT}}$ real adders. However, if we set ${L_{SF}} = {2^n} + 1$ which is the case for our investigation with ${L_{SF}} = 5$, this process can be implemented under a very effective manner by the use of adder trees [22]. As a result, only $(n + 1){N_{FFT}}$ real adders are required.
- iii. The searching of spectral dips requires at most ${N_{FFT}}$ comparators. Considering the typical FO is limited to $[ - 3GH\textrm{z}, 3GH\textrm{z}]$, we can therefore divide the whole spectrum into N sections and search the dip within each section. In this way, the comparator requirement can be also relaxed.
- iv. The FO computation according to Eq. (2) requires $4M - 3$ real adders and 1 real multiplier. Practically, the number of spectral dips used for the FOE can be reduced without the performance penalty for the DSM signal with the growing subcarrier numbers, resulting in a further reduction of computational complexity.
6. Conclusion
We have proposed a blind FOE method for DSM signals by the detection of spectral dips at the receiver-side, with the capability of modulation format transparence, wide estimation range, and high estimation accuracy. By reusing the spectrum information for the CDC, the proposed FOE method is hardware efficient. With the help of a frequency-domain smoothing filter, the FOE accuracy can be greatly enhanced. Moreover, we identify that the proposed FOE method is robust to several transmission impairments, including the ASE noise, the optical filtering, and the fiber nonlinearity. The effectiveness of our proposed FOE method is numerically and experimentally verified under the back-to-back (B2B) and 2560 km SSMF transmission, with the estimated FO error of less than 100 MHz under the FFT size of 1024.
Funding
National Key Research and Development Program of China (2019YFB1803803); National Natural Science Foundation of China (62075046); Guangdong Provincial Pearl River Talents Program (2019ZT08X340); Special Project for Research and Development in Key areas of Guangdong Province (2018B010114002).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. O. Vassilieva, I. Kim, and T. Ikeuchi, “Enabling technologies for fiber nonlinearity mitigation in high capacity transmission systems,” J. Lightwave Technol. 37(1), 50–60 (2019). [CrossRef]
2. M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. Morsy-Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014). [CrossRef]
3. P. Poggiolini, A. Nespola, Y. Jiang, G. Bosco, A. Carena, L. Bertignono, S. M. Bilal, S. Abrate, and F. Forghieri, “Analytical and Experimental Results on System Maximum Reach Increase Through Symbol Rate Optimization,” J. Lightwave Technol. 34(8), 1872–1885 (2016). [CrossRef]
4. D. Krause, A. Awadalla, A. Karar, H. H. Sun, and K. T. Wu, “Design considerations for a digital subcarrier coherent optical modem,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper Th1D.1.
5. F. P. Guiomar, L. Bertignono, A. Nespola, and A. Carena, “Frequency-Domain Hybrid Modulation Formats for High Bit-Rate Flexibility and Nonlinear Robustness,” J. Lightwave Technol. 36(20), 4856–4870 (2018). [CrossRef]
6. M. Xiang, Q. Zhuge, X. Zhou, M. Qiu, F. Zhang, T. M. Hoang, Y. S. Mohammed, T. M. Sowailem, D. Liu, S. Fu, and D. V. Plant, “Filtering Tolerant Digital Subcarrier Multiplexing System with Flexible Bit and Power Loading,” in Optical Fiber Communication Conference, (Optical Society of America, 2017), paper W4A.7.
7. H. Sun, M. Torbatian, M. Karimi, R. Maher, S. Thomson, M. Tehrani, Y. Gao, A. Kumpera, G. Soliman, A. Kakkar, and M. Osman, “800G DSP ASIC Design Using Probabilistic Shaping and Digital Sub-Carrier Multiplexing,” J. Lightwave Technol. 38(17), 4744–4756 (2020). [CrossRef]
8. B. Baeuerle, A. Josten, M. Eppenberger, D. Hillerkuss, and J. Leuthold, “Low-Complexity Real-Time Receiver for Coherent Nyquist-FDM Signals,” J. Lightwave Technol. 36(24), 5728–5737 (2018). [CrossRef]
9. J. Lu, Y. Tian, S. Fu, X. Li, M. Luo, M. Tang, and D. Liu, “Frequency Offset Estimation for 32-QAM Based on Constellation Rotation,” IEEE Photonics Technol. Lett. 29(23), 2115–2118 (2017). [CrossRef]
10. A. Leven, N. Kaneda, U. Koc, and Y. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007). [CrossRef]
11. J. Cho, X. Chen, G. Raybon, D. Che, E. Burrows, and R. Tkach, “Full C-Band WDM Transmission of Nonlinearity-Tolerant Probabilistically Shaped QAM over 2824-km DispersionManaged Fiber,” in Proceedings of European Conference Optical Communication (2020), pp. 1–3.
12. M. Selmi, Y. Jaouën, P. Ciblat, and B. Lankl, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proceedings of European Conference Optical Communication (2009), paper P3.08.
13. M. Xiang, Q. Zhuge, M. Qiu, X. Zhou, M. Tang, D. Liu, S. Fu, and D. V. Plant, “RF-pilot aided modulation format identification for hitless coherent transceiver,” Opt. Express 25(1), 463–471 (2017). [CrossRef]
14. Q. Guo, F. Zhu, and Y. Bai, “Estimation and compensation of local oscillator frequency offset and chromatic dispersion using pilot tones in spectral-shaping subcarrier modulation,” May 9 2017, US Patent App. 14/831,123.
15. T. Kobayashi, A. Sano, A. Masuura, Y. Miyamoto, and K. Ishihara, “Nonlinear tolerant spectrally-efficient transmission using PDM 64-QAM single carrier FDM with digital pilot-tone,” J. Lightwave Technol. 30(24), 3805–3815 (2012). [CrossRef]
16. R. Ramdial, X. Liang, S. Kumar, J. Downie, and W. Wood, “Frequency offset estimation algorithm for a multi-subcarrier coherent fiber optical system,” inProceedings of SPIE OPTO (2020), pp. 113090K1.
17. M. Xiang, Q. Zhuge, M. Qiu, F. Zhang, X. Zhou, M. Tang, S. Fu, and D. V. Plant, “Multi-subcarrier flexible bit-loading enabled capacity improvement in meshed optical networks with cascaded ROADMs,” Opt. Express 25(21), 25046–25058 (2017). [CrossRef]
18. C. Pulikkaseril, L. A. Stewart, M. A. Roelens, G. W. Baxter, S. Poole, and S. Frisken, “Spectral modeling of channel band shapes in wavelength selective switches,” Opt. Express 19(9), 8458–8470 (2011). [CrossRef]
19. X. Chen, S. Chandrasekhar, J. Cho, and Peter Winzer, “Single-Wavelength and Single-Photodiode Entropy-Loaded 554-Gb/s Transmission over 22-km SMF,” in Optical Fiber Communication Conference, (Optical Society of America, 2019), paper Th4B.5.
20. L. Huang, D. Wang, A. P. T. Lau, C. Lu, and S. He, “Performance analysis of blind timing phase estimators for digital coherent receivers,” Opt. Express 22(6), 6749–6763 (2014). [CrossRef]
21. Y. Wang, E. Serpedin, and Philippe Ciblat, “An alternative blind feedforward symbol timing estimator using two samples per symbol,” IEEE Trans. Commun 51(9), 1451–1455 (2003). [CrossRef]
22. A. Bisplinghoff, C.R.S. Fludger, T. Kupfer, and B. Schmauss, “Carrier and Phase Recovery Algorithms for QAM Constellations: Real-time Implementations,” inProceedings of APC (2013), paper SP4D.1.
23. Q. Tian, A. Yang, P. Guo, and Z. Zhao, “Blind Frequency Offset Estimation Based on Phase Rotation For Coherent Transceiver,” IEEE Photonics J. 12(2), 1–9 (2020). [CrossRef]
24. F. Xiao, J. Lu, S. Fu, C. Xie, M. Tang, J. Tian, and D. Liu, “Feed-forward frequency offset estimation for 32-QAM optical coherent detection,” Opt. Express 25(8), 8828–8839 (2017). [CrossRef]
25. T. Yang, C. Shi, X. Chen, H. Chen, X. Luo, L. Wang, and Y. Zhan, “Hardware-Efficient Multi-Format Frequency Offset Estimation for M-QAM Coherent Optical Receivers,” IEEE Photonics Technol. Lett. 30(18), 1605–1608 (2018). [CrossRef]
