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Abstract
A coherent optical packet transceiver based on doubly differential star 16-ary quadrature amplitude modulation (DD-star-16-QAM) is presented for spectrally and energy efficient reconfigurable networks. The coding and decoding processes for this new modulation format are presented, simulations and experiments are then performed to investigate the performance of the DD-star-16-QAM in static and dynamic scenarios. The static results show that the influence of frequency offset (FO) can be cancelled out by doubly differential (DD) coding and the correction range is only limited by the electronic bandwidth of the receivers. In the dynamic scenario with a time-varying FO and linewidth, the DD-star-16-QAM can overcome the time-varying FO, and the switching time of around 70 ns is determined by the time it takes the dynamic linewidth to reach the requisite level. This format can thus achieve a shorter waiting time after switching tunable lasers than the commonly used square-16-QAM, in which the transmission performance is limited by the frequency transients after the wavelength switch.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Due to the rapid development of bandwidth-hungry applications, e.g. cloud computing, virtual reality, IP-TV, high-speed internet access, there is a constantly increasing demand for higher throughput in optical networks [1, 2]. Large amounts of energy used by optical networks are consumed by electronic routers, so it is envisaged that switching in the optical domain as opposed to the electrical domain will reduce the power consumption considerably [3–6]. One key technology for performing all-optical switching is wavelength tunable lasers [7], which can be used in the transmitters [8, 9] and/or receivers [10, 11]. These tunable lasers with electronic tuning mechanism can switch wavelengths on the order of nanoseconds [12, 13] to achieve high efficiency in wavelength routed networks. It would be ideal to use advanced modulation formats and coherent detections in these systems to maximize spectral efficiency (SE) and throughput [14]. However, switching tunable lasers can result in large and time-varying frequency offsets (FO) between the transmitter laser and local oscillator (LO) used at the coherent receiver, increasing the waiting time considerably before the signal can be demodulated correctly [15]. One modulation format that was suggested to overcome this issue is doubly differential quadrature phase shift keying (DDQPSK), where FO transients do not result in packet loss and the time to reach bit error rate (BER) of 10−3 can be on the order of 10’s of nanoseconds [16, 17]. To further increase the SE, higher-order modulation formats are being considered to replace QPSK and a fast wavelength switching 16-ary quadrature amplitude modulation (16-QAM) digital coherent burst mode receiver operated at 6 Gbaud has been reported [18], however, the coherence enhancement technique used for phase noise reduction results in the increased complexity of the additional receiver.
In this paper, the doubly differential (DD) technology is applied to the 16-QAM modulation format. As the mostly used square-16-QAM constellation diagram is not suitable to perform DD coding, the doubly differential star 16-ary quadrature amplitude modulation (DD-star-16-QAM) that has the same modulation efficiency has been introduced in [19], and much more comprehensive works are presented in this paper, including simulations and experimental results under different operating conditions. The coding and decoding processes for this new modulation format are first discussed, simulations and experiments are then performed to investigate the performance of the proposed scheme. The results demonstrate the ability of the DD-star-16-QAM to overcome the FO transients issue and increase the network efficiency by reducing the time after a wavelength switch when the signal can be demodulated successfully.
2. Operation principle of DD-star-16-QAM transceiver
At the transmitter side, the coding process for the DD-star-16-QAM is illustrated in Fig. 1. The original bits are first divided into blocks with 4 bits, the first bit is encoded as the amplitude of the signal, and the other three bits are Gray-encoded as an 8-ary phase shift keying (8PSK) signal. Then the DD coding is applied to the phase data , expressed as [16]:
where is the phase of the kth transmitted signal. Thus a two-level, eight-phase state constellation diagram is obtained. As shown in the constellation diagram, it is assumed that the outer ring has a radius R times that of the inner ring, which is an important parameter in optimizing the performance of this system.At the receiver side, a real-time scope is employed to capture the detected signal, which is followed by offline digital signal processing (DSP) and the flow is shown in Fig. 2. The amplitudes of the digital samples are initially normalized by their root-mean-square (RMS) values and the timing skew between the I/Q components are balanced. Then the signal is re-timed and down-sampled to the symbol stream. Afterwards, the Mth power method [17], which is able to track the time-varying parameters, is employed to correct the FO, and then the 2nd order PLL [20] is applied to overcome the excess phase noise of fast tunable lasers. In order to reduce the OSNR penalty introduced by the DD decoding, the hard decision is followed by the decoding process [17]. For the amplitude data, the magnitude of each constellation point is taken and a hard decision is made to decide whether it is part of the inner circle or the outer circle. Then the phase state for each constellation point is extracted and the DD decoding is performed by [16]:
where is the phase of the ith received complex signal. By combining the amplitude and phase data, the signal can be demodulated successfully. Generally, the received signal can be expressed as:where is the phase data, T is the symbol interval, is the FO between the modulated signal and the LO, and is the initial phase. Substituting (3) into (2), we obtain:It is observed that the FO and initial phase terms are removed, with only the encoded phase data left. Hence, from the DD coding and decoding, the influence of the FO can be cancelled out perfectly in the ideal case.3. Simulation and discussion
In order to investigate the performance of the DD-star-16-QAM, a transmission simulation is performed, which is also compared with the commonly used square-16-QAM. In all the simulations, the Baud rate is set to be 12.5 Gbaud. For simplicity, the signal is assumed to only be degraded by additive white Gaussian noise (AWGN), laser phase noise and FO, expressed as:
where is the ideal signal after modulation, accounts for the AWGN, which is usually quantified by optical signal-noise-ratio (OSNR), calculated by:where and are the power of the signal and noise, respectively, and are the equivalent noise bandwidth and reference optical bandwidth, respectively. is the sampled phase noise, which is related to the linewidth of the laser:where is a random number that has a Gaussian probability distribution function with zero mean value and unity variance. By changing or with symbol index , the modulated signal with time-resolved FO or linewidth is obtained to investigate the system performance in a dynamic scenario. Therefore, by introducing the FO from (5), the OSNR from (6) and the linewidth from (7), we can fully characterize the transmitted signal.For the DD-star-16-QAM signal, R is an important factor in determining the BER performance and it should be optimized. BER versus R curves with various OSNR are first calculated and shown in Fig. 3(a), in which the linewidth is set as 0 Hz. With fixed OSNR, there is an optimal value for R to achieve the lowest BER. Then we find that these optimal values (~1.7) are almost unchanged with the increase of OSNR. Afterwards, Fig. 3(b) shows the BER versus R curves with various linewidths at a fixed OSNR (18 dB). It is observed that the optimal R is decreasing with the increase of the linewidth. As the phase noise will lead to constellation points spreading in the tangential direction, slightly reducing R can make the constellation points in the inner ring more separate and decrease BER of DD-star-16-QAM signal with large linewidth. Although the optimal R is changing with the laser phase noise, the variation is relatively small, which means the optimal values for all cases are close to 1.7. Therefore, R = 1.7 is adopted in all the simulations hereafter.
Then the BER performance of the DD-star-16-QAM with constant FO’s is investigated and the results are shown in Fig. 4, compared with the square-16-QAM (Gray-encoded [21]). As the data modulation of square-16-QAM cannot be erased by Mth power algorithm, the Mth power frequency compensation is not possible, so we employ the fast Fourier transform (FFT) method to estimate the FO [22]. As it is not easy to obtain the theoretical curves for the star-16-QAM and the DD-star 16-QAM by using formulas, the theoretical limits is predicted by data transmission simulations with only the AWGN taken into account [23].Then the OSNR penalty between the DD-star-16-QAM and square-16-QAM is found to be introduced by the constellation mapping and DD decoding. Generally, the contribution from the constellation mapping dominates when the OSNR is large. By employing a laser source with a fixed linewidth (500 kHz) in the simulation, the performance with and without FO are calculated. For the DD-star-16-QAM, the signal can be demodulated correctly with the FO increased from 0 to 3 GHz and the BER performance shows no degradation, which is enabled by the DD coding and decoding. For the square-16-QAM, the signal has a better performance than the DD-star-16-QAM without FO, there is about 2 dB improvement to reach the 7% forward error correction (FEC) limit (BER = 3.8 × 10−3). However, the transmission of square-16-QAM with a 3 GHz FO fails, which is because this large FO is beyond the correction range of the FFT based frequency compensation method. Hence, the DD-star-16-QAM is able to cancel the influence of the FO and the correction range is only limited by the electronic bandwidth of the detectors in practical applications.
Afterwards, the transmission performance in a dynamic scenario is investigated, in which the FO or linewidth is changing over time. When the FO is set as a cosine function with damped amplitude, Fig. 5 shows the actual FO and estimated FO obtained by the Mth power method. Without unwrap function in Fig. 5(a), the FO is estimated in boundary, where is the number of phase states. After applying the unwrap function, the frequency transient is found to be tracked correctly but with a constant frequency difference, as shown in Fig. 5(b). This frequency difference is due to the difference between the initial values of the actual FO and estimated FO in Fig. 5(a). Since we do not know the actual FO in the experiments, there will be an ambiguity of (k is an integer). However, this ambiguity can be corrected by the DD coding and decoding, which makes sure the signal can still be demodulated correctly with a large and time-varying FO between the signal and LO.
The system performance of the DD-star-16-QAM signal is then investigated with a fixed OSNR (16 dB) and the same dynamic FO shown in Fig. 5. In order to achieve accurate time-resolved BER calculation, 100 sweeps with the same condition are simulated and processed, the BER is averaged over a block length of 10000 bits (200 ns) for each time point. Therefore, 106 data bits are used to calculate the BER, making sure the BER calculation limit is accurate down to values of 10−5. Figure 6(a) shows the time-resolved BER with a constant linewidth, it is found that the BER is nearly unchanged over time, proving the dynamic FO presented in Fig. 5 does not degrade the operation of the systems. In order to simulate the system performance after the wavelength switching of the tunable laser, a dynamic linewidth decreasing from 2 MHz to 500 kHz is introduced to the signal based on the measurements [24], and the instantaneous phase is obtained according to (4). Then the calculated time-resolved BER is presented in Fig. 6(b), we find in this case the BER performance is decreasing with time and the trend is similar to the time-resolved linewidth. Hence, the large and time-varying FO is not a problem for the DD-star-16-QAM signal, but the phase noise is still an important factor which will limit the BER performance.
4. Experimental results
The experimental setup for demonstrating the DD-star-16-QAM is shown in Fig. 7, including static and switching experiments. In the static transmissions, an ECL with ~50 kHz linewidth is used as the optical source, and for switching cases, a sampled grating distributed Bragg reflector (SGDBR) laser is employed. The SGDBR laser is switched between two wavelengths by applying an electrical signal (generated by an FPGA board at 100 kHz) to the grating section or phase section. In both the static and switching experiments, the laser output is modulated by an IQ modulator that is driven by an arbitrary waveform generator (AWG), which is up-sampled to have a sampling rate of 25 GSa/s and outputs two pseudo random binary sequences (PRBS) of 211-1 bits periodicity to generate the DD-star-16-QAM signal, realizing a 50 Gbit/s transmission speed. In order to achieve synchronization, a training sequence (64 symbols) is generated in front of every periodical PRBS bits. In addition, data aid is not employed for equalization and carrier phase recovery. This optical signal is then coupled with a variable level of amplified spontaneous noise (ASE) generated by the EDFA to set the OSNR level. The resulting signal is subsequently split and fed into the OSA to measure the OSNR and the optical coherent receiver from which the electrical outputs are captured by a high-speed real-time scope at 50 GSs/s. The electronic bandwidth of the coherent receivers and real-time scope is about 12.5 GHz. In the switching cases, the LO of the coherent receiver is set close to one of the two switching wavelengths, so the signal can be captured when the SGDBR laser is switched to this wavelength and several bursts can be observed in the screen shot of the real-time scope, shown in the inset of Fig. 7. Each burst lasts about 5 µs (1/2 of the period of the electrical drive signal) and the switching performance can be analyzed by extracting the data in the front of the bursts.
Fig. 7 Static and switching experiments setup. EDFA: optical amplifier, BPF: band pass filter, VOA: variable optical attenuator, IQM: IQ modulator, AWG: arbitrary waveform generator, ECL: external cavity laser, PC: polarization control, OSA: optical spectrum analyzer.
The static experiments are first performed to optimize the constellation diagram and test the performance of the DD-star-16-QAM. Figure 8(a) shows the measured BER as a function of R without adding noise, it indicates that R = 1.9 can achieve the best performance, and this ratio is used in all the experiments. The difference between the experimental results and simulation (optimal R = 1.7) is due to the nonlinearity of the I/Q modulator. The BER versus OSNR measurements are then measured and presented in Fig. 8(b). When the FO is 0 Hz, the signals for DD-star-16-QAM and square-16-QAM are both demodulated correctly, and the required OSNR at the 7% FEC limit is about 17.8 dB and 20 dB, respectively. This 2.2 dB penalty between these two modulation formats is consistent with the simulation results in Fig. 4. Due to implementation penalty, the OSNR requirement is about 5.5 dB and 5.7 dB from the theoretical plots for square-16-QAM and DD-star-16-QAM in Fig. 8(b), respectively. However, when the FO is increased, the data is only transmitted successfully with the DD-star-16-QAM modulation format. Compared with the results at FO = 0 GHz, another 1 dB penalty is observed for the DD-star-16-QAM at FO = 3 GHz. In order to clarify this, the ability of the DD-star-16-QAM format to overcome the influence of FO is further examined and Fig. 8(c) presents the BER as a function of the FO before frequency compensation. It suggests that the square-16-QAM fails when the FO is larger than 1 GHz, which is close to the correction range limitation of the FFT based FO compensation method. Whereas the DD-star-16-QAM can still work with FO’s as large as 6 GHz. Theoretically, the DD coding can cancel the influence of the FO without degradation [16], but in the experiments, some part of the signal is outside the electronic bandwidth of the receivers when the FO is large, resulting in the BER penalty in our results. It is thus reasonable to assume that a better FO tolerance can be expected for the DD-star-16-QAM signal with higher speed coherent receivers.
Fig. 8 Static performance of DD-star-16-QAM including (a) R optimization results, (b) BER performance and (c) FO limitation.
The SGDBR laser is then employed in the system and the switching performance of the DD-star-16-QAM is studied. For the SG-DBR laser, wavelength switching involves super-mode jumping (related to coarse tuning) and longitudinal modes jumping (related to fine tuning) [25], which are both investigated in the experiments.
When the switching signal is applied to the front grating section, the wavelength of the laser is switched between two super-modes (1542.62 nm and 1548.28 nm), and the optical spectra before modulation and after modulation are shown in Fig. 9(a). As the OSA gets the spectrum from a time integration, it displays the two switching longitudinal modes simultaneously. Without data modulation, the dynamic phase noise properties of the switched laser are subsequently measured by using the same experiment setup in Fig. 7 [26] and the results are presented in Fig. 9(b). By calculating the differentiation of the instantaneous phase, we can get the time-varying FO. In addition, the time-resolved linewidth is obtained from the variance of the instantaneous phase and a 3 GHz low-pass filter is used in the analysis to suppress the AWGN from the receivers. As the linewidth estimated by the phase error variance is related to the integration of frequency modulation (FM) noise in the frequency range [0, ∞] [27], the contribution from the serious low frequency phase noise is really small, so the estimated linewidth value is almost determined by the white noise, which results in the linewidth of only several hundred kHz [28]. In order to increase accuracy, these two parameters are averaged by a similar method to the time-resolved BER described in the simulations. For the dynamic linewidth and FO, it is observed that they still need around 100 nanoseconds after a wavelength switch to achieve stability, which maybe limiting factors for the waiting time before the signal can be demodulated successfully. The time-resolved BER is then calculated without adding noise and the results are shown in Fig. 9(c), in which 1000 × 160 bits are used toobtain the BER, making sure the BER calculation limit is accurate down to ~10−5. The degraded BER in comparison with the static results in Fig. 8 is mainly due to the additional phase noise of the SGDBR laser (low linewidth ECL is used in the static measurements). The waiting time to achieve BER under 7% FEC limit after the wavelength switch is found to be 70 ns and 160 ns for the DD-star-16-QAM and square-16-QAM, respectively. These results can be understood more clearly by Fig. 9 (b) and the constellation diagrams of the two modulation formats at 100 ns. We find that the location of the constellation points of the DD-star-16-QAM is correct, but they suffer considerable residual phase noise, which means that the influence of dynamic FO is mitigated for the DD-star-16- QAM, so its switching time is only limited by the time it takes the dynamic linewidth to reach the level required for this modulation format. From Fig. 9(b), the linewidth can achieve stability after about 125 ns, which is close to the time when the BER of the DD-star-16-QAM becomes stable, as shown in Fig. 9(c). For the square-16-QAM, the constellation diagram is degraded by the FO and the signal cannot be demodulated correctly before the dynamic FO becomes stable, which takes about 175 ns as shown from the inset of Fig. 9(b) and results in a longer waiting time after the wavelength switch. By changing the wavelength of the LO, the BER performance of DD-star-16-QAM with an additional 2 GHz steady-state FO is also investigated in Fig. 9(c). The signal can still be demodulated correctly with the steady BER below the FEC limit, which relaxes the frequency accuracy of the LO and increases the robustness of the system. Note that the system degradation in this case is due to the limited bandwidth of the receivers as explained earlier.
Fig. 9 Results for switching the front grating section including (a) optical spectra before modulation and after modulation, (b) dynamic phase noise properties and (c) time-resolved BER performance.
The same switching signal is subsequently applied to the phase section of the SGDBR laser, and the spectra of the laser output before and after modulation are shown in Fig. 10(a), in which the laser is switched between two adjacent longitudinal modes (1542.63 nm and 1542.89 nm). Then the dynamic phase noise properties and time-resolved BER performance are obtained and presented in Fig. 10(b) and (c), respectively. The switching times for the DD-star-16-QAM and square-16-QAM are slightly longer than the grating section switching case and are about 90 ns and 178 ns, respectively. The constellation diagrams at 100 ns after the wavelength switch further proves that the performance of the square-16-QAM is limited by the FO fluctuation, whereas the settling down time of the dynamic linewidth determines the switching time of the DD-star-16-QAM, leading to a short waiting time after wavelength switching. When the steady-state FO is set as 2 GHz, the signal with DD-star-16-QAM modulation format can still transmit successfully, which is consistent with the results in Fig. 9. The penalty between the BER performance obtained at 0 and 2 GHz FO’s is similar to the results in Fig. 8(b) and it is due to the limited electronic bandwidth of the detectors.
Fig. 10 Results for switching the phase section including (a) optical spectra before modulation and after modulation, (b) dynamic phase noise properties and (c) time-resolved BER performance.
It has been demonstrated that the DD-star-16-QAM could be a promising scheme to achieve high efficient OPS networks, but only back to back results are presented here. For full system assessment, the transmission links and wavelength routing devices should be included in our future work. In relation to wavelength selective elements in the optical networks, they are normally designed to handle frequency shifts of at least ± 2 GHz, which would be compatible with the drift of the FO, with which DD-star-16-QAM can significantly improve performance. Furthermore, doubling of the data rate can be realized by performing dual-polarization multiplexing, however in this case, the convergence time for polarization demultiplexing may be longer than the laser switching time, and this will be an important factor that will affect the waiting times of the OPS receivers [17].
5. Conclusion
We have described a coherent optical packet transceiver based on the DD-star-16-QAM modulation format, which is tolerant to time-varying FO’s and increases the network efficiency by reducing the waiting time after switching tunable lasers to successfully transmit data. Simulated and experimental results demonstrate that the DD-star-16-QAM can still work well with FO’s as large as 6 GHz, which can be further extended by using larger electronic bandwidth receivers. The waiting time after a wavelength switch for the DD-star-16-QAM to achieve BER better than the 7% FEC limit is found to be as low as 70 ns, which is less than half the waiting time (~160 ns) required when employing the commonly used square-16-QAM signal. Therefore, the frequency accuracy requirement of the LO is significantly relaxed for coherent systems employing the DD-star-16-QAM format, and it is a robust scheme to increase the throughput of the optical packet switched networks.
Funding
Science Foundation Ireland (SFI) (IPIC-12/RC/2276 and CONNECT-13/RC/2077); National Natural Science Foundation of China (NSFC) (61675073); China Scholarship Council (CSC); 111 Program (B07038); Fundamental Research Funds for the Central Universities (2016YXZD004).
References and links
1. E. Agrell, M. Karlsson, A. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016). [CrossRef]
2. Cisco Visual Networking Index, “The Zettabyte era: trends and analysis,” White Paper, Cisco (2017), https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/vni-hyperconnectivity-wp.pdf.
3. C.-H. Huang, H.-F. Chou, J. E. Bowers, F. Toudeh-Fallah, and R. Gyurek, “Dynamically reconfigurable optical packet switch (DROPS),” Opt. Express 14(25), 12008–12014 (2006). [CrossRef] [PubMed]
4. S. Shinada, H. Furukawa, and N. Wada, “Huge capacity optical packet switching and buffering,” Opt. Express 19(26), B406–B414 (2011). [CrossRef] [PubMed]
5. S. B. Yoo, “Energy efficiency in the future internet: the role of optical packet switching and optical-label switching,” IEEE J. Sel. Top. Quantum Electron. 17(2), 406–418 (2011). [CrossRef]
6. Y. Ji, J. Zhang, Y. Zhao, H. Li, Q. Yang, C. Ge, Q. Xiong, D. Xue, J. Yu, and S. Qiu, “All optical switching networks with energy-efficient technologies from components level to network level,” IEEE J. Sel. Areas Comm. 32(8), 1600–1614 (2014). [CrossRef]
7. R. Maher, S. J. Savory, and B. C. Thomsen, “Fast wavelength switching transceiver for a virtualized coherent optical network,” J. Lightwave Technol. 33(5), 1007–1013 (2015). [CrossRef]
8. J. A. O’Dowd, K. Shi, A. J. Walsh, V. M. Bessler, F. Smyth, T. N. Huynh, L. P. Barry, and A. D. Ellis, “Time resolved bit error rate analysis of a fast switching tunable laser for use in optically switched networks,” J. Opt. Commun. Netw. 4(9), A77–A81 (2012). [CrossRef]
9. J. M. Fabrega, B. Schrenk, F. B. Bo, J. A. Lázaro, M. Forzati, P.-J. Rigole, and J. Prat, “Modulated grating Y-structure tunable laser for-routed networks and optical access,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1542–1551 (2011). [CrossRef]
10. B. C. Thomsen, R. Maher, D. S. Millar, and S. J. Savory, “Burst mode receiver for 112 Gb/s DP-QPSK with parallel DSP,” Opt. Express 19(26), B770–B776 (2011). [CrossRef] [PubMed]
11. J. E. Simsarian, J. Gripp, S. Chandrasekhar, and P. Mitchell, “Fast-tuning coherent burst-mode receiver for metropolitan networks,” IEEE Photonics Technol. Lett. 26(8), 813–816 (2014). [CrossRef]
12. J. E. Simsarian, M. C. Larson, H. E. Garrett, H. Xu, and T. A. Strand, “Less than 5-ns wavelength switching with an SG-DBR laser,” IEEE Photonics Technol. Lett. 18(4), 565–567 (2006). [CrossRef]
13. F. Smyth, E. M. Connolly, B. Roycroft, B. Corbett, P. Lambkin, and L. P. Barry, “Fast wavelength switching lasers using two-section slotted Fabry-Perot structures,” IEEE Photonics Technol. Lett. 18(20), 2105–2107 (2006). [CrossRef]
14. P. J. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightwave Technol. 30(24), 3824–3835 (2012). [CrossRef]
15. A. J. Walsh, J. A. O’Dowd, V. M. Bessler, K. Shi, F. Smyth, J. M. Dailey, B. Kelleher, L. P. Barry, and A. D. Ellis, “Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions,” Opt. Lett. 37(10), 1769–1771 (2012). [CrossRef] [PubMed]
16. A. J. Walsh, H. Shams, J. Mountjoy, A. Fagan, J. Zhao, L. P. Barry, and A. D. Ellis, “Demonstrating doubly-differential quadrature phase shift keying in the optical domain,” IEEE Photonics Technol. Lett. 25(11), 1054–1057 (2013). [CrossRef]
17. A. J. Walsh, J. Mountjoy, H. Shams, A. Fagan, A. D. Ellis, and L. P. Barry, “Highly robust dual-polarization doubly differential PSK coherent optical packet receiver for energy efficient reconfigurable networks,” J. Lightwave Technol. 33(24), 5218–5226 (2015). [CrossRef]
18. R. Maher, D. Lavery, M. Paskov, P. Bayvel, S. J. Savory, and B. C. Thomsen, “Fast wavelength switching 6 GBd dual polarization 16QAM digital coherent burst mode receiver,” IEEE Photonics Technol. Lett. 26(3), 297–300 (2014). [CrossRef]
19. F. Liu, Y. Lin, A. J. Walsh, Y. Yu, and L. P. Barry, “Doubly differential two-level 8PSK for enabling optical packet switching in coherent systems,” in Proceeding of Optical Fiber Communication Conference (OFC) (2018), paper W2A.35. [CrossRef]
20. T. N. Huynh, A. T. Nguyen, W. C. Ng, L. Nguyen, L. A. Rusch, and L. P. Barry, “BER performance of coherent optical communications systems employing monolithic tunable lasers with excess phase noise,” J. Lightwave Technol. 32(10), 1973–1980 (2014). [CrossRef]
21. J. Lu, K. B. Letaief, J. C. I. Chuang, and M. L. Liou, “M-PSK and M-QAM BER computation using signal-space concepts,” IEEE Trans. Commun. 47(2), 181–184 (1999). [CrossRef]
22. Y. Cao, S. Yu, Y. Chen, Y. Gao, W. Gu, and Y. Ji, “Modified frequency and phase estimation for M-QAM optical coherent detection,” inProceeding of European Conference and Exhibition on Optical Communication (ECOC)(2010), paper We.7.A.1. [CrossRef]
23. L. N. Binh, Noises in Optical Communications and Photonic Systems (CRC, 2016).
24. K. Shi, R. Watts, D. Reid, T. N. Huynh, C. Browning, P. M. Anandarajah, F. Smyth, and L. P. Barry, “Dynamic linewidth measurement method via an optical quadrature front end,” IEEE Photonics Technol. Lett. 23(21), 1591–1593 (2011). [CrossRef]
25. J. Zhao, H. Zhou, F. Liu, and Y. Yu, “Numerical analysis of phase noise characteristics of SGDBR lasers,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1502009 (2015).
26. R. Maher and B. Thomsen, “Dynamic linewidth measurement technique using digital intradyne coherent receivers,” Opt. Express 19(26), B313–B322 (2011). [CrossRef] [PubMed]
27. X. Chen, A. Al Amin, and W. Shieh, “Characterization and monitoring of laser linewidths in coherent systems,” J. Lightwave Technol. 29(17), 2533–2537 (2011). [CrossRef]
28. M. Larson, Y. Feng, P.-C. Koh, X.-d. Huang, M. Moewe, A. Semakov, A. Patwardhan, E. Chiu, A. Bhardwaj, and K. Chan, “Narrow linewidth high power thermally tuned sampled-grating distributed Bragg reflector laser,” in Proceeding of Optical Fiber Communication Conference (OFC) (2013), paper OTh3I. 4. [CrossRef]
