Joint CD and PMD monitoring based on a pair of low-bandwidth coherent receivers

Yuli Chen; Qi Sui; Zhaohui Li; Zihao Liang; Weiping Liu

doi:10.1364/OE.24.026756

1. Introduction

The new continuous innovation of fiber communication technology has contributed to the multiplication of fiber transmission distance year by year. It is necessary to estimate the distortion at the intermediate nodes and facilitate intelligent routing [1]. Optical performance monitoring (OPM) plays an important role for maintenance and management of high-speed and reconfigurable optical networks. The fiber system can be measured accurately and reflected rapidly on the physical states of network elements, paths, and the quality of propagating data signals [2, 3]. OPM in dynamic reconfigurable applied network enables routing tables to be modified based on the physical changes of the links so that the network controller can agilely control and manage the heterogeneous networks [4].

Among the parameters of the optical signals that need to be monitored, chromatic dispersion (CD) and polarization mode dispersion (PMD) are two key parameters limiting the performance of optical transmission systems [5, 6]. In a long haul communication systems, CD may be up to number of thousands ps/nm. And 1st order PMD, characterized by differential group delay (DGD), may also cause an unacceptable system outrage [7, 8]. In order to achieve CD and PMD monitoring, numerous OPM techniques have been proposed, which can be roughly classified into traditional OPM techniques and OPM in coherent receivers. Traditional OPM techniques have concrete hardware setups and can work at the intermediate nodes. However, the stringent cost requirement for OPM limits its performance and adaption to various optical signal transmitted simultaneously in a heterogeneous network. E.g. CD monitoring techniques [9, 10] can only work for intensity modulated signal and have an finite estimation range around −500 to 500 ps/nm. PMD monitoring techniques [11, 12] can only work for single polarization signal. In comparison, OPM in coherent receivers exists as channel estimation algorithm in the DSP. And it is much more powerful than traditional OPM techniques because it can fully utilize all the information gathered by the coherent receiver [13, 14]. However, the overwhelmed cost of a full-bandwidth coherent receiver prohibits the usage of such OPM technique at the intermediate nodes.

To combine the merits of both traditional OPM techniques and OPM in coherent receiver, we propose a joint CD and PMD monitoring technique by a pair of low-bandwidth coherent receivers detecting the signal in the narrow band around ± 1/2 baud rate. Here we assume the baud rate information of each channel is known to the monitor. With two tunable laser, the two coherent receivers can locate any desired channel of the whole WDM system for monitoring. The CD estimation range is supposed to be boundless and the PMD range is within 1/2 symbol period. In the simulation, for 28 G baud dual polarization (DP)-16QAM system, with a pair of 1 GHz bandwidth coherent receivers, the monitoring error for CD and PMD is 30 ps/nm and 0.5 ps, respectively. And in the experiment of 12 GBit/s OOK transmission system with a full-bandwidth coherent receiver and two 1 GHz digital filter to simulate dual 1 GHz coherent receivers, the monitoring error for CD and PMD is 60 ps/nm and 1.5 ps, respectively.

2. Operating principles

2.1 CD estimating

A single-carrier modulated signal in time and frequency domain can be expressed as

d (t) = \sum_{k} s_{k} δ (t - k T) ⋆ p (t) \overset{ℱ}{\leftrightarrow} D (f) = S (f) P (f),

where T, s_k,

δ (t)

and

p (t)

denote symbol rate, information symbols, Dirac delta function and pulse shape, respectively.

‘ ⋆ ’

and

‘ ℱ ’

denote convolution and Fourier transform, respectively. Due to the property of Dirac delta function,

S (f)

is periodic,

S (f) = S (f + n / T), n \in Z .

In the presence of CD, the induced different group delay with 1/T frequency spacing equals to

τ_{0} = - \frac{2 π β_{2} L}{T},

where

β_{2}

and L denote group velocity dispersion (GVD) coefficient and the fiber length. Since

S (f)

is periodic, by performing a time domain cross-correlation between the signal around

\pm \frac{1}{2 T}

baud rate, as shown in Fig. 1, τ₀ can be found according to the position of correlation peak. Although this correlation relation can be found in both power and electrical field domain, power correlation is preferred since it is independent of PMD effect. And the estimated CD is given by [13]

C D = \frac{τ_{0} T c}{λ^{2}},

where λ and c denote laser wavelength and light speed, respectively.

Fig. 1 CD estimation by cross correlation between the upper and lower narrow band around ± 1/2 baud rate.

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2.2 PMD estimating

A dual-polarization (DP) single-carrier signal can be expressed as

E_{t} (f) = S (f) \cdot P (f) .

In the presence of CD and 1st order PMD, the received signal becomes

E_{r} (f) = e^{2 i π^{2} β_{2} L f^{2}} \cdot R^{- 1} [\begin{matrix} e^{- 2 π i f Δ τ / 2} & 0 \\ 0 & e^{2 π i f Δ τ / 2} \end{matrix}] R \cdot S (f) \cdot P (f),

where Δτ denotes the DGD,

R = [\begin{matrix} \cos θ e^{- i φ} & \sin θ e^{i φ} \\ - \sin θ e^{- i φ} & \cos θ e^{i φ} \end{matrix}]

denotes random unitary polarization rotation matrix.

By using two coherent receivers detecting the signal around frequency $\pm \frac{1}{2 T}$ , the upper and lower narrow band signal is given by

\begin{array}{l} E_{U (L)} (f) = e^{2 i π^{2} β_{2} L {(f \pm \frac{1}{2 T})}^{2}} \cdot R^{- 1} [\begin{matrix} e^{- 2 π i (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} & 0 \\ 0 & e^{2 π i f (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} \end{matrix}] R \\ \cdot S (f \pm \frac{1}{2 T}) \cdot P (f \pm \frac{1}{2 T}) \cdot H_{e} (f), \end{array}

where

H_{e} (f)

denotes the transfer function of the electrical low-pass filter. Let

S^{'} (f) = S (f + \frac{1}{2 T}) = S (f - \frac{1}{2 T}) .

Then Eq. (7) becomes

\begin{array}{l} E_{U (L)} (f) = e^{\frac{i π^{2} β_{2} L}{2 T^{2}}} \cdot e^{\frac{\pm 2 i π^{2} β_{2} L f}{T}} \cdot R^{- 1} [\begin{matrix} e^{- 2 π i (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} & 0 \\ 0 & e^{2 π i (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} \end{matrix}] R \\ \cdot e^{2 i π^{2} β_{2} L f^{2}} \cdot S^{'} (f) \cdot P (f \pm \frac{1}{2 T}) \cdot H_{e} (f), \end{array}

where

e^{i π^{2} β_{2} L / 2 T^{2}}

is a common phase shift and can be neglected in the following derivation,

e^{\pm 2 i π^{2} β_{2} L f / T}

represents the CD induced delay, which can be estimated using correlation and compensated afterwards. Since

H_{e} (f)

is narrow bandwidth filter, we can neglect the filtering effect of

P (f \pm \frac{1}{2 T})

for simplicity.

After compensating for CD, the electrical fields becomes

E_{U (L)}^{'} (f) = R^{- 1} [\begin{matrix} e^{- 2 π i (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} & 0 \\ 0 & e^{2 π i (f \pm \frac{1}{2 T}) \frac{Δ τ}{2}} \end{matrix}] R \cdot e^{2 i π^{2} β_{2} L f^{2}} \cdot S^{'} (f) \cdot H_{e} (f) .

And

E_{U}^{'} (f) = R^{- 1} [\begin{matrix} e^{- 2 π i (f \pm \frac{1}{T}) \frac{Δ τ}{2}} & 0 \\ 0 & e^{2 π i (f \pm \frac{1}{T}) \frac{Δ τ}{2}} \end{matrix}] R \cdot E_{L}^{'} (f) .

Transform Eq. (11) into Stokes space, it yields

{\hat{S}}_{U} (f) = M_{P M D} \cdot {\hat{S}}_{L} (f),

where

M_{P M D} = \hat{r} \hat{r} + \sin \frac{2 π Δ τ}{T} \cdot (\hat{r} \times) - \cos \frac{2 π Δ τ}{T} \cdot (\hat{r} \times) (\hat{r} \times)

is an unitary

3 \times 3

Müller matrix describing the rotation with respect to the unitary principal state of polarization (PSP) vector

\hat{r} = {[\begin{matrix} r_{1} & r_{2} & r_{3} \end{matrix}]}^{T}

by angle

2 π Δ τ / T

.

\hat{r} \hat{r}

and

(\hat{r} \times)

are given by

\hat{r} \hat{r} = [\begin{matrix} r_{1} r_{1} & r_{1} r_{2} & r_{1} r_{3} \\ r_{2} r_{1} & r_{2} r_{2} & r_{2} r_{3} \\ r_{3} r_{1} & r_{3} r_{2} & r_{3} r_{3} \end{matrix}], (\hat{r} \times) = [\begin{matrix} 0 & - r_{3} & r_{2} \\ r_{3} & 0 & - r_{1} \\ - r_{2} & r_{1} & 0 \end{matrix}] .

And it is easy to find that the trace of M_PMD is independent of the orientation of

\hat{r}

.

Tr (M_{P M D}) = 1 + 2 \cos \frac{2 π Δ τ}{T},

from which Δτ can be estimated.

After sampled in the coherent receiver, ${\hat{S}}_{U} (f)$ and ${\hat{S}}_{L} (f)$ can be expressed as

{\hat{S}}_{U (L)} (f) = [\begin{array}{l} S_{1, U (L)} (f) \\ S_{2, U (L)} (f) \\ S_{3, U (L)} (f) \end{array}] = [\begin{matrix} S_{1, U (L)} (f_{1}) & \dots & S_{1, U (L)} (f_{m}) \\ S_{2, U (L)} (f_{1}) & \dots & S_{2, U (L)} (f_{m}) \\ S_{3, U (L)} (f_{1}) & \dots & S_{3, U (L)} (f_{m}) \end{matrix}] .

Solve for M from

{\hat{S}}_{U} (f) = M \cdot {\hat{S}}_{L} (f)

yields

M = \frac{{\hat{S}}_{U} (f) {\hat{S}}_{L}^{H} (f)}{{\hat{S}}_{L} (f) {\hat{S}}_{L}^{H} (f)}

. Then Δτ can be solved by

Δ τ = \cos^{- 1} \frac{Tr (M \cdot \det {(M)}^{- 1 / 3}) - 1}{2} \cdot \frac{T}{2 π},

where

\det {(M)}^{- 1 / 3}

is used for normalization. And due to the periodic nature of cosine function, the estimation range of DGD is from 0 to T/2.

3. Simulation results

As shown in Fig. 2, we perform the simulation in VPI. 28 G baud DP-16QAM signal is modulated on a 1552 nm laser. CD and 1st order PMD are added by SMF and PMD emulator. At the monitoring site, a pair of coherent receivers with 3 dB bandwidth of 1 GHz are used to detect the signal around ± 14 GHz with respective to the center wavelength. The electrical signal is sampled at 3.5 GS/s and processed with 4096 samples.

Fig. 2 Simulation setup of the CD and PMD measuring system. PBS: polarization beam splitter; VDL: variable delay line; PBC: polarization beam combiner; PC: polarization controller.

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In the simulation we also consider the case that the two local oscillators (LO) are free-running and each has a random frequency offset (FO) between 10 MHz to 100 MHz. Hence before PMD estimation, FO estimation is necessary. It is done by finding the cross-correlation peak between the two power spectrums. In the monitoring of each channel, the FO information also provides a feedback for the calibration of the two lasers so that they can have stable and accurate FO in the sweep of the whole WDM system. The FO estimation is transparent of both CD and PMD as they do not modify the signal power spectrum.

The CD is added in the range of −4000 to 4000 ps/nm. According to Eq. (4), with a sampling rate of 3.5 GHz, the resolution of CD estimation results is 1296 ps/nm, which thus causing significant quantization error, as shown in Fig. 3.

Fig. 3 CD estimation results.

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In order to recover the actual peak in the continuous form of power auto-correlation, we can perform quadratic fitting with the original correlation peak and two neighboring points as shown in Fig. 4, whose offset with respective to the original correlation peak is $s_{1} \in [- 0.5, 0.5]$ , in the unit of sample.

Fig. 4 Fitting arithmetic in power cross-correlation.

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As shown in Fig. 5(a), quadratic fitting has removed substantial quantization error.

Fig. 5 CD estimation results, (a) with quadratic fitting, (b) modified fitting.

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In order to further remove the residual fitting error between the quadratic fitting and ideal sinc fitting, we empirically find a modified offset based on s₁

s_{2} = s i g n (s_{1}) . \frac{\sqrt{5 - {(2 - 2 | s_{1} |)}^{2}} - 1}{2} .

As shown in Fig. 5, the maximum quadratic fitting error is less than 140 ps/nm, and the maximum modified fitting error is less than 40 ps/nm.

As shown in Fig. 6, in the 28 G Baud rate system the PMD is added in the range of 0 to 17.8 ps. The maximum estimated PMD error is less than 0.5 ps.

Fig. 6 PMD simulation results.

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As shown in Fig. 7, the proposed monitoring technique is immune to laser linewidth up to 1Mhz and 13 dB OSNR. Moreover, with the receiver bandwidth decrease to 100MHz, the monitoring results are not affected as well.

Fig. 7 Monitored CD and PMD with different (a-b) linewidth, (c-d) OSNR, (e-f) receiver bandwidth.

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As shown in Fig. 8, polarization dependent loss (PDL) may affect the PMD monitoring results only if it takes place after PMD.

Fig. 8 Monitored PMD in the presence of PDL.

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4. Experimental results

We also experimentally verified the proposed technique for 12 GBit/s NRZ-OOK system. The system setup is the same as Fig. 2 except that the monitor is composed by a 20 GHz, 50 GSa/s full-bandwidth coherent receiver and two 1 GHz digital filter to simulate dual 1 GHz coherent receivers. The two narrow band is down-sampled to 4 GSa/s and processed with 8000 samples. As shown in Fig. 9, With 50 to 350 km SMF, 850 to 5950 ps/nm CD is added. The maximum CD estimation error is less than 60 ps/nm. With 0 to 41.6 ps PMD added by a PMD emulator, the estimated PMD error is less than 1.5ps.

Fig. 9 Experimental CD and PMD monitoring results.

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5. Conclusions

We proposed a CD and PMD estimating method based on a pair of low-band coherent receivers.

By jointly detecting the narrow band around ± 1/2 baud rate, CD and PMD can be estimated simultaneously by time domain correlation and Stokes space rotational angle recovery, respectively.

Funding

National Natural Science Foundation of China (NSFC) (61525502, 61435006, 61490715, 61605066); the Program for New Century Excellent Talents in University (NCET-12-0679); National Natural Science Foundation of Guangdong (2015A030313328); the National High Technology 863 Research (2015AA015501); Development Program of China (No. 2013AA013300); Fundamental Research Funds for the Central Universities (No. 21616337).

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Joint CD and PMD monitoring based on a pair of low-bandwidth coherent receivers

Abstract

1. Introduction

2. Operating principles

2.1 CD estimating

2.2 PMD estimating

3. Simulation results

4. Experimental results

5. Conclusions

Funding

References and links

Cited By

Figures (9)

Equations (18)

Optics Express