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A two-stage fast and adaptive chromatic dispersion (CD) estimation algorithm is proposed and demonstrated for coherent polarization-division-multiplexed (PDM) systems. The first stage uses signal power auto-correlation function for the coarse estimation while the second stage utilizes a modified constant modulus algorithm (MCMA) to obtain much more accurate accumulated CD. Simulation results show that the proposed algorithm is sufficient for CD estimation in non-dispersion-managed optical transmission of 112-Gb/s PDM-QPSK or 224-Gb/s PDM-16QAM signals. The concept is further experimentally verified in a 40-Gb/s PDM-QPSK system. Only ~7% estimation time is required to achieve similar accuracy compared to previous MCMA algorithm.
© 2015 Optical Society of America
1. Introduction
Driven by the ever-growing demands of the data traffic, scientists and engineers have spent tremendous efforts in recent years to improve the system overall capacity and channel spectral efficiency (SE) [1–3 ]. Among them, coherent detection, digital signal processing (DSP), polarization-division-multiplexing (PDM) and advanced modulation formats are considered or deployed for the next generation optical networks [4]. In principle, enhanced DSP technology can perfectly compensate for all linear impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) [5–8 ]. Hence, dispersion-compensating-fiber (DCF) is no longer necessary in future coherent systems. To facilitate DSP-based CD compensation, it is highly desirable to have accurate and fast estimation algorithms. So far, various effective CD estimation and mitigation schemes have been proposed, including channel estimation based on training symbols [9], blind equalization in dynamic optical networks and long-haul coherent optical communication systems [10–15 ]. The estimation technique based on modified constant modulus algorithm (MCMA) has attracted more interests and it is accomplished by scanning a range of preset CD values with two iterations in different steps [15]. However, as the length of the transmission link increases (e.g. for long-haul or ultra-long-haul), the algorithm may suffer from complicated or time-consuming calculations. On the other hand, CD estimation algorithm based on the auto correlation of signal power waveform (ACSPW) is proposed with much improved efficiency [12,13 ], while its estimation may not be accurate enough for certain applications.
In this paper, we propose a fast and adaptive CD estimation algorithm with high accuracy based on a two-stage structure. The coarse estimation is accomplished in the first stage by finding the peak value of signal power auto-correlation (similar to ACSPW [12]), while much more accurate accumulated CD is obtained in the second stage after scanning a small range of CD values. Since the concept of constant modulus is still used in the proposed algorithm with much improved efficiency, we call it FCMA (i.e. fast CMA). Simulation results show that the proposed algorithm is sufficient to estimate the accurate accumulated CD for 40/112-Gb/s PDM-QPSK and 80/224-Gb/s PDM-16QAM systems. To further investigate the performance of proposed FCMA algorithm, we also experimentally demonstrate this algorithm in a 40-Gb/s PDM-QPSK system. Only ~7% estimation time is required to achieve similar accuracy compared to previous MCMA algorithms.
2. Theory of proposed FCMA and frequency-domain equalization
The flow schematic of the proposed FCMA algorithm using a two-stage structure is shown in Fig. 1 . For the previous MCMA algorithm, it has to scan through a range of preset CD values with different scanning steps to ensure certain degree of estimation accuracy. For long-haul non-dispersion-managed optical transmission systems, the accumulated CD may be up to tens of thousands ps/nm. In addition, the accumulated CD value may vary a lot in dynamic or reconfigurable network environments. Therefore, it is quite difficult to determine the range of preset CD values. While for the proposed FCMA algorithm, due to the fine estimation of the second-stage, we only need to scan a small range of CD values (i.e. many hundreds of ps/nm) to achieve similar accuracy.
The digital signal Ein[n] firstly launches into the first-stage regarded as the coarse estimation module as shown in Fig. 1. The coarse estimation module utilizes auto-correlation function following the Wiener-Khintchine theorem [16] to calculate the accumulated CD. The auto-correlation function of Ein[n] can be defined as
where Ein[n] is the digital signal, P[n] is the auto-correlation function of Ein[n], FFT and IFFT are the Fourier transform and Fourier inverse transform, respectively. However, in the case of NRZ pulse shape, the peak value of the auto-correlation function employing Eq. (1) is too weak for estimating the accumulated CD. To solve the problem, a delay-and-subtract operation on the sampled electrical waveform can be regarded as a high-pass filter to boost the peak [12]. The corresponding P[n] can be altered as:The location of the peak value in P[n], τ 0, can be given
where T 0 is the Gaussian pulse width, β 2 is the group velocity dispersion (GVD) coefficient, z is the fiber length and T is the symbol period. When the long-haul transmission system is applied, the product of β 2z is far greater than T 0 2 . So the expression of τ 0 can be modified asTherefore, the accumulated CD can be obtainedwhere c is the speed of light and λ is the carrier wavelength. As can be seen from Eq. (5), the calculated dispersion value is sensitive to the transmission rate. For example, when the transmission rate is 10-Gbaud, the estimation resolution δres for the first stage is about 624 ps/nm. But for the 25-Gbaud system, the resolution is improved up to 100 ps/nm. Obviously, the estimation error is still too large for the practical applications, but it could significantly reduce the MCMA complexity. Therefore, for the second stage, the coarse value δestc obtained by the first stage is considered as the center of the range (i.e. from δestc - δres to δestc + δres). In this case, we only require a small range of CD values (i.e. many hundreds ps/nm) to achieve high accuracy. Here, the error function of the second stage [15] derived from Godard’s CMA is given bywhere ε is the error function, E[2n-1] and E[2n] are odd and even samples, R1 and R2 are odd and even constant power which is defined byThe proposed adaptive chromatic dispersion compensation scheme consists of two steps, including CD estimation and frequency-domain dispersion equalization (FDE) [15]. In the FDE step, the all-pass transfer function is defined as
where Dlc, and ω are accumulated CD estimated by the second stage and angular frequency, respectively. Therefore, the regenerated signal (i.e. CD compensation) is expressed aswhere Ein[n] is the digital signal, Efinc is the regenerated signal after CD compensation.3. Simulation results
Before experimental measurements, we carry out numerical simulation for 40/112-Gb/s PDM-QPSK and 80/224-Gb/s PDM-16QAM coherent optical communication systems using the VPI platform. Throughout the simulations, the QPSK/16QAM signal is generated by driving the IQ modulator with a binary 28-Gbaud electrical signal with 231-1 PRBS. The wavelength of the laser source is 1550nm with the linewidth of 100 kHz. The transmission optical link has a dispersion parameter of D = 16 ps/nm/km, an attenuation of α = 0.2 dB/km and a nonlinear coefficient of γ = 1.9 km−1•W−1. Here we use 16384 symbols to estimate the dispersion value and calculate the mean error in all simulations. Figures 2(a) and 2(b) depict the estimation value employing the previous coarse algorithm (i.e. ACSPW algorithm) and new FCMA algorithm with different modulation formats in 10-Gbaud and 28-Gbaud, respectively. The estimation resolutions δres of the ACSPW algorithm are ~624 ps/nm for 10-Gbaud data and ~80 ps/nm for 28-Gbaud data. The estimation error of the FCMA method with different modulation formats and different symbol rates are less than ~40ps/nm in numerical simulations.
Fig. 2 Simulated results of different transmission rates for previous ACSPW algorithm and new FCMA algorithm: fiber length versus dispersion value in (a) 10-Gbaud; (b) 28-Gbaud; Here OSNR = 14dB, DGD = 15ps, PDL = 15dB, Launching power = 0dBm;
The mean error of the FCMA algorithm is shown in Fig. 3(a) with different polarization dependent loss (PDL) values varying from 0 to 25 dB for 112-Gb/s PDM-QPSK and 224-Gb/s PDM-16QAM. Here the transmission link is 10 × 100-km SMF with 14dB-OSNR (optical-signal-to-noise-ratio) and 10/15ps-DGD (differential-group-delay). As can be seen from Fig. 3(a), the FCMA algorithm is insensitive to PDL. Figure 3(b) depicts the mean error versus different DGD values with different OSNR values (i.e. 14dB and 20dB). The estimation error keeps relatively constant for both OSNR values when the DGD is less than 10-ps. However, as DGD increases to be more than 10-ps, the estimation error starts to increase since the signal may be significantly distorted (even CD is compensated). The precision could be further improved by increasing the number of estimation symbols.
Fig. 3 Simulated results with 10 × 100-km SMF for 112-Gb/s PDM-QPSK and 224-Gb/s PDM-16QAM: (a) mean error versus different PDL values with 14dB-OSNR, 10ps and 15ps-DGD; (b) mean error versus different DGD values with different OSNR (i.e. 14dB, 20dB);
4. Experimental setup and results
The experimental setup for 40-Gb/s PDM-QPSK coherent optical communication system over 720-km SMF transmission is shown in Fig. 4 . At the transmitter side, the light from an external cavity laser (ECL) oscillating at ~1550 nm with ~100 kHz linewidth is modulated by an IQ modulator with 10-Gb/s 231-1PRBS to generate 20-Gb/s QPSK signal. The encoded signals are polarization multiplexed to generate 40-Gb/s PDM-QPSK signals employing a interleave scheme that is composed of a coupler, two polarization controllers (PCs), a variable optical attenuator (VOA), 1-km SMF, and a polarization beam combiner (PBC). Here, two PCs, 1-km SMF and the VOA are used to generate two data streams with orthogonal sate of polarization SOPs, decorrelate two data streams, and balance the optical power between two arms, respectively. The transmission optical link is composed of 9 × 80 km spans of SMF (720- km) whose dispersion parameter, attenuation, and nonlinear coefficient are D = 16.5 ps/nm/km, α = 0.2 dB/km, γ = 1.27 km−1•W−1, respectively. Fiber loss of each span is completely compensated using an erbium doped fiber amplifier (EDFA) with a noise figure of ~5dB. At the coherent homodyne receiver side, the received signal and the LO are combined using an optical 90° hybrid. The electrical signals passing through a pair of balanced photodiodes are processed using MATLAB code in the off-line DSP module. CD compensation is also performed using different DSP algorithms. The CD estimation algorithm employs FCMA, ACSPW and MCMA to obtain the accumulated CD value. The frequency-domain dispersion equalization is applied to compensate the accumulated CD value in the experiment. The carrier phase recovery module utilizes the Viterbi-Viterbi phase estimator (V-VPE) to compensate for the laser phase noise.
Fig. 4 Experimental setup of the 40-Gb/s PDM-QPSK system. ECL: External Cavity Laser; VOA: Variable Optical Attenuator; Delay: Variable Optical Delay Line; PBS: Polarization Beam Splitter; PBC: Polarization Beam Combiner; PC: Polarization Controller; EDFA: Erbium Doped Fiber Amplifier; LO: Local Oscillator; Tx: Transmitter; Rx: Receiver.
The auto-correlation curves are shown in Fig. 5(a) with different fiber lengths (i.e. 600-km, 660-km, 715-km) for 40-Gb/s PDM-QPSK. As can be seen, there are three different peak values for the auto-correlation function when the fiber lengths are set to be 600-km, 660-km and 715-km, respectively. Here, all the accumulated CD value can be calculated by using Eq. (5).
Fig. 5 Experimental results: (a) The auto-correlation curves with different fiber lengths (i.e. 600-km, 660-km, 715-km); (b) CD monitoring results using ACSPW and FCMA algorithms with different fiber lengths.
➢ Accuracy
The estimation accuracy with the different fiber lengths is shown in Fig. 5(b). The estimation error of the FCMA algorithm is less than ~60ps/nm, about 10-time improvement compared to that of ACSPW algorithm. This improvement is further verified through CD compensation. Figure 6(a) shows the measured BER performances over 80-km transmission after CD compensation. The power penalty improvement of ~1.5-dB is achieved using the FCMA algorithm compared to that using the ACSPW one at 10−3 bit-error-rate (BER).
Fig. 6 Experimental results: (a) BER performance after CD compensation over 80-km SMF for back-to-back, using ACSPW and FCMA algorithms; (b) BER versus the step number employing MCMA and FCMA algorithms over 720-km SMF.
➢ Complexity/Efficiency
We measure the complexity of the FCMA algorithm and MCMA algorithm [15] as shown in Fig. 6(b). In proposed algorithm, the main computation consumption depends on FFT and auto-correlation. When the block length of FFT is N, FFT algorithm and complex multiplication require O(N*log10N) and O(N) operations to complete the transformation, respectively. On the other hand, the first stage based on auto-correlation includes two FFT operations and one complex multiplication. Therefore, the complexity of the first stage can be expressed as O(2N*log10N + N). For the second stage, the accurate CD value is estimated by performing FDE defined as Eq. (9) and error function repeatedly. Since FDE consists of two FFT operations and one complex multiplication, the complexity of FDE is the same to the auto-correlation, which is given by O(2N*log10N + N) as well. Furthermore, assuming the number of loop is Nc, and the complexity of error function is O(N), the computation of the second stage can be expressed as O(Nc*(2N*log10N + 2N)). Therefore, the total complexity of proposed algorithm is O((Nc + 1)*(2N*log10N) + (2Nc + 1)*N). According to the Fig. 6(b), the step number of the MCMA algorithm with two iterations in different steps is more than that of the FCMA algorithm. Therefore, the estimation time employing FCMA is only ~7% compared to that of MCMA with the same BER.
5. Discussion and conclusion
We have proposed a fast and adaptive CD estimation algorithm (i.e. FCMA) with high accuracy based on a two-stage structure. The effectiveness of the proposed FCMA algorithm is demonstrated by both simulation (40/112-Gb/s PDM-QPSK and 80/224-Gb/s PDM-16QAM) and experiment (40-Gb/s PDM-QPSK over 720-km SMF). The algorithm is robust to other impairments (i.e. PDL, OSNR, nonlinear effect) while may be affected by large PMD values. The experimentally measured BER results show that the power penalty improvement compared to the coarse algorithm (i.e. ACSPW) is ~1.5-dB at 10−3 BER. More important, the estimation time employing the FCMA algorithm is only ~7% compared to that of MCMA one.
Acknowledgments
This research is supported by the Natural Science Foundation of China (No. 61325023, 61335005, 61275068, 61401378), the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China, the Fundamental Research Funds for the Central Universities, China, and Key Lab of Optical Fiber Sensing & Communications (UESTC), Ministry of Education, China.
References and links
1. L. S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J. 3(2), 325–330 (2011). [CrossRef]
2. P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010). [CrossRef]
3. Z. Chen, L. Yan, W. Pan, B. Luo, Y. Guo, H. Jiang, A. Yi, Y. Sun, and X. Wu, “Transmission of multi-polarization-multiplexed signals: another freedom to explore?” Opt. Express 21(9), 11590–11605 (2013). [CrossRef] [PubMed]
4. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]
5. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. 27(16), 3614–3622 (2009). [CrossRef]
6. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]
7. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010). [CrossRef]
8. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” Proc. European Conference on Optical Communication 2008 (ECOC 2008), paper We.2.E.3. [CrossRef]
9. A. V. Tran, C. Zhu, C. Do, S. Chen, T. Anderson, D. Hewitt, and E. Skafidas, “8x40-Gb/s optical coherent Pol-Mux single carrier system with frequency domain equalization and training sequences,” IEEE Photon. Technol. Lett. 24(11), 885–887 (2012). [CrossRef]
10. R. Borkowski, X. Zhang, D. Zibar, R. Younce, and I. T. Monroy, “Experimental demonstration of adaptive digital monitoring and compensation of chromatic dispersion for coherent DP-QPSK receiver,” Opt. Express 19(26), B728–B735 (2011). [CrossRef] [PubMed]
11. D. Wang, C. Lu, A. P. T. Lau, and S. He, “Adaptive chromatic dispersion compensation for coherent communication systems using delay-tap sampling technique,” IEEE Photon. Technol. Lett. 23(14), 1016–1018 (2011). [CrossRef]
12. Q. Sui, A. P. T. Lau, and C. Lu, “Fast and robust blind chromatic dispersion estimation using auto-correlation of signal power waveform for digital coherent systems,” J. Lightwave Technol. 31(2), 306–312 (2013). [CrossRef]
13. F. C. Pereira, V. N. Rozental, M. Camera, G. Bruno, and D. A. A. Mello, “Experimental analysis of the power auto-correlation-based chromatic dispersion estimation method,” IEEE Photon. J. 5(4), 7901608 (2013). [CrossRef]
14. C. Xie, “Chromatic Dispersion Estimation for Single-Carrier Coherent Optical Communications,” IEEE Photon. Technol. Lett. 25(10), 992–995 (2013). [CrossRef]
15. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” Proc. Optical Fiber Communication Conference2009(OFC'2009), paper OMT1. [CrossRef]
16. J. Proakis Digital Signal Processing: Principles, Algorithms, and Applications (Prentice Hall, 1996).
