## Abstract

The emerging transparent optical networks, employing spectrally-efficient modulation formats require new methods for supervision of signal quality in the optical domain. In this paper we demonstrate the optical performance monitoring (OPM) of optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD) in return-to-zero differential phase-shift keying (RZ-DPSK) signals using asynchronous delay-tap sampling and pattern recognition algorithms. We experimentally show noise measurement of OSNR from 8.7 dB to 32 dB with low optical input power requirement. Moreover, residual CD can be evaluated in the range from -600 to +600 ps/nm. The results indicate that careful adjustment of delay is necessary in order to ensure accurate measurement.

© 2008 Optical Society of America

## 1. Introduction

In recent years, communication networks have seen a rapid development of IP-based services, like the IP-telephony, or IP television. This trend, paired with the proliferation of broadband access to the Internet, has lead to a large increase in data traffic volume and a shift towards dynamic provisioning of bandwidth. In order to cope with the growing demand for capacity and scalability, optical networks are experiencing a shift towards transparent transmission technologies, higher bit rates, and efficient usage of available spectrum while the electrical cross-connect switches are being replaced with the optical counterparts [1]. High spectral efficiency has been achieved through the deployment of advanced modulation formats [2,3]. The format which has gained special interest due to its good performance in wavelength-division multiplexed (WDM) systems is return-to-zero differential phase-shift keying (RZ-DPSK). This format provides 3 dB higher receiver sensitivity when compared to on-off keying (OOK) formats. It has also been shown to be more robust towards nonlinear impairments as well as narrow-band filtering [4,5].

However, even in the case of advanced modulation formats the transparent transmission leads to the accumulation of impairments. Moreover, the dynamic nature of traffic requires frequent reconfigurations of optical paths, which leads to changes in transmission parameters and, thereby, fluctuations of signal quality at the receiver. In order to assure the high quality of signal, various performance monitoring techniques are employed. In the transparent section of the network the signal is not converted into electrical domain; therefore, the traditionally employed electronic monitoring must be replaced by optical performance monitoring (OPM) techniques [6,7]. The principal role of an OPM system is the identification and location of impairments. It can also support advanced management functions. In conjunction with higher layer protocols, OPM can provide valuable information for routing of traffic basing on actual, rather than analytically-calculated quality of signal [8,9].

Until now, several monitoring methods have been demonstrated for RZ-DPSK signals. They can be broadly divided into time-averaged and time-resolved methods. The former group comprises of methods based on monitoring of clock tone [10,11], pilot tone [12], and degree of polarization [13]. The time-resolved methods are based on asynchronous amplitude histograms [14,15]. The approaches presented to date have either been limited to monitoring only of dispersion, or the noise measurement range has been limited in the low optical signal-to-noise ratio (OSNR) regime for RZ-DPSK signals.

In this contribution we demonstrate an OPM method for monitoring RZ-DPSK signals using asynchronous delay-tap sampling. The principle of delay-tap sampling has been demonstrated [16–18]; however, what remains to be done is to provide a well-defined manner to relate the optical signal impairments to their physical origin. The method has been applied to non-return-to-zero DPSK (NRZ-DPSK) format [19] with narrowband optical filtering, yet the presented qualitative analysis is not sufficient to form a basis of a robust OPM system because the outcome of monitoring cannot be used to estimate the level of signal degradation. Instead, we employ a numerical approach to the analysis of samples acquired using the delay-tap method and propose monitoring parameters bearing a direct relationship to the physical origins of the impairments. The technique has been employed for numerical evaluation of optical impairments in RZ-DQPSK signals in [20,21]. In this contribution, we experimentally demonstrate the monitoring of OSNR and accumulated chromatic dispersion (CD) in RZ-DPSK signals.

## 2. Delay-tap sampling method

OPM based on delay-tap sampling is an asynchronous method using pairs of signal amplitude samples to analyze the properties of the waveform. The principle was demonstrated [16] using optical power splitter, optical delay line and a pair of photodiodes. We modified the method in order to simplify the implementation. The general principle is shown in Fig. 1(a). An optical band-pass filter (OBPF) selects a single channel from WDM transmission. We do not define the specific technology for selecting the single channel, but it should provide tuning range covering the entire WDM spectrum and rapid tuning to allow channel polling. The filter is followed by a photodiode (PD) and power splitter dividing the electrical signal into two branches: X and Y. The signal in branch Y is delayed by Δt, tunable in range from 0 to 1 bit period. Finally, the signal in both branches is fed into a sampling oscilloscope operating in X-Y mode. The signals are sampled simultaneously at sampling instants and repetition rate determined by the external clock. This provides for the asynchronous nature of the method and allows dispensing with the clock recovery circuitry, further simplifying the design. Because the analysis following the delay-tap sampling considers only the intensity of the waveform, it is not necessary to employ a Mach-Zehnder interferometer (MZI) for demodulation of the phase-modulated signal.

The sampling instants on an RZ pulse train are illustrated in Fig. 1(b). Because the signal is split, delayed, and simultaneously sampled in two branches, effectively the original waveform is sampled at two instants separated by the delay Δt. The sample in branch X is acquired at time X_{n}, while the sample in branch Y at Y_{n}. The consecutive pair of samples is captured after a period T_{samp} determined by the frequency of the internal clock. The frequency of the clock does not influence the analysis but it has an impact on the overall acquisition time.

Sampling at instants X_{n} and Y_{n} generates samples E(X) and E(Y), as shown in Fig. 2(a). The samples are used to construct the delay-tap plot, as illustrated in Fig. 2(b). Sample pairs serve as coordinates in Cartesian system to plot individual points. The overlapping points from consecutive sampling instants form the delay-tap plot. This allows graphically decomposing the waveform peak and valley without synchronizing with the signal. The shape of the plot depends on the delay Δt and is influenced by the changes of signal waveform due to transmission impairments. The plot with delay of 1/10 bit period, shown in Fig. 2(b), is used for monitoring OSNR. Conversely, for the monitoring of CD the delay of 1 bit is used. A 1-bit delay allows comparing two consecutive bits.

The delay-tap plot is a graphical representation which allows for qualitative estimation of signal properties. Therefore, further analysis of the plot is necessary in order to extract the quantitative information. In our study we introduce an algorithm based on Hough transform in order to analyze the plot [22,23]. The principle of the transform is shown in Fig. 3. As an example, the analysis of a line is illustrated in Fig. 3(a). The origin of the coordinate system is assumed to be at the center. The line in the plot is constructed of individual points. Every point can be crossed by an infinite number of straight lines ‘S’ described in polar coordinates as lying at a distance *R* and at an angle *ϕ* from the origin. The values *R* and *ϕ* are stored in an accumulator array, shown in Fig. 3(b). The set of coordinates of all straight lines crossing one point forms a sinusoidal curve in the accumulator array. The curves describing all points of the shape are stored in the accumulator array. In Fig. 3(b) the curves cross at point *A*. The coordinates *R* and *ϕ* of point *A* describe the position of the analyzed shape (line) in the delay-tap plot. Because the location of the delay-tap plot features depends on the shape of the waveform, the changes in waveform can be numerically described as *R* or *ϕ* coordinates. The analysis based on Hough transform is used to monitor the influence of CD.

## 3. Experimental results

#### 3.1 Experimental setup

In order to generate the RZ-DPSK signal and to introduce the distortion due to reduced OSNR and residual CD, the setup shown in Fig. 4 was used. A continuous wave (CW) light at *λ* = 1550.1 nm was fed through a polarization controller (PC) into a pair of modulators. The dual-drive Mach-Zehnder modulator (DD-MZM) biased at zero transmission point was driven with voltage V_{p-p} = 2V_{π} in order to generate the DPSK signal. The data signal was a 2^{31}-1 pseudo-random bit sequence (PRBS) operated at 9.95328 Gbit/s. The following MZM biased at the quadrature point was driven by the clock synchronized with the data, thereby generating the RZ-DPSK signal. The erbium-doped fiber amplifier 1 (EDFA1) was used to boost the signal power and the consecutive variable optical attenuator 1 (VOA1) and EDFA2 were used to set the level of OSNR of the signal. The VOA2 was used to maintain a constant input power to the receiver. The level of OSNR was measured using an optical spectrum analyzer (OSA) with resolution bandwidth of 0.1 nm. By changing the attenuation in VOA1 it was possible to achieve OSNR of up to 32 dB.

Subsequently, the signal was filtered by a 1 nm OBPF followed by a 3 dB splitter, dividing the optical power between the photodiode (PD) and the power monitor (PM). In case of CD measurement, a tunable dispersion compensator (TDC) was inserted between the filter and the splitter. The TDC comprised of two independent fiber Bragg gratings (FBG), each tunable within range -350~-150 ps/nm and +150~+350 ps/nm. The PD used in the experiment was a 50 GHz bandwidth pin photodiode. It was followed by a radio frequency (RF) amplifier and an RF power splitter. The signal in the lower branch was delayed by an RF phase shifter and both branches were subsequently coupled into a free-running oscilloscope. The oscilloscope used in the experiment was a 20 GHz bandwidth digital oscilloscope operating in X-Y mode.

#### 3.2 OSNR monitoring

In order to monitor the OSNR of the RZ-DPSK signal, we use the fact that the amplified spontaneous emission (ASE) noise generated by EDFA2 beats with the signal in the PD, leading to the fluctuation of the resulting waveform. We employ the delay-tap sampling method with a short delay Δt of 10 ps to observe the influence of reduced OSNR. The intensity waveforms of the RZ-DPSK signal with OSNR of 30 and 15 dB, as well as the corresponding delay-tap plots are shown in Fig. 5(a). The short delay between samples X and Y forms a narrow delay-tap plot resilient to changes in signal waveform. The plot allows separating the distribution of waveform peak from the distribution of waveform valley which can be observed along the diagonal D of the plot. The frequency of occurrence of sample pairs along the plot diagonal forms a histogram with two peaks, as shown in Fig. 5(b). If the distributions are assumed to be Gaussian, their mean values and standard deviations can be denoted respectively as *μ _{0}* and

*σ*for the distribution corresponding to the waveform valley and

_{0}*μ*and

_{1}*σ*for the distribution corresponding to the waveform peak. The values of the parameters are calculated by fitting the Gaussian curves to the respective distributions.

_{1}For the calculation of OSNR we introduce a noise parameter *F _{snr,rz}* defined as:

This definition is similar to the synchronous Q-parameter, however, the results are not equivalent because the sample pairs along the diagonal D do not have the same statistical distribution as the actual waveform.

The results of monitoring OSNR in the RZ-DPSK signal are presented in Fig. 6. Figure 6(a) plots the noise parameter as a function of OSNR measured in 0.1 nm resolution bandwidth. The OSNR can be evaluated in the range from 8.7 to 32 dB. The measurement is not linear over the entire range due to the influence of receiver noise above OSNR of 20 dB. The plot also indicates the standard deviation of 100 measurements taken at OSNR of 10.5, 20, and 31 dB with 50 000 sample pairs. The respective standard deviations are 1.93, 0.77, and 0.68 dB.

The upper limit of measurement is determined by the experimental setup; the lower limit occurs because of the overlap of peaks in the histogram taken along the diagonal D of the plot. The measurement of OSNR of 8.7 dB is the lowest reported measured OSNR among the OPM methods for RZ-DPSK.

In order to minimize the impact of the OPM system on the transmitted signal, only a small fraction of optical power can be tapped from the channel. Therefore, the optical power available to the monitor is limited, which may influence the precision of noise measurement. For this reason, the noise measurement was also conducted for input power of -11 and -15 dBm using a 10 GHz bandwidth PD with sensitivity of -20 dBm. The results and comparison to the measurement taken with the 50 GHz PD at input power of -0.5 dBm are shown in Fig. 6(b). For low input power a reduction in measurement sensitivity is visible in the high OSNR region. However, the measurement range remains unaltered and the difference can be calibrated.

Because the calculation of the noise parameter is based on the statistical analysis of the histogram, a sufficient number of sample pairs must be available along the diagonal of the delay-tap plot in order to ensure a precise calculation. The plot in Fig. 7(a) shows the results of analysis of the deviation of noise parameter as a function of acquired number of sample pairs for OSNR of 10, 20, and 30 dB. The standard deviation of *F _{snr,rz}* was calculated over 100 consecutive measurements. The deviation resulting in error of 1 dB OSNR is indicated in the plot. For all cases, the precision increases with the increasing number of acquired sample pairs. For OSNR of 20 dB and 30 dB the error is smaller than 1 dB for 25 000 sample pairs, or more. The measurement at OSNR of 10 dB does not reach the limit of 1 dB but the error continues to drop as the number of sample pairs increases. All noise calculations except the results in Fig. 7(a) have been performed with 50 000 sample pairs.

Another parameter which influences the precision of noise measurement is the delay Δt. In the experiment, the *F _{snr,rz}* parameter was obtained from the delay-tap plot formed with Δt=10 ps, which assures the highest dynamic range of noise measurement. An error in delay changes the shape of the plot and, accordingly, the measurement result. The dependence of noise parameter on delay Δt for OSNR of 30, 20, and 15 dB is shown in Fig. 7(b). The delay of 10 ps is indicated together with ±1 dB error from the

*F*value at each OSNR level. The influence of delay error is the largest for OSNR of 30 dB. This is due to the fact that the

_{snr,rz}*F*parameter has the highest value at 30 dB and, therefore, the absolute error is the largest. A delay shorter than 10 ps closes the delay-tap plot along the diagonal. For a longer delay the samples corresponding to pulse peak and valley cannot be translated to points lying on the diagonal D. In such case, the histogram is formed from samples of rising and falling edge of the pulse, which leads to the underestimation of OSNR. In order to assure that the OSNR measurement is within 1 dB of the predetermined value at Δt=10 ps, the error of delay Δt must be within -2~+14 ps for a 10 Gbit/s RZ-DPSK signal.

_{snr,rz}#### 3.3 Chromatic dispersion monitoring

The CD monitoring of the RZ-DPSK signal using delay-tap sampling OPM relies on the pulse carving of the waveform and the relative phase of the neighboring bits. The DPSK modulation conveys information in phase shifts of 0 or π between two consecutive bits. When an optical pulse is distorted by CD it spreads beyond the allocated bit slot. The bit symbol interference between two neighboring pulses alters the peak power and the shape of the waveform of a bit. Therefore, the amplitude of signal between the RZ pulses depends on the phase shift between the bits, as the constructive or destructive interference occurs. In order to track this phenomenon with the delay-tap sampling method the delay Δt of one bit is employed. This allows comparing the waveforms of two neighboring bits. The principle is illustrated in Fig. 8(a). For an undistorted waveform (CD=0 ps/nm), the samples X and Y have the same value. Therefore, the delay-tap plot is constructed only along the diagonal. However, when the signal experiences distortion due to the residual CD, the values of X and Y samples differ depending on the relative phase of the bits. This can be observed in the delay-tap plot, in which the trace deviates from the diagonal, as is illustrated in Fig. 8(a) for CD=500 ps/nm. The amount of deviation is proportional to the difference in waveform intensity between two consecutive symbols. Therefore, a dispersion parameter *F _{dis,rz}* is employed in order to measure the amount of accumulated CD in RZ-DPSK signals.

The dispersion parameter *F _{dis,rz}* is defined as the maximum distance between two straight lines parallel to the diagonal D, containing the points of the delay-tap plot, as shown in Fig. 8(a). The Hough transform is used to determine the distance by analyzing the accumulator array. Figure 8(b) plots the accumulator array formed from the delay-tap plot of RZ-DPSK signal with residual CD of 500 ps/nm. Because the Hough transform effectively changes the coordinate system to polar system, the localization of the lines corresponds to analyzing the accumulator array at angles

*ϕ*= 135° and at

*ϕ*= 315°, indicated by arrows. Parameter

*F*is calculated as the sum of maximum distance values R at angles

_{dis,rz}*ϕ*= 135° and

*ϕ*= 315°. The dispersion parameter can also be employed to monitoring of influence of differential group delay due to polarization-mode dispersion (PMD) on phase-modulated signals, as was demonstrated in [21]. However, due the lack of PMD emulator, the principle could not be verified experimentally at this moment.

The result of monitoring CD in a 9.95328 Gbit/s RZ-DPSK signal is shown in Fig. 9. The dispersion parameter *F _{dis,rz}* is plotted as a function of residual CD. The measurement ranges from -600 to +600 ps/nm and is symmetric with respect to the origin. The measurement is limited by pulse overlap at ±600 ps/nm at which point the measurement ceases to increase monotonically with the amount of accumulated dispersion. The horizontal error bars represent the accuracy with which the TDC could be adjusted (±25 ps/nm). The vertical error bars represent the standard deviation of

*F*parameter assessed over 100 measurements with 50 000 sample pairs. The deviation of dispersion parameter is 1.28 for 0 ps/nm, 1.88 for ±300 ps/nm, and 6.14 for ±600 ps/nm. The deviation at ±600 ps/nm corresponds to a measurement error of 38 ps/nm.

_{dis,rz}The precision of the dispersion measurement depends on the number of sample pairs used to create the delay-tap plot. This is due to the fact that a sufficient number of points must be used to form the envelope of the signal in the plot. The dependence of measurement accuracy expressed as the standard deviation of dispersion parameter on the number of sample pairs for CD of 0, 300, and 600 ps/nm is plotted in Fig. 10(a). The deviation decreases with the number of acquired samples and is smaller for lower accumulated CD. For all values of CD, an accuracy better than 25 ps/nm can be achieved if 100 000 sample pairs are used. Accuracy better than 10 ps/nm can be achieved in range from 0 to approximately 300 ps/nm if more than 50 000 sample pairs are used.

Furthermore, the influence of delay error on the dispersion parameter was analyzed. In Fig. 10(b) the value of *F _{dis,rz}* is plotted as a function of delay Δt for residual CD of 0 ps/nm, 300 ps/nm, and 600 ps/nm. As can be seen from the plot, even a small deviation from the default value of 100 ps (1-bit duration) results in measurement error. The error is caused by the difference between values of sample X and Y, regardless of the signal distortion. The difference results in deviation of the delay-tap plot from the diagonal, thereby increasing the value of

*F*. This result implies that the adjustment of delay Δt must be precise.

_{dis,rz}## 4. Discussion

The OPM method using the delay-tap sampling with Hough transform allows evaluating the OSNR and residual CD in a RZ-DPSK signal. The measurement of OSNR reaches as low as 8.7 dB. The previous demonstration of delay-tap monitoring method for DPSK signals showed the evaluation range from 25 to 35 dB [16]. The increase in measurement range stems from the fact that our method does not require phase-to-intensity demodulation through narrow band filtering. The lower limit of OSNR measurement exceeds the results of asynchronous amplitude histogram method, which can measure OSNR down to 15 dB [14,15]. Although the two methods use the histogram to assess the level of noise, the approach used in the delay-tap sampling method avoids the cross-over points of the waveform which are the limiting factor for the asynchronous amplitude histogram method. The ability to measure the OSNR as low as 9 dB for RZ-DPSK signals enables the delay-tap sampling method to be employed in systems operating in low OSNR regimes and taking advantage of forward error correction (FEC) [3,24].

The monitoring range for residual CD is comparable with other methods based on observation of the dispersion influence on signal waveform. Both the asynchronous histogram method [14,15] and the method based on clock tone [10] have a measurement range from 0 to 600 ps/nm for a 10 Gbit/s signal. The OPM method based on clock power and degree of polarization estimation in DPSK signals [13] has a broader measurement range of 0 to 900 ps/nm; however, it is limited to monitoring only of dispersive phenomena.

The precision of monitoring result for both OSNR and CD is dependent on the number of sample pairs used in the creation of the delay-tap plot, as was shown in Fig. 7(a) and Fig. 10(a). The number of acquired samples determines the acquisition time, which is the primary contributor to the total measurement time. If the number of sample pairs is set to 50 000 and the sampling rate is assumed to be 1 GHz, the resulting acquisition time is 50 µs. This time is equivalent to transmitting of 500 000 bits in a 10 Gbit/s RZ-DPSK channel. Therefore, the delay-tap sampling OPM is suitable for burst- or lambda-switched, rather than packet-switched networks.

Although the parameters *F _{snr,rz}* and

*F*focus on the influence caused by the respective impairments, normally the signal is affected by many impairment sources. Therefore, it is important to realize the level to which the particular measurement is influenced by other phenomena. We focus on the mutual dependence of CD and OSNR. The plot in Fig. 11(a) illustrates the influence of residual CD on the measurement of OSNR. The value of noise parameter is plotted as a function of OSNR for CD of 0, 300, and 600 ps/nm. The dispersion influences the measurement by spreading the peaks of the histogram acquired along the diagonal of the delay-tap plot. This results in a gradual reduction of sensitivity of

_{dis,rz}*F*parameter in the high OSNR region and limitation of the measurement range in the low OSNR region for CD of 600 ps/nm.

_{snr,rz}Similarly, the dependence can be observed for the dispersion parameter. In this case, the increased fluctuation of signal in the low OSNR region causes a deviation of the delay-tap plot from the diagonal regardless of the level of residual CD. The influence of OSNR on the measurement of CD is shown in Fig. 11(b). The *F _{dis,rz}* parameter is plotted as a function of residual CD for OSNR of 30, 20, and 15 dB. As the noise increases, the sensitivity of dispersion parameter is reduced. However, the measurement range, 0~600 ps/nm, remains unaffected, regardless of the level of noise.

## 5. Conclusion

In this paper we have experimentally demonstrated OPM of OSNR and CD in 10 Gbit/s RZ-DPSK signals using delay-tap sampling method with Hough transform. The presented method has an improved dynamic range, allowing assessing of OSNR in range from 8.7 dB to 32 dB, which enables effective monitoring of signals employing FEC. The measurement of residual CD covers the range from -600 to +600 ps/nm, which is comparable with previously presented OPM methods. The method has been shown to operate at power levels as low as -15 dBm. The presented OPM solution forms a robust building block for future transparent optical networks.

## Acknowledgments

Authors would like to thank Dr. Hidehiko Takara from NTT Network Innovation Laboratories for encouragement and fruitful discussion.

## References and links

**1. **A. Saleh and J. Simmons, “Evolution toward the next-generation core optical network,” J. Lightwave Technol. **24**, 3303–3321 (2006). [CrossRef]

**2. **G. Charlet, “Progress in optical modulation formats for high-bit rate WDM transmissions,” IEEE J. Sel. Top. Quantum Electron. **12**, 469–483 (2006). [CrossRef]

**3. **P. J. Winzer and R.-J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE **94**, 952–985 (2006). [CrossRef]

**4. **A. Gnauck and P. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. **23**, 115–130 (2005). [CrossRef]

**5. **C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. **10**, 281–293 (2004). [CrossRef]

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

**7. **G. Bendelli, C. Cavazzoni, R. Girardi, and R. Lano, “Optical performance monitoring techniques,” in *Proc. 26 ^{th} European Conference on Optical Communication (ECOC)*, 2000, 11.4.1.

**8. **I. Tomkos, D. Vogiatzis, C. Mas, I. Zacharopoulos, A. Tzanakaki, and E. Varvarigos, “Performance engineering of metropolitan area optical networks through impairment constraint routing,” IEEE Commun. Mag. **42**, S40–S47 (2004). [CrossRef]

**9. **Y. Huang, W. Wen, J. P. Heritage, and B. Mukherjee, “Signal-quality consideration for dynamic connection provisioning in all-optical wavelength-routed networks,” in *Proc. Opt. Netw. and Commun. conference* (OptiComm, 2003), pp. 163–173.

**10. **Y. K. Lize, L. Christen, J. Yang, P. Saghari, S. Nuccio, A. E. Willner, and R. Kashyap, “Independent and simultaneous monitoring of chromatic and polarization-mode dispersion in OOK and DPSK transmission,” IEEE Photon. Technol. Lett. **19**, 3–5 (2007). [CrossRef]

**11. **Y. K. Lize, J. Yang, L. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, and F. Seguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZOOK, DPSK and duobinary,” in *Proc. Optical Fiber Commun. Conf. (OFC)*, 2007, OThN2.

**12. **S. Jun, H. Kim, P. Park, J. Lee, and Y. Chung, “Pilot-tone-based WDM monitoring technique for DPSK systems,” IEEE Photon. Technol. Lett. **18**, 2171–2173 (2006). [CrossRef]

**13. **Z. Pan, Y. Wang, Y. Song, R. Motaghian, S. Havstad, and A. E. Willner, “Monitoring chromatic dispersion and PMD impairments in optical differential phase-shift-keyed (DPSK) systems,” in *Proc. Optical Fiber Commun. Conf. (OFC)*, 2003, WP1.

**14. **H. Takara, T. Ohara, and B. Kozicki, “Optical signal quality monitoring based on asynchronous amplitude histogram for DPSK systems,” in *Proc. Symp. Photon. Fiber Measurements (SOFM, 2006)*, pp.129–132.

**15. **Z. Li and G. Li, “In-line performance monitoring for RZ-DPSK signals using asynchronous amplitude histogram evaluation,” IEEE Photon. Technol. Lett. **18**, 472–474 (2006). [CrossRef]

**16. **T. B. Anderson, S. D. Dods, E. Wong, and P. M. Farrell, “Asynchronous measurement of chromatic dispersion from waveform distortion,” in *Proc. Optical Fiber Commun. Conf. ( OFC)*, 2006, OWN4.

**17. **S. D. Dods, T. B. Anderson, K. Clarke, M. Bakaul, and A. Kowalczyk, “Asynchronous sampling for optical performance monitoring,” in *Proc. Optical Fiber Commun. Conf. (OFC)*, 2007, OMM5.

**18. **S. D. Dods and T. B. Anderson, “Optical performance monitoring technique using delay tap asynchronous waveform sampling,” in *Proc. Optical Fiber Commun. Conf. (OFC)*, 2006, OThP5.

**19. **K. Clarke, T. B. Anderson, and S. D. Dods, “Monitoring of multiple modulation formats using asynchronous delay-tap sampling,” in *Proc. Intern. Conf. Opt. Internet - Australian Conf. Optical Fibre Technol. (COIN-ACOFT)*, 2007, MoA1-2.

**20. **B. Kozicki, A. Maruta, and K. Kitayama, “Asynchronous optical performance monitoring of RZ-DQPSK signals using delay-tap sampling,” in *Proc. 33 ^{rd} European Conference on Optical Communication (ECOC)*, 2007, P060.

**21. **B. Kozicki, A. Maruta, and K. Kitayama, “Transparent performance monitoring of RZ-DQPSK systems employing delay-tap sampling,” J. Opt. Netw. **6**, 1257–1269 (2007). [CrossRef]

**22. **J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision Graph. Image Process. **44**, 87–116 (1988). [CrossRef]

**23. **M. S. Nixon and A. S. Aguado, *Feature Extraction and Image Processing*, (Newnes, 2002).

**24. **T. Mizuochi, “Recent progress in forward error correction and its interplay with transmission impairments,” IEEE J. Sel. Top. Quantum Electron. **12**, 544–554 (2006). [CrossRef]