Abstract

We report a new optical performance monitoring technique based on the amplitude and phase histograms of the optical signal. The amplitude and phase histograms are obtained by using an intradyne receiver and the asynchronous delay-tap sampling method. From these histograms, we can evaluate the amplitude and phase Q-factors of the optical signal regardless of its modulation format. In addition, by using these Q-factors, we can estimate the bit-error rate (BER) of the monitoring signal.

© 2009 OSA

1. Introduction

It is now apparent that multilevel modulated signals, such as the quadrature phase-shift-keying (QPSK) and quadrature amplitude modulation (QAM) signals, will play an important role in the next-generation high-speed optical networks [13]. Thus, for the efficient operation and management of these networks, we should be able to monitor the quality of multilevel signals directly in the optical layer. So far, the optical signal-to-noise ratio (OSNR) has been used as one of the essential monitoring parameters since it can be directly related to the bit-error rate (BER) of the conventional intensity-modulated binary signal (assuming that the amplified spontaneous emission noise is the dominant error source) [4,5]. However, in the case of the multilevel signal, the OSNR may not be able to properly represent its quality by itself since it can be seriously affected by the nonlinear phase noise as well (caused by the use of the high signal power required for the transmission of multilevel signal). Thus, for the proper monitoring of these networks, there have been several attempts to utilize the constellation diagram [68]. For example, it has been proposed to monitor the constellation diagram by using the linear optical sampling technique (which utilizes a coherent receiver with short sampling pulses) [6]. This technique can extract the information related to the OSNR and phase shift of the monitoring signal from the measured constellation diagram. However, to reduce the monitoring errors, it should remove the samples measured at the transition between the data symbols (since the pulsed local oscillator (LO) used in this technique is not synchronized with the data rate of the monitoring signal). Thus, this technique should utilize only the samples existing in a specific area in the constellation diagram, which is not a simple task in practice. It has also been proposed to monitor the quality of the multilevel differential phase-shift-keying (DxPSK) signal by using a differential phasor diagram [7]. This technique utilizes a delay interferometer made of a 3x3 coupler and two Faraday rotator mirrors. However, this technique should use a synchronized trigger signal for the sampling of the monitoring signal.

In this paper, we propose a new optical performance monitoring technique for the multilevel modulated signals based on the amplitude and phase histograms. This technique utilizes an intradyne receiver and the asynchronous delay-tap sampling method [8]. Thus, there is no need to use the complicate optical phase-locked loop (since the intradyne receiver utilizes a free-running laser as LO). In addition, due to the use of the asynchronous delay-tap sampling method, this technique can acquire only the data located at the center of the bit of the monitoring signal without using the synchronized trigger signal [5,8]. Using the proposed technique, we first obtain the amplitude and phase histograms of the monitoring signal by using the delayed and non-delayed parts of the in-phase and quadrature components. We then evaluate the amplitude and phase Q-factors from these histograms. We also show that these Q-factors can be used to estimate the BER of the multilevel modulated signal. For a demonstration, we monitor the amplitude and phase Q-factors of 20-Gb/s QPSK signal by using the proposed technique and estimate its BER by using these Q-factors. The results show that the estimated BERs agree well with the directly measured values.

2. Principle of operation

Figure 1(a) shows the schematic diagram of the proposed monitoring technique based on the asynchronous amplitude and phase histograms. We first detect the electric field (i.e., in-phase and quadrature components) of the optical signal by using an intradyne receiver. Since the intradyne receiver utilizes a free-running LO laser, the proposed technique does not require the stringent wavelength control used in the homodyne receiver. We then sample the detected electric field by using the asynchronous delay-tap sampling method. This sampling method is implemented by using a radio-frequency (RF) power splitter, variable delays, and an analog-to-digital converter (ADC) [5]. A portion of the signal is passed through a delay line after the RF power splitter and experienced a delay of Δt. The delayed and original (i.e., non-delayed) signals are then sampled by using an ADC. We designate a sampled pair of these delayed and non-delayed signals as x and y, respectively. Using this sampled pair, we can obtain the x-y plot (which is referred as a two-tap plot (TTP) in this paper) as shown in Fig. 1(b). We then convert the in-phase and quardrature components [measured by using two single-ended, AC-coupled photodetectors (PDs) in Fig. 1(a)] to the amplitude and phase information. However, due to the use of the free-running LO laser in the intradyne receiver, a substantial phase drift can be observed in the trajectory, as shown in Fig. 2(a) . We utilize the M-th power algorithm to reduce the effect of this phase drift [9]. This is interesting to note that, despite the asynchronous sampling used here, the M-th power algorithm is still effective in compensating the phase drift originating from the free-running LO, as shown in Fig. 2(b).

 

Fig. 1 (a) Configuration of the proposed technique. ADC: analog-to-digital converter (b) Signal waveform and two-tap plot. Tsampling: sampling period, Δt: tap delay.

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Fig. 2 Trajectories of the QPSK signal (a) before and (b) after the use of the M-th power algorithm.

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After compensating the phase drift, we obtain the TTPs of the amplitude and phase of the monitoring signal by using the sampled data. Figure 3 shows an example of the QPSK signal. It should be noted that the shape of the amplitude TTP shown in Fig. 3(a) is different from the shape of the TTP shown Fig. 1(b). This is because we obtain the amplitude TTP by using the magnitudes of the samples measured from the origin in the trajectory shown in Fig. 2(b). The phase TTP of the QPSK signal in Fig. 3(b) clearly illustrates four symbols. The data along the diagonal dashed lines in these TTPs correspond to the data measured at the center of the bit [5,8]. Thus, using these data, we obtain the amplitude and phase histograms of the monitoring signal, as shown in Fig. 3.

 

Fig. 3 (a) Amplitude and (b) phase TTPs and their corresponding histograms obtained along the diagonal lines of the QPSK signal.

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The Q-factor, which is often used to evaluate the quality of the optical signal, is defined as the ratio between the difference of the means and the sum of the standard deviations of the signal’s intensity distributions [10]. However, we define the Q-factors of the amplitude and phase of the monitoring signal by using their corresponding histograms. For example, as shown in Fig. 3(a), there is only one mean (Ia) and standard deviation (σa) value for the amplitude histogram of the QPSK signal. On the other hand, Fig. 3(b) shows that there are four mean (Ip,n) and standard deviation (σp,n) values for the phase histogram, where n represents the index of the phase symbols of the QPSK signal. By using the means and standard deviations of these histograms, we define the amplitude Q-factor (QA) and the phase Q-factor (QP) as follows;

QA=Iaσa,
QP=Ipσp=|Ip,nIp,(n+1)|σp,n+σp,(n+1),
where Ip = |Ip,n-Ip, ( n +1)| and σp = σp,n + σp, ( n +1) represent the minimum phase difference between phase symbols (i.e., π/2 for the QPSK signal) and the sum of the standard deviations of their corresponding distributions in the phase histogram, respectively. Thus, we can monitor the amplitude and phase Q-factors of the monitoring signal using the amplitude and phase TTPs obtained by the proposed technique.

In general, for an additive white Gaussian noise (AWGN) channel, we can calculate the BER by using the signal-to-noise ratio (SNR) [11]. In addition, we note that the SNR of the monitoring signal can be obtained from the amplitude and phase Q-factors since these values are basically composed of the signal and noise powers. Thus, in principle, we should be able to estimate the BER of the monitoring signal by using the amplitude and phase Q-factors. For example, in the case of QPSK signal, the SNR is calculated to be QA2QP2/(QP2+Ip2QA2) since the total noise power is determined by the sum of the amplitude and phase noise powers. Thus, the BER can be obtained as erfc(SNR)/2.

3. Experiments and results

Figure 4 shows the experimental setup to evaluate the performance of the proposed monitoring technique. The signal under test was a 20-Gb/s QPSK signal at 1548 nm. The QPSK signal was generated by using a nested Mach-Zehnder modulator. To investigate the effect of the phase noise imposed on the QPSK signal, we utilized an additional phase modulator operating with a 3-GHz RF sinusoidal signal [12]. Using this phase modulator, we changed the phase of the QPSK signal up to ± 25 degrees. To simulate the amplitude and phase noises, we also varied the OSNR from 10 to 30 dB by using an amplified spontaneous emission (ASE) noise source. The monitoring module consisted of an intradyne receiver and a digital storage oscilloscope (DSO). For the intradyne receiver, we utilized a commercial tunable laser as the LO, a 90-degree optical hybrid, and two PDs. We set the optical powers of the LO and input signal incident on the monitoring module to 0 and −10 dBm, respectively. The frequency difference between the LO and input signal was less than a few hundred MHz. The DSO was used as an ADC and sampled the data at the rate of 50 Gs/s. To realize the asynchronous delay-tap sampling method, we selected a pair of consecutive samples at a time. Thus, there was no need to use the variable RF delays, and the delay time was determined to be 20 ps by the sampling rate of the DSO. The number of the sampled data used for obtaining the amplitude and phase histograms was ~15,000. We then evaluated the amplitude and phase Q-factors of the QPSK signal offline under various conditions.

 

Fig. 4 Experimental setup. TLD: tunable laser diode, MZM: QPSK modulator, PM: phase modulator, ASE: amplified spontaneous emission, DSO: digital storage oscilloscope.

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Figure 5 shows the measured amplitude and phase Q-factors obtained by using Eqs. (1) and (2) while varying the OSNR and phase deviation. The results showed that the amplitude Q-factor depended only on the OSNR (i.e., it is not affected by the phase deviation). On the other hand, the phase Q-factor was sensitive to both the OSNR and phase deviation. As expected, the amplitude and phase noises imposed on the monitoring signal were well reflected by the amplitude and phase Q-factors, respectively. In addition, the proposed technique can monitor the BER of the optical signal by measuring the amplitude and phase Q-factors. To confirm this capability, we estimated the BER by using the measured amplitude and phase Q-factors and compared with the actual BER of the 20-Gb/s QPSK signal. For the BER measurement, we used the data length of 105 symbols, and the digital frequency estimation and the carrier phase estimation algorithms [9,13]. However, due to the limited number of data, we could not measure the BER lower than 10−5. Figure 6 shows the estimated BER curves of the QPSK signal as a function of the OSNR and phase deviation. In this figure, the open and close symbols represent the actual BERs measured by using a coherent receiver and the estimated BERs obtained by using the amplitude and phase Q-factors, respectively. For the BER estimation, we used the well-known equation for the BER calculation of the QPSK signal using the SNR [11]. The estimated BER using the proposed technique agreed well with the actual measured BER. As shown in Fig. 6, the BER became worse as the phase noise was increased, and eventually resulted in the error floor. This result indicates that the BER of the multilevel signal can be seriously degraded by the phase noises (e.g., caused by the fiber nonlinearities), even if the OSNR of the multilevel signal is sufficiently high for the error-free transmission. However, the proposed technique can properly monitor the quality of the multilevel signal by utilizing both the amplitude and phase Q-factors.

 

Fig. 5 Measured (a) amplitude and (b) phase Q-factors of the QPSK signal. Δθ: peak-to-peak phase deviation

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Fig. 6 BER estimation from the proposed technique. Δθ: peak-to-peak phase deviation

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4. Summary

We have developed a new optical performance monitoring technique based on the asynchronous amplitude and phase histograms of the optical signal. These histograms are measured by using an intradyne receiver and the asynchronous delay-tap sampling method. This technique is, in principle, independent of the modulation format since it utilizes both information on the amplitude and phase distributions. In addition, the proposed technique can monitor the wavelength-division-multiplexed (WDM) signals without using a tunable optical filter because of the outstanding frequency selectivity inherent in the coherent receiver. For a demonstration, we have experimentally confirmed that the proposed technique can monitor the BER of the 20-Gb/s QPSK signal by using the amplitude and phase Q-factors.

Acknowledgement

This work was supported by the IT R&D program of MKE/IITA [2008-F017-02, 100Gbps Ethernet and optical transmission technology development].

References and links

1. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Adjustment-free DxPSK receiver based on single delay interferometer using 120-degree optical hybrid,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OMM2.

2. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Betran Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper PDP3.

3. A. H. Gnauck, P. J. Winzer, C. R. Doerr, and L. L. Buhl, “10x112-Gb/s PDM 16-QAM transmission over 630 km of fiber with 6.2-b/s/Hz spectral efficiency,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper PDPB8.

4. J. H. Lee, H. Y. Choi, S. K. Shin, and Y. C. Chung, “A review of the polarization-nulling technique for monitoring optical-signal-to-noise ratio in dynamic WDM networks,” J. Lightwave Technol. 24(11), 4162–4171 (2006). [CrossRef]  

5. T. B. Anderson, S. D. Dods, K. Clarke, J. Bedo, and A. Kowalczyk, “Multi-impairment monitoring for photonic networks,” in Proceedings of European Conference on Optical Communications (ECOC 2007), paper 3.5.1.

6. C. Dorrer, “Monitoring of optical signals from constellation diagrams measured with linear optical sampling,” J. Lightwave Technol. 24(1), 313–321 (2006). [CrossRef]  

7. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Measurement of differential phasor diagram of multilevel DPSK signals by using an adjustment-free delay interferometer composed of a 3x3 optical coupler,” J. Lightwave Technol. 27(6), 718–730 (2009). [CrossRef]  

8. H. Y. Choi, Y. Takushima, and Y. C. Chung, “Multiple-impairment monitoring technique using optical field detection and asynchronous delay-tap sampling method,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OThJ5.

9. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]  

10. G. P. Agrawal, Fiber-optic communication systems (John Wiley & Sons, Inc., 2002), Chap. 4.

11. J. G. Proakis, Digital communications (McGraw-Hill, 2001), Chap. 5.

12. K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007). [CrossRef]  

13. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007). [CrossRef]  

References

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  1. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Adjustment-free DxPSK receiver based on single delay interferometer using 120-degree optical hybrid,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OMM2.
  2. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Betran Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper PDP3.
  3. A. H. Gnauck, P. J. Winzer, C. R. Doerr, and L. L. Buhl, “10x112-Gb/s PDM 16-QAM transmission over 630 km of fiber with 6.2-b/s/Hz spectral efficiency,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper PDPB8.
  4. J. H. Lee, H. Y. Choi, S. K. Shin, and Y. C. Chung, “A review of the polarization-nulling technique for monitoring optical-signal-to-noise ratio in dynamic WDM networks,” J. Lightwave Technol. 24(11), 4162–4171 (2006).
    [CrossRef]
  5. T. B. Anderson, S. D. Dods, K. Clarke, J. Bedo, and A. Kowalczyk, “Multi-impairment monitoring for photonic networks,” in Proceedings of European Conference on Optical Communications (ECOC 2007), paper 3.5.1.
  6. C. Dorrer, “Monitoring of optical signals from constellation diagrams measured with linear optical sampling,” J. Lightwave Technol. 24(1), 313–321 (2006).
    [CrossRef]
  7. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Measurement of differential phasor diagram of multilevel DPSK signals by using an adjustment-free delay interferometer composed of a 3x3 optical coupler,” J. Lightwave Technol. 27(6), 718–730 (2009).
    [CrossRef]
  8. H. Y. Choi, Y. Takushima, and Y. C. Chung, “Multiple-impairment monitoring technique using optical field detection and asynchronous delay-tap sampling method,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OThJ5.
  9. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [CrossRef]
  10. G. P. Agrawal, Fiber-optic communication systems (John Wiley & Sons, Inc., 2002), Chap. 4.
  11. J. G. Proakis, Digital communications (McGraw-Hill, 2001), Chap. 5.
  12. K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
    [CrossRef]
  13. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
    [CrossRef]

2009 (1)

2007 (2)

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

2006 (2)

1983 (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

Chen, Y.-K.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

Choi, H. Y.

Chung, Y. C.

Croussore, K.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

Dorrer, C.

Kaneda, N.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

Koc, U.-V.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

Lee, J. H.

Leven, A.

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

Li, G.

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

Shin, S. K.

Takushima, Y.

Viterbi, A. J.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

Viterbi, A. M.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

K. Croussore and G. Li, “Phase regeneration of NRZ-DPSK signals based on symmetric-pump phase-sensitive amplification,” IEEE Photon. Technol. Lett. 19(11), 864–866 (2007).
[CrossRef]

A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19(6), 366–368 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[CrossRef]

J. Lightwave Technol. (3)

Other (7)

G. P. Agrawal, Fiber-optic communication systems (John Wiley & Sons, Inc., 2002), Chap. 4.

J. G. Proakis, Digital communications (McGraw-Hill, 2001), Chap. 5.

T. B. Anderson, S. D. Dods, K. Clarke, J. Bedo, and A. Kowalczyk, “Multi-impairment monitoring for photonic networks,” in Proceedings of European Conference on Optical Communications (ECOC 2007), paper 3.5.1.

Y. Takushima, H. Y. Choi, and Y. C. Chung, “Adjustment-free DxPSK receiver based on single delay interferometer using 120-degree optical hybrid,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OMM2.

G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. Betran Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2550 km using PDM QPSK modulation format and coherent receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper PDP3.

A. H. Gnauck, P. J. Winzer, C. R. Doerr, and L. L. Buhl, “10x112-Gb/s PDM 16-QAM transmission over 630 km of fiber with 6.2-b/s/Hz spectral efficiency,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper PDPB8.

H. Y. Choi, Y. Takushima, and Y. C. Chung, “Multiple-impairment monitoring technique using optical field detection and asynchronous delay-tap sampling method,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper OThJ5.

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Figures (6)

Fig. 1
Fig. 1

(a) Configuration of the proposed technique. ADC: analog-to-digital converter (b) Signal waveform and two-tap plot. Tsampling: sampling period, Δt: tap delay.

Fig. 2
Fig. 2

Trajectories of the QPSK signal (a) before and (b) after the use of the M-th power algorithm.

Fig. 3
Fig. 3

(a) Amplitude and (b) phase TTPs and their corresponding histograms obtained along the diagonal lines of the QPSK signal.

Fig. 4
Fig. 4

Experimental setup. TLD: tunable laser diode, MZM: QPSK modulator, PM: phase modulator, ASE: amplified spontaneous emission, DSO: digital storage oscilloscope.

Fig. 5
Fig. 5

Measured (a) amplitude and (b) phase Q-factors of the QPSK signal. Δθ: peak-to-peak phase deviation

Fig. 6
Fig. 6

BER estimation from the proposed technique. Δθ: peak-to-peak phase deviation

Equations (2)

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Q A = I a σ a ,
Q P = I p σ p = | I p , n I p , ( n + 1 ) | σ p , n + σ p , ( n + 1 ) ,

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