Chromatic dispersion estimation methods using polynomial fitting in PDM-QPSK or other multilevel-format coherent optical systems

Optical Fiber Technology 19 (2013) 162–168

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Optical Fiber Technology www.elsevier.com/locate/yofte

Chromatic dispersion estimation methods using polynomial fitting in PDM-QPSK or other multilevel-format coherent optical systems Junyi Wang a, Xin Jiang b, Xuan He a, Yi Weng a,⇑, Zhongqi Pan a a b

Department of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, United States Department of Engineering Science and Physics, College of Staten Island, New York, NY 10314, United States

a r t i c l e

i n f o

Article history: Received 21 September 2012 Revised 13 December 2012 Available online 23 January 2013 Keywords: Chromatic dispersion estimation Measurement Monitoring Polynomial fitting algorithm 50%-RZ QPSK 16QAM PDM-QPSK

a b s t r a c t We propose a polynomial fitting algorithm based method for non-data-aided chromatic dispersion (CD) estimation in single carrier (SC) coherent optical systems with arbitrary modulation formats, and compare it with our previously proposed CD estimation method which is also based on the polynomial fitting algorithm but requires special modulation formats thus is a data-aided CD estimation method for systems with PDM-QPSK or other multilevel modulation formats. For the data-aided CD estimation method, an extra chirp-free OOK signal is transmitted. The curve of the average phase at the frequency ± f as a function of the frequency f is measured at the coherent receiver. The accumulated CD is then estimated with a polynomial fitting algorithm. In the simulation of a 50 Gbaud 50%-RZ OOK system through 12.5  80 km standard single mode fiber (SSMF), the estimation errors are within ± 50 ps/nm in 20 tests when the launch power is from 5 dBm to 1 dBm. Non-data-aided CD estimation for arbitrary modulation formats is achieved by measuring the differential phase between frequency f ± fs/2 (fs is the symbol rate) in digital coherent receivers. The estimation errors are within ± 200 ps/nm, in a 50 Gbaud PDMQPSK system through 10  80 km SSMF with the launch power from 3 dBm to 1 dBm. The estimation accuracy can be potentially improved by averaging multiple results. The data-aided CD estimation method has an inherently bigger estimation range than that of the newly proposed non-data-aided method, while the newly proposed non-data-aided method can tolerate a much larger frequency offset between the transmitter and the local oscillator. These methods are promising for future optical fiber networks with dynamic optical routing and coherent detection. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Chromatic dispersion (CD) in an optical fiber link acts as an allpass filter to the electric field of the input optical signal, i.e., the different spectral components of the input signal will experience only different phase shifts. Since the phase of the input optical signal can be detected by a digital coherent receiver, the CD induced impairments thus can potentially be reversed or compensated completely by a finite impulse response (FIR) or frequency domain equalization (FDE) filter in the electrical domain using digital signal processing (DSP) techniques [1,2]. Unlike traditional CD monitoring/measurement and mitigation approaches, digital coherent receivers do not require any additional optical devices, thus enable a low cost and reliable in-line estimation and optimum equalization of CD induced impairments. On the other hand, since the future coherent systems may not be dispersion managed [3], CD monitoring/measurement and mitigation in the coherent receivers ⇑ Corresponding author. Fax: +1 337 482 6687. E-mail address: [email protected] (Y. Weng). 1068-5200/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2012.12.010

should accommodate a wide range of accumulated dispersion value. In-service CD measurement or monitoring would become more important, when optical route reconfigurable networks enabled by optical add-drop multiplexer (ROADM) [4] become more popular. Most CD measurement instruments for characterizing fiber spools or fiber communication links use the principle that CD causes the optical pulses at different wavelengths propagating at different speeds inside a fiber, thus leading to relative delays in arrival times. Directly measuring the relative delays between the pulses at different wavelengths (time-of-flight method) requires accurate timing of pulse arrival times [5]. A more common phase-shift method uses sinusoidal-intensity modulated optical signal. CD then can be accurately calculated from the phase differences of input and output signals at different wavelengths [6]. Both methods require complex setup and wide bandwidth which are not suitable for in-service measurement or monitoring. Recently, several in-service CD measurement or monitoring methods have been proposed and demonstrated. One report used two optical supervisory channels to measure CD of more than 80 km of single mode fiber with an accuracy of ±25 ps/nm [7]. An-

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other report is capable of measuring residual CD of up to ±3000 ps/ nm with an accuracy of better than ±30 ps/nm [8]. Mitigation of CD impairments can typically be performed using optimized equalizer filters by blind equalization algorithms [9,10]. One report estimated CD from the weights of a blind equalizer. The monitoring range is ±4000 ps/nm with an accuracy of ±90 ps/nm [10]. A drawback of this method is that most of the blind estimation approaches need a priori knowledge of the modulation formats, thus need to be individually designed for each modulation scheme [11]. Another report used an analytical formula derived from phases at four different frequencies which can monitor the accumulated CD for arbitrary modulation formats, with a CD range about ±3000 ps/nm and an accuracy of ±200 ps/nm [12]. Although the measurement or monitoring range of these methods may be enough for traditional chromatic dispersion managed system, the next generation of coherent fiber system may not be dispersion managed [13], with the accumulated CD up to 16,000 ps/nm for a typical 1000 km fiber link. In such non dispersion managed systems, wide range CD estimation methods are desirable. Wide range CD estimation can be achieved in the coherent receiver by measuring the auto-correlation-function (ACF) of the received signal [13,14], or measuring the phase shift at different frequencies due to chromatic dispersion [15–18]. In [14], the location of the pulse in ACF is used to estimate CD with a CD range of ±80,000 ps/nm and an accuracy of ±224 ps/nm for a 112 Gbit/s PDM-QPSK system. The drawback of the ACF method is its computation complexity. Another way to achieve wide CD estimation range with possibly less computation complexity could be measuring the phase shift at different frequencies due to chromatic dispersion. The challenge of the phase shift method is how to obtain the initial phase at different frequencies. Some data-aided techniques have been explored. In [17], complementary Golay sequences are used to achieve a constant initial phase at different frequencies, then curve fitting is used on the phase at different frequencies of the received signal to estimate CD with a range of ±35,360 ps/nm and an accuracy of ±318 ps/nm for a 40 Gbit/s PDM-QPSK system. In [18], we proposed and verified a method to estimate CD by polynomial fitting on the average phase of frequency ± f using extra chirp-free OOK/BPSK signals. Such method can be used as data-aided CD estimation method for PDM-QPSK or other multilevel-format systems. In a system simulation with a 50 Gbit/s (or 50 Gbaud) 50%-RZ single-polarization OOK signal, the estimation range can be up to ±16,000 ps/nm with an accuracy of ±50 ps/nm [18]. All these CD estimation methods using polynomial fitting algorithms require extra special data to aid the estimation. However, in SC coherent systems there is usually no training sequence, and a data-aided CD estimation would definitely add more extra complexity or cost to the system. In this paper, we propose and verify a non-data-aided modulation-format independent CD estimation method based on the polynomial fitting algorithm using coherent detection and DSP in SC systems with arbitrary modulation formats. The results are compared with our previously proposed data-aided CD estimation method for PDM-QPSK or other multilevel-format coherent systems, which is also based on the polynomial fitting algorithm. To our best knowledge, no other non-data-aided CD estimation using the polynomial fitting algorithm for PDM-QPSK or other multilevel-format coherent systems has been proposed yet. This paper is organized as follows. The principles of our dataaided CD estimation and non-data-aided CD estimation with polynomial fitting for SC systems are reviewed/ introduced in Section 2. Section 3 shows the simulation setup for the CD estimation methods. Section 4 presents the simulation results for the data-aided CD estimation in 50-Gbaud systems with 50%-RZ OOK and the nondata-aided CD estimation in 50 Gbaud QPSK, 16QAM and PDMQPSK coherent systems. Section 5 concludes this paper.

2. Principle of CD estimation methods using polynomial fitting Polynomial fitting algorithm is used to find the coefficient of polynomial P(x) with x the variable, which makes P(x) closest to target data Y in the sense of least-squares. As CD is proportional to the second order coefficient of the phase of the transfer function [19], so polynomial fitting is quite suitable for CD estimation by measuring the phase shifts. However, if the initial phases are unknown, it is still not easy to know the phase shifts at different frequencies. In this section, we introduce two initial-phaseindependent functions, average_phase(f) and differential_phase(f), either of which is a polynomial of frequency f with CD proportional to a coefficient. Based on measuring and polynomial fitting these two functions, CD estimations are achieved. The ‘‘polyfit’’ function in MATLAB is used for polynomial fitting. 2.1. Data-aided CD estimation for PDM-QPSK or other multilevel coherent systems by polynomial fitting on average_phase(f) For a binary chirp-free modulation, such as chirp-free OOK or BPSK, complex amplitude of an optical signal can be expressed with A(t)eiu, where A(t) is the real amplitude, u is the original phase. The Fourier transform of the modulated signal can be expressed as

FðxÞ ¼

Z

þ1

AðtÞei/ eixt dt

1

¼ ei/

Z

þ1

AðtÞ cosðxtÞ dt  i

1

Z

þ1

AðtÞ sinðxtÞ dt

 ð1Þ

1

With spectral symmetry of a real signal A(t), assuming that the phase at frequency f is u(f), it is easy to have

/ðf Þ þ /ðf Þ ¼ 2/

ð2Þ

After transmitting through optical fiber of length z with group velocity dispersion (GVD) of b2, the phase at frequency f of the received optical signal becomes

  x2 /ðf ; zÞ ¼ /ðf Þ þ z b0 þ b1 x þ b2 2

ð3Þ

If average-phase is defined as the average of the phase at frequency ± f, from (2) and (3), and considering the fiber’s dispersion parameter Dk ¼  2k2pc b2 , one can have ref

/ðf ; zÞ þ /ðf ; zÞ zb x2 ¼ / þ zb0 þ 2 2 2 ¼ const1 þ const2 ðDtotal Þf 2

average phaseðf Þ ¼

ð4Þ

In (4), x = 2pf, const1 and const2 are two constants at the receiver, and Dtotal is the total accumulated CD. To recover the phase at discrete frequency in the digital coherent receiver, a fast Fourier transform (FFT) is used. Assume AIQ = EI + i  EQ represents the complex signal of the optical signal at coherent receiver, while EI and EQ represent in-phase signal and quadrature signal respectively. Both EI and EQ are sampled at the symbol rate (e.g. 1 sample per symbol). A FFT is done on a block in AIQ with a FFT size of N = 2n. The FFT transform gives the complex representation of the components at different discrete frequencies, with which the phases at those discrete frequencies can be calculated directly. If the symbol rate is fs, the sampling rate is also fs, then the spectrum range of the FFT transform cover [fs/2, fs/2). If a given frequency f is within those discrete frequency points of the FFT transform except fs/2, then f is also among the discrete frequency points of the FFT transform. Therefore, the averge_phase as a function of f can be calculated. As shown in (4), average phase function is a parabolic curve whose second order coefficient is proportional to Dtotal. With

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a polynomial fitting algorithm, the second order coefficient can be estimated, and then Dtotal can be calculated. Fig. 1a shows how the curve changes with different CD, or Dtotal. Because of the phase noise, the curve is actually noisy and may consist of phase-jumping, as shown in Fig. 1b. However, the phasejumping only tends to happened in high frequency range (or when frequency f is large). This can be explained with high power spectral density and small slope of the parabolic curve in low frequency range. High power spectral density indicates the impairment from ASE is small, and small slope indicates small phase differences between neighbor frequency points. This trend is in fact beneficial to the CD estimation algorithm. By using a low-frequency range for the CD estimation where no phase-jumping or phase-jumping is negligible, this method can tolerate large noise from ASE and some other impairment in the system. In another aspect, this trend makes it straightforward on how to choose an optimum fitting range as long as possible, as the starting frequency is already known to be 0. Above analysis does not consider the frequency offset between the transmitter and the local oscillator (LO). When heterodyne coherent detection is used, a small frequency offset only increases a small first order coefficient of the curve and does not affect the accuracy. However, a big frequency offset may greatly increase the possibility of the phase jumping in the curve and can affect the accuracy/range of the estimation. Actually, this method requires the frequency offset to be limited to a small value. First order PMD does not affect the second order coefficient of the curve, thus PMD, to its first order, is not an impact factor. Nonlinearity may contribute to the inaccuracy of the CD estimation. The estimation range is expected to be very huge because of the polynomial fitting algorithm. The polynomial fitting algorithm also helps to increase the accuracy. 2.2. Non-data-aided CD estimation for PDM-QPSK or other multilevel coherent systems by polynomial fitting on differential_phase(f) According to [12], the phase of a modulated optical signal at symbol rate fs is a periodic function with the fundamental frequency of fs. This is valid for arbitrary modulation formats. Assuming that the phase at frequency f is u(f), this periodicity property then can be expressed as

/ðf þ fs =2Þ  /ðf  fs =2Þ ¼ 0

ð5Þ

After the modulated optical signal transmits through an optical fiber with the length z and GVD b2, the phase of the output signal at frequency f, /ðf ; zÞ, can be expressed as

  x2 /ðf ; zÞ ¼ /ðf Þ þ z b0 þ b1 x þ b2 2

ð6Þ

Fig. 1a. Principle of the CD estimation method using average_phase(f): The theoretical curve of average_phase(f).

Fig. 1b. Principle of the CD estimation method using average_phase(f): An example of the measured average_phase(f).

If differential_phase(f) is defined as the subtraction of the phase at frequency f + fs/2 and the phase at frequency f  fs/2, with (5) and (6) and fiber’s dispersion parameter Dk ¼  2k2pc b2 , one can have ref

differential phaseðf Þ ¼ /ðf þ fs =2; zÞ  /ðf  fs =2; zÞ ¼ const1 þ const2 Dtotal f

ð7Þ

where x is 2pf, and Dtotal is zDk, the accumulated total dispersion. The differential_phase(f) is a function of frequency f and Dtotal, as shown in (7). If one can find the slope of the differential_phase(f), the accumulated CD, or Dtotal can then be estimated. Fig. 2a shows theoretical difference_phase(f) function as a straight line whose slope varies with the accumulated CD as shown in Fig. 2a. Notes that (7) is independent of modulation formats, therefore can be used to estimate CD with arbitrary modulation formats. In the digital coherent receiver, to obtain the differential phase at some discrete frequency points, a similar FFT method as described in Section 2.1 is used. However, to make sure both f ± fs/2 are covered within the spectrum range of FFT transform, the sampling rate of 2 times the symbol rate is required. In this situation, the FFT spectrum range is [fs + fs). For any discrete frequency f of the FFT transform in [fs/2, fs/2), f ± fs/2 are among the discrete frequency points of the FFT transform. Due to the phase noise, the curve is actually noisy and may consist of several discrete line segments with almost same slopes, as shown in Fig. 2b. The estimation algorithm is to find the common slope among these line segments with the minimized estimation error. In the simulation, the error between the original (or measured) curve and the fitting curve is evaluated by reducing the fitting frequency range until the estimated slope converges, i.e., the average absolute error between the original curve and the fitting

Fig. 2a. Principle of the CD estimation method using differential_phase(f): The theoretical curve of differential_phase(f).

J. Wang et al. / Optical Fiber Technology 19 (2013) 162–168

Fig. 2b. Principle of the CD estimation method using differential_phase(f): An example of the measured differential_phase(f).

curve is below a threshold. An appropriate threshold can be determined by the phase noise, the time window and the target CD. When heterodyne coherent detection is used, the frequency offset does not affect the algorithm’s validity as it only adds a constant to the curve differential_phase(f). First order PMD only contribute to a constant component of the curve differential_phase(f), thus has no effect on either the validity or the accuracy. Nonlinearity may contribute to the inaccuracy of the CD estimation, which is similar as that for the data-aided CD estimation method in Section 2.1. The estimation range is wide and the accuracy is good because of the polynomial fitting algorithm, which is the same as those in the data-aided method. Due to its format independency, this method using the differential phase curve can be implemented in general transmission systems to monitor CD variations in real time.

165

estimation. The laser line-widths of the transmitter and receiver are both 100 kHz, and the offset between two center frequencies is 1 MHz. PMD is set to be 0.1 ps/km0.5 for SSMF, fiber nonlinearity is also included with the nonlinear index n2 = 2.6  1020 m2/W. With the same system structure in Fig. 3, we then investigate the performance of the non-data-aided CD estimation for PDMQPSK or other multilevel coherent systems by polynomial fitting differential_phase(f). The transmitter generates 50 Gbaud QPSK, 16QAM or PDM-QPSK. And combined with two transmission setups the CD estimation method is investigated in three scenarios, which are QPSK with CD emulator, 16QAM with CD emulator and PDM-QPSK with transmission spans. In the first two scenarios, CD emulator adds CD only. In the last scenario, 10 spans of standard single mode fiber (SSMF) are used to evaluate the estimation performance with all other impairments included. Each fiber span consists of an EDFA and 80 km SSMF with a total accumulated dispersion of 12800 ps/nm. The noise figure of the EDFAs, the fiber’s PMD and the nonlinear refraction index are the same as those for investigating the data-aided CD estimation method. At the receiver a 100 GHz optical filter is used before the coherent receiver to remove the out-of-band ASE noise. After coherent detection, the signal is oversampled at two times of the symbol rate before sending to DSP for CD estimation. The frequency offset between the transmitter and the LO is 1 MHz most of the time, and can be 1 MHz to 1 GHz on investigating the offset tolerance. The laser line-widths of the transmitter and receiver and the total symbol number used in each test are the same as those for investigating the data-aided CD estimation method.

4. Results and discussion 4.1. Data-aided CD estimation for PDM-QPSK or other multilevel coherent systems by polynomial fitting average_phase(f)

3. Simulation setup To verify the validity and investigate the performance of the CD estimation methods for PDM-QPSK or other multilevel coherent systems by polynomial fitting average_phase(f) or differential_phase(f),we simulate a single channel coherent optical system with VPI transmission maker and MATLAB. Fig. 3 shows the simulation setup. With this setup we firstly investigate the performance of the data-aided CD estimation for PDM-QPSK or other multilevel coherent systems by polynomial fitting average_phase(f). The transmitter generates a 50 Gbaud 50%-RZ OOK signal to aid the CD estimation. There are two setups for the transmission line. One uses CD emulator, adding CD only. The other setup consists of 12 spans with an EDFA and 80 km SSMF in each span, and 40 km SSMF after the 12 spans to give a total accumulated CD of 16,000 ps/nm. The noise figure of EDFA is 5 dB. At the receiver a 66 GHz optical filter is used before coherent detection. After coherent detection, the signal is sampled at the symbol rate and then sent to DSP for the CD estimation. 16,384 symbols are used for each

To investigate the data-aided CD estimation method for PDMQPSK or other multilevel coherent systems by polynomial fitting average_phase(f), we firstly use a CD emulator in the transmission line. We also add some optical noise to set the OSNR. Fig. 4 shows that the measured CD is approximately equal to the target CD set in the CD emulator, with the OSNR 15 dB. Fig. 5 shows the distribution of the estimation error with the OSNR 15 dB and the CD 16,000 ps/nm, which is close to a Gaussian distribution. Therefore, the overall estimation error can be reduced by taking multiple tests and averaging the results. Fig. 6 and Table 1 show the relation between the estimation error and the OSNR. Obviously, the estimation errors are smaller with a higher OSNR. Then we use transmission spans to include the effects of PMD and nonlinearity, with totally 1000 km SSMF. The accumulated CD is 16,000 ps/nm. Fig. 7 shows the accuracy is better than ±50 ps/nm in 20 estimations, when the launch power per channel is from 5 dBm to 1 dBm. For reference, the OSNR after transmission with different launch powers is shown in Table 2.

Fig. 3. Simulation setup.

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Fig. 4. Measured CD vs. the target CD with 50 Gbaud 50%-RZ OOK (OSNR = 15 dB).

Fig. 7. Estimation results after 12.5  80 km SSMF with 50 Gbaud 50%-RZ OOK.

Table 2 OSNR after transmission with different launch powers for 50%-RZ OOK. Launch power (dBm) OSNR after transmission (dB)

5 15.9

4 18.1

3 19.9

2 21.6

1 23.1

Fig. 5. Distribution of the estimation error with 50 Gbaud 50%-RZ OOK (OSNR = 15 dB, CD = 16000 ps/nm).

Fig. 8. Measured CD vs. the target CD for 50 Gbaud QPSK (OSNR = 20 dB).

Fig. 6. Estimation results with different OSNR with 50 Gbaud 50%-RZ OOK (CD = 16000 ps/nm).

Table 1 Error mean and standard deviation for Fig. 6. OSNR (dB) Error mean (ps/nm) Error standard deviation (ps/nm)

15 6.00 19.04.

20 5.00 10.20

25 5.11 8.83

4.2. Non-data-aided CD estimation for PDM-QPSK or other multilevel coherent systems by polynomial fitting differential_phase(f) To investigate the non-data-aided CD estimation method for PDM-QPSK or other multilevel coherent systems by polynomial fitting differential_phase(f), we firstly use QPSK and a CD emulator in the transmission line. Fig. 8 shows the estimation results using the CD emulator with the OSNR of 20 dB. The measured CD is approx-

Fig. 9. Distribution of error between the measured CD and the target CD for 50 Gbaud QPSK (OSNR = 20 dB, CD = 12800 ps/nm).

imately equal to that of the emulator. Fig. 9 shows the distribution of the estimation error with the CD of 12,800 ps/nm and the OSNR of 20 dB. The distribution is still close to a Gaussian distribution in this scenario. Therefore, the overall estimation error could be reduced by taking multiple tests and averaging the results. Fig. 10 and Table 3 show the relation between the estimation error and the OSNR with the accumulated CD of 12,800 ps/nm. The results show the CD estimation is more accurate with a higher OSNR.

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Fig. 10. Estimation results with different OSNR for 50 Gbaud QPSK (CD = 12800 ps/ nm).

Fig. 12. Distribution of the error between the measured CD and the target CD for 50 Gbaud 16QAM (OSNR = 20 dB, CD = 12800 ps/nm).

Table 3 Error mean and standard deviation for Fig. 10. OSNR (dB) Error mean (ps/nm) Error standard deviation (ps/nm)

15 42.98 194.84

20 4.61 13.02

25 1.51 5.24

30 0.04 1.54

Fig. 13. Estimation (CD = 12800 ps/nm).

results

with

different

OSNR

for

50 Gbaud

16QAM

Table 5 Error mean and standard deviation for Fig. 13.

Fig. 11. Estimation results with (OSNR = 20 dB, CD = 12800 ps/nm).

frequency

offsets

for

50 Gbaud

QPSK

OSNR (dB) Error mean (ps/nm) Error standard deviation (ps/nm)

15 37.66 247.58

20 7.84 28.21

25 4.48 10.19

30 1.09 4.28

Table 4 Error mean and standard deviation for Fig. 11. Frequency offset Error mean (ps/nm) Error standard deviation (ps/nm)

1 MHz 4.61 13.02

500 MHz 6.09 13.47

1 GHz 6.50 14.41

Fig. 11 and Table 4 show some other results with QPSK format and a CD emulator, to prove the high tolerance to the frequency offset. With the frequency offset from 1 MHz to 1 GHz, the estimation accuracy keeps almost the same. Compared to the data-aided CD estimation method for PDM-QPSK or other multilevel coherent systems by polynomial fitting average_phase(f), which requires a small frequency offset or a frequency offset estimation before CD estimation if the frequency offset is big, this method would definitely simplify the system design. Then we use 16QAM and a CD emulator to verify the modulation format independency. The results are shown in Figs. 12 and 13 and Table 5. The target accumulated CD and the OSNR keep the same. The results are similar as that with QPSK. But the estimation error is bigger for 16QAM than QPSK. This is because the spectrum of 16QAM is narrower. Wider spectrum implies bigger search

Fig. 14. Estimation results after 10  80 km SSMF for 50 Gbaud PDM-QPSK.

range for a valid line segment, thus contribute to a better estimation performance. Finally, the performance of the CD estimation algorithm is evaluated through a 10-span fiber link for PDM-QPSK signal transmission. Other impairments such as PMD and nonlinearity are also included in the fiber link. The total transmission is 800 km SSMF

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Table 6 OSNR after transmission with different launch powers for PDM-QPSK. Launch power (dBm) OSNR after transmission (dB)

5 17.8

4 19.6

3 21.3

2 22.9

References 1 24.3

with the accumulated CD of 12,800 ps/nm. Fig. 14 shows that the estimation error is less than ±200 ps/nm in 10 estimations, when the launch power changes from 3 dBm to 1 dBm. For reference, the OSNR after transmission with different launch powers is shown in Table 6. Since the curve for the non-data-aided CD estimation is a straight line, a smooth algorithm with a large average window on the straight line would reduce the effect from the noise related with OSNR, which is worth of further research. 5. Conclusion We proposed a non-data-aided polynomial fitting based CD estimation for PDM-QPSK or other multilevel SC coherent optical systems, and compared it with another data-aided polynomial fitting based CD estimation also for such systems. For the data-aided CD estimation, we measured the curve of average phase at the frequency ± f vs. the frequency f, and estimated the cumulated CD with a polynomial fitting algorithm. In the simulation of a 50 Gbaud system through 12.5  80 km SSMF with a 50%-RZ OOK signal to aid the estimation, the estimation errors are within ±50 ps/nm in 20 tests when the launch power per channel is from 5 dBm to 1 dBm. Non-data-aided CD estimation for arbitrary modulation formats is achieved by measuring the differential phase between the frequency f ± fs/2 in digital coherent receivers. The estimation range for a 50 Gbaud PDM-QPSK system can be up to ±12,800 ps/nm with an accuracy of better than ±200 ps/nm. The estimation accuracy can be potentially improved by averaging multiple results. The CD range of the data-aided polynomial fitting based method is inherently bigger than that of the non data-aided polynomial fitting based method, while the latter can tolerate a very big frequency offset between the transmitter and the local oscillator which the data-aided one cannot. These methods are promising for future optical fiber networks with dynamic optical routing and coherent detection.

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