Open Access
Add to BibSonomyAbstract
We present a digital pilot aided carrier frequency offset estimation (FOE) method for coherent optical transmission systems. Unlike the conventional pilot tone insertion scheme, the pilot of the proposed method is generated in a digital manner and can serve as a good FOE indicator. Aided by this kind of digital pilot, the FOE is implemented by determining the location of the digital pilot in the spectrum. Theoretical analysis and numerical simulations show that the proposed method has the advantages in wide range, high accuracy, modulation formats independent, no need to remove the modulation, and high tolerance to the residual chromatic dispersion (CD) and polarization mode dispersion (PMD).
© 2015 Optical Society of America
1. Introduction
Enabled by coherent detection and digital signal processing (DSP) techniques, 100G and beyond coherent optical transmission systems have achieved great success in both research fields and commercial applications during the past decades [1,2 ]. With coherent detection and DSP, the incoming optical signal is linearly downconverted into the electric domain and the various impairments experienced by the optical signal can be compensated digitally by proper DSP algorithms [2,3 ]. One of these impairments is the carrier frequency offset, which origins from the mismatch between the carrier frequency of the transmitter laser and that of the local laser. Generally carrier frequency offset leads to the rotation of the received constellation with time and degrades the performance of the system severely. Moreover, since many carrier phase recovery methods are only unbiased in the presence of zero carrier frequency offset [3], carrier frequency offset estimation (FOE) is essential in the DSP process.
Recently, many FOE methods have been proposed. Some methods need to remove the data modulation in the first step. One way to remove the modulation is using Mth-power operation. And then the carrier frequency offset is estimated by either the differential phase based methods [4–10 ] or the spectrum based methods [11]. However, these methods have a common drawback that their estimation ranges are limited to ± Rs/2m, where Rs is the symbol rate and m is the number of constellation stages [12]. This drawback makes these methods face malfunction in the worst case scenario, especially for higher order modulation formats. The usual strategy to expand the estimation range is using a dual-stage scheme, which combines the differential phase method with a wide range coarse FOE method [13].
Besides, some FOE methods avoid removing the modulation. In these methods, the frequency offset is estimated by exploring the spectrum symmetry [12,14 ], or searching the peak of the spectrum of the phase of the signal [15–17 ]. In addition, a FOE method using training sequence to eliminate the modulation is proposed [18], which has a wide estimation range up to ± Rs/2 and is modulation formats independent. FOE can also be implemented by decision directed method [19].
The above proposed FOE methods mainly focus on single carrier coherent optical systems. And for coherent optical-orthogonal frequency division multiplexing (CO-OFDM), a radio frequency (RF) -pilot assisted FOE method is proposed. The RF-pilot assisted FOE method inserts a pilot tone in the center of the OFDM spectrum and has the widest estimation range [20,21 ]. A similar one for single carrier coherent optical systems is the residual carrier aided method [22]. The key to this method is the residual carrier, which serves as the pilot tone but is absent in most of the commonly used modulation formats. In conventional pilot tone aided single carrier coherent systems, the pilot tone is usually added electrically or optically by additional devices. But the schemes of this kind have the limitations in cost and flexibility [23]. Recently, the differential pilots generated by training sequence are proposed, which aim to monitor the optical signal to noise ratio (OSNR) [24].
In this paper, inspired by [24], we propose a new digital pilot aided FOE method. The pilot is generated in a digital manner and serves as a good FOE indicator. With the aid of the digital pilot, the FOE is implemented by determining the location of the digital pilot in the spectrum. The proposed method, which combines the pilot tone and the pilot symbols together, has the advantages in modulation formats independent and no need to remove the modulation. In addition, theoretical derivation of the proposed method is given in details. And numerical simulations verify that the proposed method is well performed for different modulation formats and pulse shapes.
2. Operating principle
2.1 The frame structure
Figure 1(a) shows the frame structure adopted in this method, which is identical in both polarizations. Each frame is composed of pilot and payload. The pilot is designed for FOE and the payload is used to convey useful information. Generally, to be compatible with the following payload, the pilot can be constructed by repeating the symbol S M times, which is arbitrarily chosen from the corresponding constellation diagram shown in Fig. 1(b). The pilot of this special structure manifests a pilot tone like spectrum, which can serve as a good indicator to the carrier frequency offset. Using this feature, the FOE can be realized easily. Note that the constellation diagrams shown in Fig. 1(b) are just for illustration purpose. In theory, this method is applicable to additional modulation formats, as long as the chosen symbol for the pilot is nonzero.
Fig. 1 Frame structure. (a) The frame structure for both polarizations; (b) The common constellation diagrams.
2.2 The operating principle of the digital pilot aided FOE
In this subsection, the operating principle of the digital pilot aided FOE is explained in details. Above all, the different power spectral density (PSD) of the pilot and the payload are given, respectively.
To simplify the derivation and without loss of generality, the amplified spontaneous emission (ASE) noise is ignored and a single polarization coherent optical transmission system is assumed. The typical system block diagram is shown in Fig. 2 . Generally, the received signal r(t) can be represented as
where an is the transmitted symbols, g(t) is the equivalent channel model, which is the convolution of the transmit filter p(t), the channel c(t) and the receive filter q(t), Ts is the symbol period, ∆f is the carrier frequency offset and rb(t) is the baseband representation of the received signal r(t).According to Eq. (1) and the modulation property of Fourier transform, the PSD of the received signal r(t) is the PSD of its baseband representation rb(t) shifted by ∆f in frequency. So the PSD of rb(t) can be derived firstly.
As a linear modulated signal, the PSD of rb(t) is [25]
where Pa(f) is the PSD of the transmitted symbols an, and G(f) is the Fourier transform of g(t). It is clear that the PSD of the signal rb(t) is determined by two factors: the PSD of the transmitted symbols an and the the Fourier transform of the g(t). Obviously, with the same G(f), the difference between the PSD of the pilot and that of the payload is determined by the PSD of the transmitted symbols of each.Generally, the transmitted symbols in the payload are modeled as a zero mean, independent and identically distribution. So its autocorrelation function is
where is the variance of the transmitted symbols in the payload and the subscript pa denotes the payload.According to the Wiener-Khintchine theorem, its PSD is
With the Eq. (4) instituded in the Eq. (2), the PSD of the payload iswhich means the PSD of the payload has no discrete components and its shape is determined by the shape of the spectrum of the equivalent channel.According to the spectial structure of the pilot, its autocorrelation function is
where S is the repeated symbol chosen from the constellation and the subscript pi denotes the pilot.Likewise, its PSD is
With the Eq. (7) instituted in the Eq. (2), the PSD of the pilot isNote that the PSD of the pilot is a periodic impulse train, which is modulated by G(f) and the period is 1/Ts. Since G(f) is band limited, the impulses with m ≠ 0 in Eq. (8) are suppressed and the PSD of the pilot is reduced towhich means the PSD of the pilot remains only a discrete direct current (DC) component.Figure 3 illustrates the PSD of the pilot and the payload intuitively, where the semi-ellipses denote the PSD of the payload and the arrows denote the PSD of the pilot. Under the effect of the carrier frequency offset, both of the PSD of the pilot and the payload shift in frequency. And the frequency shift equals the carrier frequency offset. The pilot tone-like spectrum of the pilot, which is distinguished, enables it to be a good FOE indicator. So the carrier frequency offset can be estimated easily by determining the location of the pilot tone in the spectrum of the pilot.
Fig. 3 Power spectral density of the pilot and the payload under zero carrier frequency offset (solid lines) and carrier frequency offset equals ∆f (dashed lines).
2.3 The estimation range and precision
In theory, the estimation range of this method, which depends on the sampling rate at the receiver side, can be as large as (-Fs/2, + Fs/2) (Fs is the sampling rate of the analog to digital converter (ADC) at the receiver) [21]. The periodicity resulting from the sampling will lead to a singular problem. Therefore the boundary values of the interval of the estimation range are excluded.
The estimation precision of this method is limited by the frequency resolution. According to the basic theory of the discrete Fourier transform (DFT), the frequency resolution is determined by the time window, which equals the product of the length of the pilot in symbols and the symbol rate. For a given coherent optical transmission system, the symbol rate is fixed. So the longer the pilot, the higher the frequency resolution. Howerever, there is a trade-off between the length of the pilot and the spectral efficiency. As an alternative method, zero padding is used to increase the frequency resolution [26].
2.4 The effect of the CD, PMD and various filters
When the optical signal propagates through the optical transmission systems, it will experience various impairments. These impairments contain chromatic dispersion (CD), polarization mode dispersion (PMD) and various filters.
As linear impairments, CD and PMD have no effect on the power spectrum density of the signal. However, to combat the interference from the adjacent payload, it is necessary to surround the pilot with cyclic prefix and cyclic postfix as shown in Fig. 1. Under this configuration, this method has high tolerance to the residual CD and PMD.
The typical filters in the optical transmission systems comprise the pulse shaping filter in the transmitter side, optical band-pass filter and electrical low-pass filter. Note that these filters are incorporated into the equivalent channel model. According to the theoretical derivation in Subsection 2.2, these filters have little effect on the shape of the pilot tone-like spectrum of the pilot and only affect the height of the pilot tone. That means this method is applicable to various pulse shapes, including non-return-to-zero (NRZ) pulse and Nyquist pulse, and has high tolerance to the effects of the optical band-pass filters and the electrical low-pass filters.
3. Simulation setup and results
To verify the proposed method, numerical simulations using VPITransmissionMaker 9.0 are carried out. First of all, a 28 GBaud polarization multiplexing coherent optical transmission system is built as shown in Fig. 4 . On the basis, four cases are simulated, including non-return-to-zero quadrature phase shift keying (NRZ-QPSK), Nyquist-QPSK, non-return-to-zero 16-ary quadrature amplitude modulation (NRZ-16QAM) and Nyquist-16QAM. For Nyquist cases, the raised cosine pulse with roll off factor of 0 is adopted. In all the subsequent simulations, absolute mean frequency offset estimation (FOE) error is obtained from 100 independent trials.
Fig. 4 The simulation setup. AWG: arbitrary waveform generator; IQM: IQ modulator; PBC: polarization beam combiner; OBPF: optical band-pass filter; PMD: polarization mode dispersion; OSNR: optical signal to noise ratio; LPF: low-pass filter; ADC: analog to digital converter; DSP: digital signal processing
The entire simulation setup is divided into 3 parts: the transmitter, the channel and the receiver. In each polarization of the transmitter, the total frame length is 32768 symbols and the pilot is 128 symbols. Each pilot is surrounded by the cyclic prefix and the cyclic postfix both of 32 symbols. After pulse shaping by the AWG, the modulated symbols form the I and Q driving signals, which are used to drive the IQ modulator (IQM). Then, the two modulated optical signals are combined by a polarization beam combiner (PBC) to form the polarization multiplexed optical signal, which is launched into the channel subsequently. Both the linewidth of the transmitter laser and the local laser are set to be 100 kHz.
The optical channel is band limited by two 3-order Gaussian optical band-pass filters (OBPF) with 3 dB bandwidth of 50 GHz individually. In between the two OBPF, the PMD emulator to simulate PMD, the optical fiber to simulate CD and the set OSNR module to set the OSNR are placed successively.
In the receiver, after coherent detection, low-pass filtering by 4-order Bessel electrical low-pass filters and two-fold oversampling, four tributaries of Ix[n], Qx[n], Iy[n] and Qy[n] are acquired and sent to the DSP module subsequently. Figure 5 shows the structure of the DSP module, which is implemented using MATLAB. After CD compensation and frame synchronization, the pilot is extracted and used to estimate the carrier frequency offset.
Fig. 5 The DSP module. FFT: fast Fourier transform; CFR: carrier frequency offset recovery; CPR: carrier phase recovery.
In the first simulation, the method of zero padding to increase the estimation precision is investigated. For NRZ-QPSK, the pilot is 128 symbols and the oversampling factor is 2, so the initial FFT length is 256. By zero-padding, the FFT length is set as [28, 29, 210, 211, 212, 213, 214, 215, 216, 217], respectively. The OSNR is 15 dB. Two FO values are chosen, including 4 GHz and 8 GHz. Figure 6 shows the absolute mean FOE error as a function of the FFT length NFFT. It shows that the mean FOE error decreases with the increase of the FFT length and changes little when the FFT length increases to 215. Therefore the effectiveness of zero padding is confirmed. Furthermore, to keep balance between the estimation precision and the computational complexity, the FFT length is set to be 215 in the following simulations.
In the second simulation, the performance of the proposed method under different OSNR is investigated. In this simulation, the four cases are simulated, including NRZ-QPSK, Nyquist-QPSK, NRZ-16QAM and Nyquist-16QAM. The FO is set as [-28 GHz, 28 GHz] with a step size of 4 GHz for NRZ pulse and [-14 GHz, 14 GHz] with a step size of 2 GHz for Nyquist pulse. Note that the span of FO is different for NRZ pulse and Nyquist pulse. This difference is induced by the different bandwidth and sampling rate of the two kind of pulses. For 28 GBaud NRZ pulse, the corresponding bandwidth is 28 GHz and the sampling rate is 56 GSa/s with twofold oversampling. While for 28 GBaud Nyquist pulse with roll off factor of 0, the corresponding bandwidth is 14 GHz and the sampling rate is 28 GSa/s with twofold oversampling. The OSNR is set as [10dB, 15dB, 20 dB, 25dB]. Figure 7 shows the estimation results of the absolute mean FOE error under different OSNR for all four cases. The results indicate that the FOE error is below 4 MHz for all four cases except the edge FO, which agree with the above theoretical analysis in Subsection 2.3 and 2.4 and confirm the wide range feature of the proposed method.
Fig. 7 The absolute mean FOE error under different OSNR for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.
In the third simulation, the tolerance of the proposed method to the residual CD is investigated. Generally, the residual CD is less than 1000 ps/nm after CD compensation. So in this simulation, the residual CD is set from 100 ps/nm to 1000 ps/nm with a step size of 100 ps/nm. Five chosen FO values contain 0 GHz, ± 4 GHz and ± 8 GHz. The OSNR is 15 dB. Figure 8 shows the estimation results of the absolute mean FOE error as a function of residual CD for all four cases, including NRZ-QPSK, Nyquist-QPSK, NRZ-16QAM and Nyquist-16QAM. The results indicate that the residual CD affects little on the FOE error, which agree with the above theoretical analysis in Subsection 2.3 and confirm the high tolerance of the proposed method to the residual CD.
Fig. 8 The absolute mean FOE error vs the residual CD for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.
In the fourth simulation, the performance of the proposed method under the effect of the first-order PMD is investigated. The first-order PMD is quantified by the differential group delay (DGD). In this simulation, the DGD is set from 0 ps to 100 ps with a step size of 10 ps. Five chosen FO values cover 0 GHz, ± 4 GHz and ± 8 GHz. The OSNR is 15 dB. Figure 9 shows the estimation results of the absolute mean FOE error as a function of DGD for all four cases, including NRZ-QPSK, Nyquist-QPSK, NRZ-16QAM and Nyquist-16QAM. The results indicate that the first-order PMD affects little on the FOE error, which agree with the theoretical analysis in Subsection 2.4 and confirm the high tolerance of the proposed method to the first-order PMD.
Fig. 9 The absolute mean FOE error vs the DGD for (a) NRZ-QPSK; (b) Nyquist-QPSK; (c) NRZ-16QAM; (d) Nyquist-16QAM.
4. Conclusion
In this paper, we have proposed and demonstrated a digital pilot aided FOE method. The pilot is generated in a digital manner and serves as a good FOE indicator. Aided by the digital pilot, the FOE is performed by determining the location of the digital pilot in the spectrum. Theoretical derivation and simulation results indicate that the proposed method has the advantages in wide range, high accuracy, modulation formats independent, no need to remove the modulation, and high tolerance to the residual CD and PMD.
Acknowledgments
The authors would like to acknowledge the support of the National Natural Science Foundation of China (61205065, 61571057) and the National High Technology Research and Development of China (863 Program) (2013AA013401).
References and links
1. X. Liu, S. Chandrasekhar, and P. J. Winzer, “Digital signal processing techniques enabling multi-Tb/s superchannel transmission: an overview of recent advances in DSP-enabled superchannels,” IEEE Signal Process. Mag. 31(2), 16–24 (2014). [CrossRef]
2. X. Zhou and L. Nelson, “Advanced DSP for 400 Gb/s and beyond optical networks,” J. Lightwave Technol. 32(16), 2716–2725 (2014). [CrossRef]
3. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010). [CrossRef]
4. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photonics Technol. Lett. 19(6), 366–368 (2007). [CrossRef]
5. S. Hoffmann, S. Bhandare, T. Pfau, O. Adamczyk, C. Wordehoff, R. Peveling, M. Porrmann, and R. Noe, “Frequency and phase estimation for coherent QPSK transmission with unlocked DFB lasers,” IEEE Photonics Technol. Lett. 20(18), 1569–1571 (2008). [CrossRef]
6. I. Fatadin and S. J. Savory, “Compensation of frequency offset for 16-QAM optical coherent systems using QPSK partitioning,” IEEE Photonics Technol. Lett. 23(17), 1246–1248 (2011).
7. M. Li and L. Chen, “Blind carrier frequency offset estimation based on eighth-order statistics for coherent optical QAM systems,” IEEE Photonics Technol. Lett. 23(21), 1612–1614 (2011). [CrossRef]
8. D. Huang, T. Cheng, and C. Yu, “Accurate two-stage frequency offset estimation for coherent optical systems,” IEEE Photonics Technol. Lett. 25(2), 179–182 (2013). [CrossRef]
9. M. Li, J. Zhao, and L. Chen, “Multi-symbol QPSK partitioning for improved frequency offset estimation of 16-QAM signals,” IEEE Photonics Technol. Lett. 27(1), 18–21 (2014). [CrossRef]
10. Y. Liu, Y. Peng, Y. Zhang, Y. Liu, and Z. Zhang, “Differential phase-based frequency offset estimation for 16-QAM coherent optical systems,” IEEE Photonics Technol. Lett. 26(24), 2492–2494 (2014). [CrossRef]
11. M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. European Conference and Exhibition on Optical Communication (ECOC 2009), paper P3.08.
12. J. C. M. Diniz, J. C. R. F. de Oliveira, E. S. Rosa, V. B. Ribeiro, V. E. S. Parahyba, R. da Silva, E. P. da Silva, L. H. H. de Carvalho, A. F. Herbster, and A. C. Bordonalli, “Simple feed-forward wide-range frequency offset estimator for optical coherent receivers,” Opt. Express 19(26), B323–B328 (2011). [CrossRef] [PubMed]
13. S. Zhang, L. Xu, J. Yu, M. F. Huang, P. Y. Kam, C. Yu, and T. Wang, “Dual-stage cascaded frequency offset estimation for digital coherent receivers,” IEEE Photonics Technol. Lett. 22(6), 401–403 (2010). [CrossRef]
14. T. Nakagawa, K. Ishihara, T. Kobayashi, R. Kudo, M. Matsui, Y. Takatori, and M. Mizoguchi, “Wide-range and fast-tracking frequency offset estimator for optical coherent receivers,” in Proc. European Conference and Exhibition on Optical Communication (ECOC 2010), paper We.7.A.2. [CrossRef]
15. Y. Cao, S. Yu, J. Shen, W. Gu, and Y. Ji, “Frequency estimation for optical coherent MPSK system without removing modulated data phase,” IEEE Photonics Technol. Lett. 22(10), 691–693 (2010). [CrossRef]
16. Y. Liu, Y. Peng, S. Wang, and Z. Chen, “Improved FFT-based frequency offset estimation algorithm for coherent optical systems,” IEEE Photonics Technol. Lett. 26(6), 613–616 (2014). [CrossRef]
17. S. Yu, Y. Cao, H. Leng, G. Wu, and W. Gu, “Frequency estimation for optical coherent M-QAM system without removing modulated data phase,” Opt. Commun. 285(18), 3692–3696 (2012). [CrossRef]
18. X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photonics Technol. Lett. 24(1), 82–84 (2012). [CrossRef]
19. A.-L. Yi, L.-S. Yan, C. Liu, M. Zhu, J. Wang, L. Zhang, C.-H. Ye, and G.-K. Chang, “Frequency offset compensation and carrier phase recovery for differentially encoded 16-QAM vector signal in a 60-GHz RoF system,” IEEE Photonics J. 5(4), 7200807 (2013). [CrossRef]
20. S. Cao, S. Zhang, C. Yu, and P.-Y. Kam, “Full-range pilot-assisted frequency offset estimation for OFDM systems,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper JW2A.53. [CrossRef]
21. X. Zhou, X. Yang, R. Li, and K. Long, “Efficient joint carrier frequency offset and phase noise compensation scheme for high-speed coherent optical OFDM systems,” J. Lightwave Technol. 31(11), 1755–1761 (2013). [CrossRef]
22. Y. Gao, A. P. T. Lau, and C. Lu, “Residual carrier-aided frequency offset estimation for square 16-QAM systems,” in 2013 18th OptoElectronics and Communications Conference held jointly with 2013 International Conference on Photonics in Switching, (Optical Society of America, 2013), paper TuPR_8.
23. C. C. Chan, Optical Performance Monitoring: Advanced Techniques for Next-Generation Photonic Networks (Academic Press, 2010).
24. L. Dou, Z. Tao, Y. Zhao, S. Oda, Y. Aoki, T. Hoshida, and J. C. Rasmussen, “Differential pilots aided in-band OSNR monitor with large nonlinear tolerance,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper W4D.3. [CrossRef]
25. J. G. Proakis and M. Salehi, Digital Communications, 5 ed. (McGraw-Hill, 2007).
26. J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, 3rd ed. (Pentice Hall, 1996).
