Experimental evaluation of chromatic dispersion estimation method using polynomial fitting

Optics Communications 331 (2014) 119–123

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Experimental evaluation of chromatic dispersion estimation method using polynomial fitting Xin Jiang a,n, Junyi Wang b, Zhongqi Pan b a b

Department of Engineering Science and Physics, College of Staten Island, City University of New York, Staten Island, NY 10314, USA Department of Electrical Engineering and Computer Engineering, University of Louisiana at Lafayette USA

art ic l e i nf o

a b s t r a c t

Article history: Received 25 March 2014 Received in revised form 1 June 2014 Accepted 2 June 2014 Available online 12 June 2014

We experimentally validate a non-data-aided, modulation-format independent chromatic dispersion (CD) estimation method based on polynomial fitting algorithm in single-carrier coherent optical system with a 40 Gb/s polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) system. The non-data-aided CD estimation for arbitrary modulation formats is achieved by measuring the differential phase between frequency f7 fs/2 (fs is the symbol rate) in digital coherent receivers. The estimation range for a 40 Gb/s PDM-QPSK signal can be up to 20,000 ps/nm with a measurement accuracy of 7 200 ps/nm. The maximum CD measurement is 25,000 ps/nm with a measurement error of 2%. & 2014 Elsevier B.V. All rights reserved.

Keywords: Chromatic dispersion estimation Polynomial fitting algorithm Optical fiber communications and subsystems Polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) Measurement

1. Introduction Chromatic dispersion (CD) is one of major impairments in optical fiber transmission system with a data rate of 10 Gb/s or higher. It can cause different spectral components of an optical signal experiencing different phase shifts in optical fiber link. These different phase shifts may induce signal distortions, thus impact data recovery at the receiver. Therefore CD needs to be compensated either optically or electronically. In optical systems using coherent detection technology, the phase of an optical signal can be detected by a digital coherent receiver, therefore, the CD induced phase shift can be removed or compensated in electrical domain using digital signal processing (DSP) techniques ([1–5]). Since CD can be compensated electronically, optical CD compensator may not be needed in the future coherent networks, which lead to a large amount of CD accumulated at the optical receiver after long distance transmission without dispersion management. In general, the DSP process can use some kind of adaptive algorithm to estimate CD and perform compensation. The adaptive algorithm can be much simplified if the approximate CD value of the incoming signal is known. It is an interest of research to find a simple method to monitor or measure

n

Corresponding author. Tel.: þ 1 718 982 3475; fax: þ1 718 982 2830. E-mail address: [email protected] (X. Jiang).

http://dx.doi.org/10.1016/j.optcom.2014.06.003 0030-4018/& 2014 Elsevier B.V. All rights reserved.

CD that can help simplifying the DSP process. Suitable in-service CD measurement will be more important for reconfigurable optical networks which may have large CD variation after different path through the network. Consider a typical system with 1000 km of single mode fiber (SMF), the accumulated CD can be up to 16,000 ps/ nm without optical dispersion compensation. A desirable CD estimation method should have a wide range up to 16,000 ps/nm. Various approaches for wide range CD measurement for coherent system have been proposed recently ([6–11]). One method was to use auto-correlation-function (ACF) of the receiving signal ([6]). A good result of measurement of 80,000 ps/nm was obtained in simulation. Another type of approaches was to measure phase shifts directly in digital receiver ([7–11]). The challenge of this type of measurements is to obtain the initial phase shifts at the transmitter. In [7,8], complementary Golay sequences were used to maintain a constant initial phase at different frequencies. A measurement range of 735,360 ps/nm with an accuracy of 7318 ps/nm for a 40 Gb/s polarization division multiplexed (PDM) quadrature phase shift keying (QPSK) system was achieved in experiment [8]. In [9], CD was estimated for some special modulation formats, such as chirp-free on-off-keyed (OOK) signals or binary phase shift keying (BPSK) signals, using polynomial fitting on average phase of frequency 7f. Methods for modulation format independent were also proposed. In [10], Zweck and Menyuk used the phases of signal at four special frequencies to calculate the CD for arbitrary modulation format data

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and achieved a CD measurement of approximately 3000 ps/nm with 2% accuracy in simulation. In [11], we proposed to use polynomial fitting algorithm to estimate CD for non-data-aided, modulation independent format and achieved 712,800 ps/nm with an accuracy of better than 7200 ps/nm in simulation. Considering the difficulty of accurately modeling a complex high speed transmitter and receiver for coherent system, it is worth to validate the algorithm using real experimental data. In this paper, we experimentally validate the proposed CD estimation method using polynomial fitting algorithm for modulation-format independent data. A 40 Gb/s PDM-QPSK system with a recirculating loop is used to perform the experimental validation.

large frequency offset between transmitter and receiver and is polarization independent.

3. Experimental setup

The parameters β0–β2 in Eq. (2) are the Taylor series expansion. ω is angular frequency (ω ¼2πf). The phase difference at

The experimental setup is shown in Fig. 2. A 1550 nm optical signal light is generated by an Emcore tunable external cavity laser (ECL) with a low line-width of  100 kHz. The continuous wave (CW) is modulated by a nested IQ optical modulator to generate an optical QPSK modulated signal. The IQ modulator is driven by a pseudorandom binary sequence (PRBS) pattern generator. The symbol rate is set at 10 Gbaud and the pattern length is 215-1. The modulated optical signal is then split into two parts by a polarization maintaining (PM) coupler and combined by a polarization beam combiner (PBC) to form a PDM-QPSK signal. A short PM fiber was used in one of path to decorrelate the two polarization signals. After amplification, the PDMQPSK signal is fed into a re-circulating loop. The loop consists of an 80 km SMF link with an erbium-doped fiber amplifier (EDFA). An optical band pass filter (OBPF) is used to suppress noise accumulation. The launched power into the fiber span is about  5 dBm. After the re-circulating loop, the optical signal is received by an optical coherent receiver. The optical coherent receiver consists of an ECL laser as optical local oscillator, an Optoplex dual-polarization 901 optical hybrid, and four balanced photo-detectors. The four electronic signals from balanced detectors are sampled by a 50 Gsamples/s (GSa/s) real time digital oscilloscope. The stored data are used for offline processing. The duration of a single data measurement is 0.4 μs, containing twenty-thousand samples for each channel. The data from the oscilloscope are processed by the CD estimation algorithm.

Δφðf Þ ¼ φðf þ f s =2; zÞ  φðf  f s =2; zÞ ¼ C 0 þC 1 Dtotal f

4. Results and discussions

2. Principle of CD estimation using polynomial fitting for arbitrary modulation format For an arbitrary modulation format, the phase of signal is found to be a periodic function of its fundamental symbol rate [10]. Assume the symbol rate is fs and the phase function at the transmitter is φ(f), the periodicity property can be expressed as

φðf þ f s =2Þ  φðf  f s =2Þ ¼ 0

ð1Þ

After transmits through an optical fiber with a length z, the phase of the signal φ(f,z) can be expressed [12] as   ω2 ð2Þ φðf ; zÞ ¼ φðf Þ þ z β0 þ β1 ω þ β2 2

frequency (f þfs/2) and (f fs/2) can be rewritten as

Differential Phase (rad)

where Dtotal is the accumulated total dispersion. Dtotal ¼zD, while D 2 is the fiber's dispersion parameter, D ¼  ðð2π cÞ=ðλref ÞÞβ2 [12]. C0 and C1 are constants for fixed distance z. C0 ¼ 2πfsβ1z, C1 ¼  2π(λref )2 fs/c, where λref is the wavelength of the optical carrier and c is the speed of light in vacuum. Eq. (3) shows that the phase difference Δφ(f) at the receiver is a linear function of frequency f. Dtotal can be obtained from the slope of Δφ(f) function. Fig. 1 shows the phase difference function Δφ(f). In theory, Δφ(f) is a straight line of frequency f with the slope proportional to Dtotal, as shown in Fig. 1(a). In practice, various amplitude and phase noises will distort the line and may cause glitches, as shown in Fig. 1(b). To reduce the impacts of these noises and glitches, polynomial fitting algorithm is developed to find the slope that matches with data with minimized errors. The proposed polynomial fitting algorithms have been demonstrated in simulations in previous works for various modulation formats, such as OOK, BPSK, PDM-QPSK, and PDM-16QAM [11]. It is found that polynomial fitting for CD estimation can tolerate a relatively

4.1. CD estimation from polynomial fitting The data for CD estimation are taken from 50GSa/s digital oscilloscope. The frequency of local oscillator in the receiver is set to the same nominal frequency as the transmitter. No accurate phase alignment is required since the phase offset between transmitter and receiver just introduces a fixed factor to the received signal amplitude during the short period of measurement. Since the first order polarization mode dispersion (PMD) only contributes a constant component to the phase difference curve Δφ(f), it is not an impact factor for the slope and has no effect on either the validity or the accuracy for CD estimation. Therefore, only data in one polarization is used for the CD estimation. To recover the phase at discrete frequency in the digital coherent receiver, a fast Fourier transform (FFT) is used. The FFT is done on a block with a FFT size of N¼2n, n is a positive integer and optimized by experiment data. In this experiment, n is chosen as 4096. The FFT transform gives the complex

CD = -12800 ps/nm CD = -6400 ps/nm CD = 0 ps/nm CD = 6400 ps/nm CD = 12800 ps/nm

Differential Phase (rad)

ð3Þ

f (GHz) Fig. 1. Differential phase as a function of frequency for CD estimation.

f (GHz)

X. Jiang et al. / Optics Communications 331 (2014) 119–123

IQ Mod

Balanced Detector

ECL

EDFA

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PBC EDFA

ECL

Pol. Diversit y 90° Hybrid

SW π/2 Q

Delay

50GSa/s Digital Oscilloscope

Offline DSP

OLO

PRBS

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SW

VOA OBPF EDFA SMF

Amplified Link Fig. 2. Experiment setup for 40 Gb/s PDM-QPSK system with re-circulating loop. ECL: external cavity laser, PRBS: Pseudo-Random Binary Sequence pattern generator, IQ Mod: IQ modulator, PBC: polarization bean combiner, EDFA: erbium doped fiber amplifier, SW: switch, SMF: single mode fiber, OBPF: optical bandpass filter, VOA: variable optical attenuator, OLO: optical local oscillator, DSP: digital signal processing.

100

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Phase (Radian)

15 10 5 0 -5 -10

80 60 40 20

-15 -20 -3

-2

-1

0

1

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1.21

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1.24 x 104

Fig. 3. Measurement after 720 km SMF. (a) Differential phase function and, (b) Distribution of multiple measurements (CD mean estimation is 12,150 ps/nm, standard deviation ¼ 112 ps/nm).

Diff. of Measured and Target CD (ps/nm)

Measured CD (ps/nm)

25,000 y = 16.938x -93.918 R² = 0.9997

20,000 15,000 10,000 5,000 0 0

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Fig. 4. CD measurements at different transmission distances. (a) Measured CD as a function of transmission distance for 40 Gb/s PDM-QPSK signal. The diamond points represent measurement data. The solid line is the linear fitting, corresponding to D ¼16.94 ps/nm/km; (b) Difference between the measured value and the target value for different accumulated CD.

representation of the components at different discrete frequencies, with which the phases at those discrete frequencies can be calculated directly. If the sampling rate is f0, then the spectrum range of the FFT transform covers ( f0/2, f0/2). If the symbol rate is fs, to make sure both f7fs/2 are covered within the spectrum range of FFT transform,

the sampling rate must be at least 2 times the symbol rate. In this experiment, the sampling rate is 5 times of symbol rate, so, the differential phases can be calculated from the FFT spectrum. Fig. 3 shows the measurement data of the 40 Gb/s PDM-QPSK signal after 720 km transmission in SMF fiber. Fig. 3(a) is the

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differential phase curve, which keeps a good linearity of f within 73 GHz in this case. With a linear fitting algorithm, the slope coefficient can be obtained to calculate Dtotal. The accumulated CD obtained for this curve is 12,153 ps/nm. It is found that large phase noise will induce phase jumping which causes discontinuous of the Δφ(f) curve. Since the phase-jumping tends to occur in high frequency range, in which the signal power is relatively low and the noise is relatively large, the polynomial fitting algorithm is restricted to a low-frequency range where no phasejumping or phase-jumping is negligible. By using the low-frequency range of the CD estimation, this method can tolerate a relatively large noise from ASE and other impairments in the system. To reduce the noise impacts on the CD estimation, multiple tests are taken. Fig. 3(b) shows the distribution of the multiple tests after a 720 km fiber transmission. The mean estimation of CD is 12,150 ps/ nm and the standard deviation is 112 ps/nm, which is about 1% of the total estimated CD. Using this measurement data, the dispersion parameter D of this fiber is 16.9 ps/nm/km at 1550 nm. 4.2. 40 Gb/s PDM-QPSK experiment for different fiber lengths Using the re-circulating loop, the experiments can be done for different transmission distances. Fig. 4 shows CD measurements for different transmission distances with different accumulated CDs. Each measurement point is the mean estimation from 64 multiple tests. Fig. 4(a) shows the measured CD at different distances. The solid line is the linear fitting from the data. A fitting with a coefficient of determination R2 of 0.9997 is obtained. Besides, a systematic offset of 93.9 ps/nm is found. Fig. 4 (b) compares the measurement results after the correction for 35

25

4.3. Measurement errors and estimation accuracy The measurement accuracy can be estimated from the standard deviation of multiple tests, as shown in Fig. 6. Fig. 6(a) shows the standard deviation of measurements for different measured CDs. The measurement accuracy of less than 200 ps/nm is obtained for CD less than 20,300 ps/nm which corresponding to 0–1200 km SMF. The measurement accuracy remains 60–80 ps/nm from 0 to 8,000 ps/nm, then it increases to about 188 ps/nm as the total accumulated CD increases to 20,300 ps/nm. The measurement error increases quickly after this point. The standard deviation as a function of OSNR is shown in Fig. 6(b). At high OSNR range ( 420 dB), the dominated noises are from transmitter and receiver, and the measurement error keeps relatively flat and small. At low OSNR of 15 dB, the amplifier noise and other noise in transmission link become dominated and the measurement error increases dramatically as transmission distance increasing. At distance of about 1500 km, the accumulated CD is around 25,000 ps/nm, the measurement accuracy is 500 ps/ nm, about 2% of its measured CD. The measurement error becomes too high for longer distance and cannot provide reliable result.

20

5. Conclusions 15

10 0

300

600

900

1200

1500

Transmission Distance (km) Fig. 5. OSNR vs transmission distance.

We experimentally validate a non-data-aided CD estimation method based on polynomial fitting for single carrier coherent optical systems through a 40 Gb/s PDM-QPSK recirculating fiber loop. The CD estimation is achieved by measuring the differential phase between the frequency f 7 fs/2 in digital coherent receivers. The estimation range for a 40 Gb/s PDM-QPSK signal can be up to

600

Standard Deviation (ps/nm)

500

Standard Deviation (ps/nm)

OSNR (dB)

30

system offset with the target results. The experimental results show that the proposed polynomial fitting method and algorithm can be used to measure up to 25,000 ps/nm total accumulated CD of 40 Gb/s PDM-QPSK signals with very good accuracy. The OSNR as a function of transmission distance is shown in Fig. 5. The OSNR decreases as the transmission distance increasing. At about 1462 km, the OSNR is reduced to 14 dB and the corresponding CD is about 25,000 ps/nm. Based on Fig. 4, at this OSNR level, the measured CD still matches well with the target value. However, for longer distance, as OSNR reduces further, we observe that the measurement noise increases dramatically and the measurement walks off the target quickly after 1500 km. This matches with the simulation [11], that is, the measurement error increases exponentially as the OSNR level decreasing and eventually limits the measurement range. The noise analysis will be in next section.

400

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12,000 16,000 20,000 24,000 28,000

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Fig. 6. Measurement error estimation. (a) Standard deviation vs. measured CD and (b) Standard deviation vs. OSNR.

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20,000 ps/nm with a measurement accuracy of 7 200 ps/nm. The maximum CD measurement is 25,000 ps/nm with a measurement error of 2%. The estimation accuracy can be improved by averaging multiple results as well as carefully choosing suitable fitting range. In practice, there is a trade-off between the measurement accuracy and the measurement speed. The number of multiple tests should be limited as much as possible to achieve fast detection required in network routing. This method is promising for future optical fiber networks with dynamic optical routing and coherent detection.

Acknowledgment This work was supported in part by U.S. National Science Foundation under Grant 1040223. We would like to thank Dr. B. Zhu from OFS for his support.

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