Abstract

We propose using low bandwidth coherent receivers for distributed optical performance monitoring. We demonstrate optical signal-to-noise ratio (OSNR) monitoring of both 20-Gb/s single-polarization and 40-Gb/s polarization-multiplexed coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals with a 0.8-GHz receiver using both data-aided (DA) and non-data-aided (NDA) approaches. The sampling rate of the performance monitor is much lower than the signal baud rate, so provides a cost-effective solution for distributed optical performance monitoring. The proposed method is demonstrated experimentally and through simulation. The results show that after calibration the OSNR monitoring error is less than 1 dB and the two approaches are not affected by fiber dispersion after 800-km transmission and 30-ps differential group delay (DGD).

©2012 Optical Society of America

1. Introduction

Digital coherent systems have revolutionized optical communications by offering high spectral efficiency and the ability to digitally compensate linear impairments. An additional feature is that these systems can simultaneously monitor channel impairments using information available from the digital signal processing [1]. Although this enables end-to-end performance monitoring, it relies on full-bandwidth sampling so may not be an optimal solution for distributed optical performance monitoring because the data does not need to be recovered at the signal monitoring sites.

Optical signal-to-noise ratio (OSNR) is a key indicator of optical performance. Monitoring the OSNR at different locations along an optical network provides fundamental information about its performance [2]. Several OSNR monitoring approaches for single-carrier coherent optical systems are based on using signals after equalization [36]; however, publications on optical OFDM monitoring are limited [7,8]. In this paper, we propose using low-bandwidth coherent receivers as a cost-effective solution for distributed OSNR monitoring. These could, for example, be used at reconfigurable optical add-drop multiplexer (ROADM) sites. The potential benefits include reduced cost and power requirements. The better thermal noise performance of lower-speed receivers may also enable a reduction in the optical tap powers required for monitoring. We provide a first demonstration of this approach by monitoring the OSNR of both 20-Gb/s single-polarization and 40-Gb/s polarization-multiplexed CO-OFDM signals with a 0.8-GHz coherent receiver sampling at 2.5 GSamples/s [9]. The technique is demonstrated using both data-aided (DA) and non-data-aided (NDA) approaches. The NDA method avoids the need for prior knowledge of timing sequences and training sets and exploits an analysis of the Stokes vectors to achieve OSNR monitoring without the need of polarization demultiplexing.

The paper is organized as follows: Section 2 outlines the technique of the proposed DA and NDA OSNR estimators. In Sections 3 and 4 the experimental and simulation results are shown and discussed, respectively. Finally we summarize the paper in Section 5.

2. Techniques for OSNR estimation

Data-aided OSNR monitoring

The multiple subcarriers in CO-OFDM make it amenable to monitoring with a low-bandwidth monitor. In our demonstration, a small number of the subcarriers are filtered (32 out of 256) and sampled with a low bandwidth receiver, as shown in Fig. 1 . We show that carrier frequency offset synchronization, fast Fourier transform (FFT) window timing synchronization, channel estimation and polarization demultiplexing can all be achieved with a low-bandwidth receiver for the DA approach. The OSNR can then be obtained from the constellation diagram of the subcarriers within the receiver bandwidth.

 figure: Fig. 1

Fig. 1 Comparison of the full OFDM signal spectrum (grey: 10-GHz wide) and the low bandwidth (blue: approximate 2-GHz wide) signal from the low-pass filter output. The low bandwidth receiver is sampled at 2.5 GSamples/s.

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In principle, the FFT should be performed on the full bandwidth signal to ensure orthogonality between the subcarriers; however, the inter-carrier interference decays rapidly across subcarriers [8] and for a sub-band of 32 subcarriers it is negligible, however, the OFDM symbols must be properly delineated by timing synchronization for FFT operation to avoid inter-symbol interference and inter-carrier interference. The first frame of each OFDM signal block is used for timing synchronization and the following 10 symbols are used as training sequences for two-polarization signal recovery. The beginning of the OFDM block is detected using cross correlation between the received low-bandwidth timing training sequence and the transmitted training sequence. As this operation is sensitive to carrier frequency offset, frequency offset estimation and compensation is the first processing step. The offset estimation is based on the frequency spectrum of the received OFDM signal, as is shown in Fig. 1. The three subcarriers at each side of the signal carrier are intentionally left blank to highlight the signal carrier peak.

The OFDM subcarriers are separated after the FFT. The polarization states are, however, still mixed together. Training sequences within the 0.8-GHz monitor bandwidth are used to demultiplex the polarization states, with a simple zero forcing approach [10]. The training sequences are generated by filling the odd symbols with normal transmitted data, while leaving the even symbols blank. After the polarization multiplexing emulator, the training sequence forms a pattern of alternative polarizations for two consecutive OFDM symbols as depicted in Fig. 2 .

 figure: Fig. 2

Fig. 2 Time-domain representation of the polarization-multiplexed OFDM signal including training sequence for timing synchronization, channel estimation, and data payload.

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Non-data-aided OSNR monitoring with Stokes analysis

A disadvantage of the data-aided approach is that prior knowledge of training sequences is required at the monitor. To simplify network operational requirements for an embedded monitoring solution, or alternatively for a practical test and measurement based field solution, a blind technique is preferred. In this section, we use the Stokes vector representation of the separated subcarriers to remove the need for knowledge of timing and training sequences.

The Stokes vector S [11] is given by:

S=(s1s2s3)=1s0(|ex|2|ey|22Re{ex*ey}2Im{ex*ey})
where ex and ey are the Jones vectors for the linear x and y polarization states and s0=|ex|2+|ey|2 represents the received signal power of two polarizations. ASE noise induces the scatter on the Poincaré sphere as illustrated in the Fig. 3 for a single polarization signal. Here θs denotes the angle between a sample Stokes vector and the mean Polarization state. We note that although sample has a unit magnitude the average Stokes vector has a magnitude less than one which can be interpreted as a degree of polarization. For a single-polarization signal the Stokes vectors are independent of the symbol phase while for a QPSK polarization multiplexed signal there are four mean Stokes states, ε¯i, 𝑖 = 1,2,3,4 representing relative phase differences of π/4, 3π/4, 5π/4, 7π/4 between the symbols of orthogonal polarization components. The scatter of these Stokes vectors provides a convenient means of characterizing the noise on subcarriers without the need for polarization de-multiplexing.

 figure: Fig. 3

Fig. 3 OSNR induced scatter on the Poincaré sphere for single-polarization signal.

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As illustrated in Fig. 6 the first step in extracting the Stokes vectors for the individual subcarriers is to compensate the carrier frequency offset. Carrier frequency offset compensation is required to remove the inter-subcarrier interference. This operation is performed without any data assistance. The captured OFDM signal is transformed into frequency domain and the frequency offset between DC and signal carrier can be measured, as is shown in Fig. 4 . It is notable that the gaps at the two sides of the signal carrier are null subcarriers. They have been intentionally inserted to identify the frequency offset.

 figure: Fig. 4

Fig. 4 Principle of blind carrier frequency offset estimation.

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Timing synchronization is achieved in a blind manner by minimizing the scatter on the Stokes sphere as a function of timing offset. Figure 5 illustrates the blind timing synchronization procedure at the receiver. There is only one variable parameter, the timing estimate, in the whole procedure. Changing this parameter will change the scatter of the Stokes vector because of the misalignment of the FFT window to the received OFDM symbols. This characteristic is employed to achieve blind timing synchronization. In each data capture, the first data sample is assumed to be a correct timing estimate and then the following FFT operation and Stokes vector scatter measurement are performed. The scatter is quantified using the SNRStokes expression shown in Eq. (3). As we continuously slide the FFT window along the sample index, a series of Stokes vector scatter data versus timing offset is collected. In Fig. 5, the scatter reaches its minimum periodically because at these points the sliding FFT window aligns to the OFDM symbols. It clearly shows that the scatter of Stokes vector converges when the correct timing estimate is reached for both the single-polarization signal and polarization-multiplexed signals.

 figure: Fig. 5

Fig. 5 Principle of blind timing synchronization. (a) Periodical SNR performance along with sample index; (b) Zoomed-in SNR curves with Stokes vector scatters on Poincaré spheres vs. timing offset for both single-polarization and polarization-multiplexed OFDM signals.

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We note that the Stokes vector representation has previously been used for efficient blind polarization demultiplexing [12]. Here, however, we directly use the scatter on the Stokes sphere, to determine the OSNR. For this purpose we define:

θscos1(s.ε¯i)
where θs is the angle between the Stokes vectors S and their corresponding mean Stokes state ε¯i as shown in Fig. 3. For single-polarization OFDM signal, i = 1 while for polarization-multiplexed signal i = 1, 2, 3, 4. The K-means clustering algorithm is applied to separate the four clusters of Stokes vectors.

To facilitate the measurement of OSNR from the scatter of Stokes vector we note that the average value of cosθscan be interpreted as an effective degree of polarization. In accordance with [13] we define a parameter SNRStokes given by

SNRStokes=10log10(cosθs1cosθs)
where the symbol represents the averaging operation. For regimes in which ASE is the dominant source of noise, SNRstokes is proportional to the OSNR. The OSNR for each cluster and symbol is estimated individually and then averaged.

3. Experimental demonstration and discussion

Figure 6 shows the experimental setup for low bandwidth sampling DA and NDA OSNR monitoring. The transmitted OFDM signal stream is first generated from a 215-1 pseudo random binary sequence (PRBS) in a MATLAB program and then mapped to 4-QAM symbols. The time-domain OFDM symbols are formed after inverse fast Fourier transform (IFFT) operation, and then guard intervals are inserted. The IFFT size is 256 and the guard interval is set to 16 symbols to fit the delay of a polarization multiplexing emulator. The I and Q components of the time-domain OFDM signal are uploaded onto an arbitrary waveform generator (AWG), which produces the analog signals at 10 GSymbols/s. An optical I/Q modulator comprising of two Mach-Zehnder modulators (MZM) with a 90° phase shift between them upconverts the OFDM baseband signals from the RF domain to the optical domain. A single-polarization optical OFDM signal from the I/Q modulator is evenly split into two polarization branches using a polarization-beam splitter (PBS) with one branch delayed by one OFDM symbol period. The two polarization branches are subsequently combined by a polarization-beam combiner (PBC), to emulate two independent transmitters.

 figure: Fig. 6

Fig. 6 Experimental setup of OSNR monitoring. AWG: arbitrary waveform generator; OSA: optical spectrum analyzer; LO: local oscillator.

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After transmission through 800 km of standard single mode fiber, an ASE source, consisting of two cascaded EDFAs and one optical band-pass filter (OBPF), is used to control the OSNR level. The OSNR is defined using a 0.1-nm reference bandwidth. The ASE noise is coupled into the signal path using a 50:50 coupler. After ASE noise injection, one path is connected to an optical spectrum analyzer (OSA) for OSNR monitoring and the other is detected by a coherent receiver with a local oscillator (LO) and four balanced receivers. The low bandwidth receiver is emulated with 0.8-GHz low-pass electrical filters (LPFs) on the outputs of 15-GHz balanced receivers. The signals are then captured by a 4-channel real-time oscilloscope running at 2.5 GSamples/s for offline processing. The optical local oscillator (LO) is tuned to be within 0.8 GHz of the signal carrier, enabling the carrier to pass through the LPFs and allowing frequency offset compensation for the data-aided monitoring.

Data-aided OSNR monitoring

The compensation of chromatic dispersion (CD), polarization mode dispersion (PMD) and phase noise are not required because a measurement of the radial distribution of the constellation diagram is sufficient to determine the OSNR. Figure 7 shows constellation diagrams for the demultiplexed X-polarization component. The SNR is determined from the radial distribution using the moments method [14]. Figure 8(a) shows plots of SNR versus true OSNR (measured from OSA) for back-to-back measurements with varying amounts of injected ASE. The flattening of the physical filter curves for OSNR values above 20-dB is due to quantization noise in the sampling oscilloscope. Digital magnification is applied when the input electrical signal amplitude is below 50 mV, which introduces greater quantization errors. The SNR results from the same subcarriers but using the full bandwidth signal and sampling at 10 GSamples/s are shown for comparison. For OSNRs less than 20 dB, the results are similar; however, we did measure a 2-dB difference in asymptotic SNR at high OSNRs. We believe that this difference is due to the filter loss and noise in the sampling oscilloscope. To demonstrate that inter-channel interference is negligible, even above 20-dB SNR, we implemented a 800-MHz FIR digital filter and measured SNR again on the same subcarriers. The results included in Fig. 8(a) are not discernable from the full-bandwidth result.

 figure: Fig. 7

Fig. 7 Constellation diagrams of the demultiplexed X polarization component at 8-dB and 20-dB OSNR.

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 figure: Fig. 8

Fig. 8 (a) Comparison of SNR curves for subcarriers using 800-MHz LPFs, no filters with full band sampling, and 800-MHz digital filters; (b) SNR curves using 800-MHz LPFs in presence of 800-km transmission and 30-ps DGD.

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Figure 8(b) demonstrates the insensitivity of the SNR predictions to CD and differential group delay (DGD). We find that 800-km fiber and 30-ps DGD produce less than 0.5 dB of variation from the back-to-back results. The difference in SNR between the X and Y polarization states is due to excess loss in the Y-arm of the polarization multiplexing emulator.

Calibration coefficients taking into account the receiver noise are obtained from a linear fit of OSNR−1 versus SNR−1 [11]. Figure 9(a) shows the resulting calibration curve using the back to back setup with OSA based OSNR measurements. The OSNR measurement error based on this calibration curve is shown in Fig. 9(b). All of the OSNR estimation errors are within 1 dB. The relatively large error at 25.5-dB OSNR comes from oscilloscope quantization noise. Boosting the input signal amplitude after the 800-MHz LPFs by applying matched electrical amplifiers will decrease this deviation within ± 0.5 dB.

 figure: Fig. 9

Fig. 9 (a) Calibration curve based on linear fit of SNR−1 versus OSNR−1 for back-to-back and 800-km X polarization signal; (b) OSNR estimation error vs. actual OSNR after calibration for back-to-back and 800-km transmission signal.

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Non-data-aided OSNR monitoring

Figure 10 compares the Stokes vectors scatter at different OSNR in back-to-back transmission. Figure 11(a) shows the curves of SNRStokes versus OSNR for both single-polarization and polarization-multiplexed optical OFDM signal under 0-ps and 30-ps DGD. The averaged X and Y polarization SNR values from data-aided OSNR monitoring (800-MHz narrow band signal with digital filtering) are plotted for a reference. The similarity of the results indicates that the technique is independent of CD and DGD.

 figure: Fig. 10

Fig. 10 Comparison of Stokes vectors scatter at 12-dB and 22-dB OSNR, 30-ps DGD in optical back-to-back transmission.

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 figure: Fig. 11

Fig. 11 (a) Comparison of SNRStokes curves for subcarriers using 800-MHz physical filters with and without the presence of 30-ps DGD; (b) OSNR estimation error vs. actual OSNR after calibration for back-to-back single-polarization and polarization-multiplexed signal.

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Figure 11(b) plots the estimation error versus the OSNR value measured using the OSA for both the single-polarization and the polarization-multiplexed 4-QAM optical OFDM signals, respectively. Since the curves with and without DGD in Fig. 11(a) are very similar, only the estimation error for 30-ps DGD cases are displayed. These results show that in these two scenarios the OSNR monitor performs good estimation for different configurations as the errors are all below 1-dB.

4. Simulation results and discussion

We conducted simulations using VPItransmissionMaker 8.6 to further investigate the variation of performance of the proposed NDA OSNR monitoring algorithm with fiber transmission and CD. The simulation setup is the same as Fig. 3. The data rate of polarization-multiplexed system is set to 80 Gb/s. The modulation format for the two independent transmitters is QPSK and the IFFT size is 128. The receiver sampling rate is set to 2.5 GS/s and the four electrical LPFs are 800 MHz. Moreover, we investigated a much wider OSNR range up to 33 dB. The same method as shown in Eq. (2) and Eq. (3) is used to evaluate the performance.

Figure 12 compares the results for the system operated with zero mean DGD and 30-ps DGD before and after 800-km transmission over a wide range of OSNR. Similar to the experimental data, the simulated SNR versus OSNR curves deviate from their trends and reach their plateaus at around 20-dB OSNR. The agreement between the SNR curves before and after fiber transmission indicates that the proposed NDA OSNR monitoring method is independent of DGD and fiber dispersion. For comparison we also plot the two curves for the noiseless cases before and after transmission. Both curves have unity slope and show negligible evidence of inter-carrier crosstalk at high OSNR.

 figure: Fig. 12

Fig. 12 Comparison of estimated SNR versus OSNR in ideal noiseless case and normal case with and without DGD before and after 800-km fiber transmission.

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5. Conclusions

Digital coherent receivers sampling at the full signal bandwidth offers an increasingly sophisticated means of optical performance monitoring of arbitrary formats. In this paper we propose and demonstrate two novel and cost-effective low bandwidth OSNR monitoring algorithms for coherent optical transmission systems, which offer a path toward low-cost distributed monitoring. One is based on a traditional training sequence and a radial measurement of the constellation scatter, while the other achieves non-data-aided, low computational complexity OSNR monitoring. The latter method provides a general approach to estimate optical OFDM performance. After a proper reference value is set for calibration, a good fit between SNR versus OSNR demonstrates OSNR estimation. Furthermore, we note that this approach can be applied to any optical OFDM modulation format, including constant and non-constant modulus formats. We experimentally demonstrate that the proposed technique achieves accurate estimation of OSNR for back-to-back and 800-km transmission using single-polarization or polarization-multiplexing. We also show that these two methods are not affected by DGD. Furthermore, simulation results verify that the technique can still perform well in the presence of a large amount of CD.

Acknowledgments

NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program. The research is also partially supported by the Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems.

References and links

1. F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E. D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefðcients in coherent receivers,” in Proc. OFC2008, paper OThW2.

2. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004). [CrossRef]  

3. C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012). [CrossRef]   [PubMed]  

4. W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, “Optical performance monitoring in coherent optical OFDM systems,” Opt. Express 15(2), 350–356 (2007). [CrossRef]   [PubMed]  

5. M. S. Faruk and K. Kikuchi, “Monitoring of optical signal-to-noise ratio using statistical moments of adaptive-equalizer output in coherent optical receivers,” in Proc. OECC2011, paper 6B4–3.

6. D. J. Ives, B. C. Thomasen, R. Maher, and S. Savory, “Estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, OThH5.

7. X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proc. OFC2008, paper OThW3.

8. W. Shieh and I. Djordjevic, OFDM for optical communications (Elsevier, 2010).

9. T. B. Anderson, S. Chen, A. Tran, D. F. Hewitt, L. B. Du, and A. J. Lowery, “Optical performance monitoring with sub–Nyquist coherent receivers,” in Proc. ECOC2012, paper Th.2.A.1.

10. S. Chen, Q. Yang, Y. Ma, and W. Shieh, “Real-time multi-gigabit receiver for coherent optical MIMO-OFDM signals,” J. Lightwave Technol. 27(16), 3699–3704 (2009). [CrossRef]  

11. C. Brosseau, Fundamentals of polarized light: a statistical optics approach (John Wiley & Sons, 1998).

12. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010). [CrossRef]   [PubMed]  

13. M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004). [CrossRef]  

14. D. J. Ives, B. C. Thomsen, R. Maher, and S. Savory, “Performance estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, paper Tu.6.A.6.

References

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  1. F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E. D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefðcients in coherent receivers,” in Proc. OFC2008, paper OThW2.
  2. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004).
    [Crossref]
  3. C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012).
    [Crossref] [PubMed]
  4. W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, “Optical performance monitoring in coherent optical OFDM systems,” Opt. Express 15(2), 350–356 (2007).
    [Crossref] [PubMed]
  5. M. S. Faruk and K. Kikuchi, “Monitoring of optical signal-to-noise ratio using statistical moments of adaptive-equalizer output in coherent optical receivers,” in Proc. OECC2011, paper 6B4–3.
  6. D. J. Ives, B. C. Thomasen, R. Maher, and S. Savory, “Estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, OThH5.
  7. X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proc. OFC2008, paper OThW3.
  8. W. Shieh and I. Djordjevic, OFDM for optical communications (Elsevier, 2010).
  9. T. B. Anderson, S. Chen, A. Tran, D. F. Hewitt, L. B. Du, and A. J. Lowery, “Optical performance monitoring with sub–Nyquist coherent receivers,” in Proc. ECOC2012, paper Th.2.A.1.
  10. S. Chen, Q. Yang, Y. Ma, and W. Shieh, “Real-time multi-gigabit receiver for coherent optical MIMO-OFDM signals,” J. Lightwave Technol. 27(16), 3699–3704 (2009).
    [Crossref]
  11. C. Brosseau, Fundamentals of polarized light: a statistical optics approach (John Wiley & Sons, 1998).
  12. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  13. M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
    [Crossref]
  14. D. J. Ives, B. C. Thomsen, R. Maher, and S. Savory, “Performance estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, paper Tu.6.A.6.

2012 (1)

2010 (1)

2009 (1)

2007 (1)

2004 (2)

D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004).
[Crossref]

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

Anderson, T.

Bach, R.

Blumenthal, D. J.

Chen, S.

Chen, W.

Do, C. C.

Du, L. B.

Einstein, D.

Karlsson, M.

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

Kilper, D. C.

Landolsi, T.

Lowery, A. J.

Ma, Y.

Marshall, T.

Nebendahl, B.

Olsson, B. E.

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

Ostar, L.

Pendock, G.

Petersson, M.

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

Preiss, M.

Shieh, W.

Skafidas, E.

Sunnerud, H.

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

Szafraniec, B.

Tran, A. V.

Tucker, R. S.

Willner, A. E.

Yang, Q.

Yi, X.

Zhu, C.

IEEE Photon. Technol. Lett. (1)

M. Petersson, H. Sunnerud, M. Karlsson, and B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett. 16(2), 686–688 (2004).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (3)

Other (8)

F. N. Hauske, J. C. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. R. S. Fludger, D. van den Borne, E. D. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefðcients in coherent receivers,” in Proc. OFC2008, paper OThW2.

C. Brosseau, Fundamentals of polarized light: a statistical optics approach (John Wiley & Sons, 1998).

D. J. Ives, B. C. Thomsen, R. Maher, and S. Savory, “Performance estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, paper Tu.6.A.6.

M. S. Faruk and K. Kikuchi, “Monitoring of optical signal-to-noise ratio using statistical moments of adaptive-equalizer output in coherent optical receivers,” in Proc. OECC2011, paper 6B4–3.

D. J. Ives, B. C. Thomasen, R. Maher, and S. Savory, “Estimating OSNR of equalised QPSK signals,” in Proc. ECOC2011, OThH5.

X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proc. OFC2008, paper OThW3.

W. Shieh and I. Djordjevic, OFDM for optical communications (Elsevier, 2010).

T. B. Anderson, S. Chen, A. Tran, D. F. Hewitt, L. B. Du, and A. J. Lowery, “Optical performance monitoring with sub–Nyquist coherent receivers,” in Proc. ECOC2012, paper Th.2.A.1.

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Figures (12)

Fig. 1
Fig. 1 Comparison of the full OFDM signal spectrum (grey: 10-GHz wide) and the low bandwidth (blue: approximate 2-GHz wide) signal from the low-pass filter output. The low bandwidth receiver is sampled at 2.5 GSamples/s.
Fig. 2
Fig. 2 Time-domain representation of the polarization-multiplexed OFDM signal including training sequence for timing synchronization, channel estimation, and data payload.
Fig. 3
Fig. 3 OSNR induced scatter on the Poincaré sphere for single-polarization signal.
Fig. 4
Fig. 4 Principle of blind carrier frequency offset estimation.
Fig. 5
Fig. 5 Principle of blind timing synchronization. (a) Periodical SNR performance along with sample index; (b) Zoomed-in SNR curves with Stokes vector scatters on Poincaré spheres vs. timing offset for both single-polarization and polarization-multiplexed OFDM signals.
Fig. 6
Fig. 6 Experimental setup of OSNR monitoring. AWG: arbitrary waveform generator; OSA: optical spectrum analyzer; LO: local oscillator.
Fig. 7
Fig. 7 Constellation diagrams of the demultiplexed X polarization component at 8-dB and 20-dB OSNR.
Fig. 8
Fig. 8 (a) Comparison of SNR curves for subcarriers using 800-MHz LPFs, no filters with full band sampling, and 800-MHz digital filters; (b) SNR curves using 800-MHz LPFs in presence of 800-km transmission and 30-ps DGD.
Fig. 9
Fig. 9 (a) Calibration curve based on linear fit of SNR−1 versus OSNR−1 for back-to-back and 800-km X polarization signal; (b) OSNR estimation error vs. actual OSNR after calibration for back-to-back and 800-km transmission signal.
Fig. 10
Fig. 10 Comparison of Stokes vectors scatter at 12-dB and 22-dB OSNR, 30-ps DGD in optical back-to-back transmission.
Fig. 11
Fig. 11 (a) Comparison of SNRStokes curves for subcarriers using 800-MHz physical filters with and without the presence of 30-ps DGD; (b) OSNR estimation error vs. actual OSNR after calibration for back-to-back single-polarization and polarization-multiplexed signal.
Fig. 12
Fig. 12 Comparison of estimated SNR versus OSNR in ideal noiseless case and normal case with and without DGD before and after 800-km fiber transmission.

Equations (3)

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S=( s 1 s 2 s 3 )= 1 s 0 ( | e x | 2 | e y | 2 2Re{ e x * e y } 2Im{ e x * e y } )
θ s cos 1 (s. ε ¯ i )
SN R Stokes =10 log 10 ( cos θ s 1 cos θ s )

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