Abstract

Digital symbol synchronization of optical binary phase shift keying signals is experimentally demonstrated. Algorithm of timing error feedback is proposed for coherent intradyne reception. The feedback loop operates stable in the range of symbol rate, 9.7~0.3 GSymbol/s with 20 GSampling/s at relatively high bit error rate of ~2 × 10-2.

© 2008 Optical Society of America

1. Introduction

Recently, optical coherent communication technology has gained renewed interest because high speed analog-to-digital converters and digital signal processing are realized [1]. Digital signal processing in optical coherent receivers is powerful tool to compensate optical impairments including optical dispersion, polarization mode dispersion, polarization dependent loss, etc [24]. The techniques for suppressing nonlinear impairments induced in optical fibers are widely studied and reported [46]. Digital signal processing technique can also provide intradyne reception scheme without locking the frequency of local oscillator (LO) laser. The laser frequency offset between the input optical signal and LO laser is cancelled in digital domain [7].

The clock on the receiver side should be synchronized with that of the transmitter in order to recover the received data signals. Sampling clock can be recovered with the help of VCO (voltage controlled oscillator) and digitally evaluated error signals [8]. In digital symbol synchronization, timing recovery is processed in digital domain with free-running sampling clock, which does not need VCO and analog PLL (phase locked loop). Moreover, it can accompany any other digital signal processing techniques.

Digital symbol synchronization in digital communication receivers is well known in RF/wireless communications at relatively low symbol rate [9]. However, there is no detailed report of digital symbol synchronization in coherent optical receivers at higher symbol rate, e.g., 10 Gsymbol/s and above. We addressed in this paper digital symbol synchronization in optical coherent intradyne reception. Algorithm of non-data-aided timing error feedback is adapted for optical phase shift keying (PSK) signals and the experimental results are demonstrated.

2. Theory

Received optical signal is converted to a sequence of digital signal samples in coherent receiver, and it is processed according to the block diagram proposed in Fig. 1. Phase increment estimation algorithm is used for frequency offset estimator [7, 9]. This is a non-data-aided feed-forward algorithm that can be easily applied for PSK signals, and we will only consider PSK signals in the paper. The laser frequency offset between received optical signal and LO laser is corrected after the phase accumulated by frequency offset is subtracted from each signal sample.

 

Fig. 1. Block diagram of digital symbol synchronization in optical coherent intradyne reception.

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Interpolator is used to compute intermediate values between signal samples. Let the input signal samples of interpolator, x(n T s) where T S is sample interval. The output signal samples equal to

y(kTI+εITI)=y(mkTs+μkTs)=n=I1I2x((mkn)Ts)hn(μ)

where h n(µ) is interpolating FIR(finite impulse response) filter [9, 10]. N = I 1+I 2+1 is a order of interpolating filter. We assumed two samples per symbol, and T 1=T/2 where T is symbol interval. Since T I is not equal to T S, the samples in the transmitter time reference have to be mapped onto the time scale of receiver as shown in Fig. 2. k T I+ε I T I represents the time scale at the transmitter time reference, and m k T s+µ k T s T is on the receiver time axis. From this, one has to compute corresponding basepoint index m k and fractional interval µ k.

Polynomial interpolator with Farrow structure is adopted because it can be implemented very efficiently in high speed signal processing. Linear, piecewise-parabolic (α = 0.5) and cubic interpolator are applied and the results are compared in the processing. Farrow coefficients of each interpolator are given in [11]. The interpolator is controlled to determine the basepoint mk, and the corresponding fractional interval µ k based on the output of timing processor in Fig. 1.

 

Fig. 2. Explanation of timing parameters in Eq. (1). Mapping of k T I+ε I T I onto m k T s+µ k T S is shown.

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Error signal of timing error detector can be derived from the constant modulus property of PSK signals, |y(m k T S+µ k T S)2 [9, 11]. Differentiating with respect to time yields

e(mk)=Re{y(mkTs+μkTs)y*˙(mkTs+μkTs)}
Re{y(mkTs+μkTs)[y*((mk+1)Ts+μkTs)y*((mk1)Ts+μkTs)]}

where * denotes complex conjugate, ẏ is differentiation with time, and Re{.} means real-valued. The output sample rate of timing error detector is decreased by 2, and it selects every even basepoint m k(k = 2n) and produces error signals at symbol rate. The error signal of Eq. (2) is further processed in a loop filter, and the output of loop filter is given as

eloop(m2n)=Kpe(m2n)+Kik=nq+1ne(m2k)

where K P and Ki are constants, and q is a number of error signals in the summation. The output error signal of loop filter is used to adjust the control word (w = T I/T S) of the timing processor

w(m2n)=w(m2(n1))+eloop(m2(n1))

Control word is updated only every symbol with Eq. (4), and it follows w(m 2n+1)=w(m 2n)at every odd basepoint. Basepoint and fractional interval are recursively computed in the timing processor as followings [9].

mk+1=mk+floor[μk+w(mk)]
μk+1=[μk+w(mk)]mod1

where floor[] denotes the nearest integer less than or equal to the number in the bracket, []mod-1 is remainder after divided by 1. The algorithm can be applied to non-data-aided symbol synchronization for M-ary PSK signals.

In data path, after the timing error feedback is converged, the sample rate is decreased by 2 and the output signal samples are differentially detected and decided.

 

Fig. 3. Experimental set-up. PPG: pulse pattern generator, MZM: mach-zehnder modulator, 3 dB: 3 dB coupler, PC: polarization controller, PBS: polarization beam splitter, LO: local oscillator.

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3. Experiments and results

We studied the symbol synchronization of optical BPSK signals in the experiments. Fig. 3 shows the experimental set-up for optical coherent intradyne reception. We used LiNbO3 mach-zehnder modulator (MZM) for generating BPSK signals. The modulator is biased at its transmission null and two neighboring transmission maxima have 180° phase shift which is required for binary phase modulation. MZM introduces intensity dips in modulated optical signals at the time of data transition of two symbols. MZM-based optical BPSK or QPSK transmitter is preferred because of highly accurate phase modulation [12]. Tunable laser diode (LD) with a linewidth of <500 kHz and wavelength of 1530.33 nm was used. MZM was driven by pulse pattern generator (PPG), and pseudorandom bit sequences (PRBS) of a pattern length of 211-1 was used. 2-stage EDFA with variable attenuator was used for amplifying the optical signal and adjusting optical signal-to-noise ratio (OSNR). It was filtered with demux filter with a 3-dB bandwidth of 55 GHz.

On the receiver side, LO laser was from the output of tunable DFB laser with a linewidth of 3 MHz and output power of 20 mW. The input signal power of 90° optical hybrid was set to be 0 dBm by variable attenuator regardless of OSNR. All-fiber 90 degree optical hybrid was built with 3 dB coupler, polarization beam splitter (PBS), and polarization controllers (PC). The 90 degree difference was resulted from the different polarization states of two input signals [1315]. Though the 90° optical hybrid had polarization dependency on the input signals, it was maintained stable during the experiments after adjusting the polarization states. Two output signals of the 90° optical hybrid were directed to each photo-receiver. The electrical output signals of two photo-receivers were measured with real-time digital oscilloscope (Tektronix TDS6154C). 2 million samples per channel on the oscilloscope at the sampling rate of 20 GSample/s were obtained in each measurement. Measurement time was 100 µsec. After data acquisition, the data was processed offline with Matlab.

Frequency offset was maintained within the range of 0.2 ~ 0.6 GHz during the all experiments. It does not induce considerable variation of the receiver performance if the frequency offset estimator operates well [7]. In the processing, K P and K i were determined with the experimental data by trial and error. The choice of the constants was crucial for the stability of the feedback loop. When the constants went away from the optimal value, the error signal grew fast or the locking of loop was broken. The parameter q determined the speed of convergence. If it was big, the summation in Eq. (3) was done with many error signals in long time, therefore the variance of the output parameters was slow. The constants could be used in all the experiments regardless of the experimental conditions if once they were determined. The same values of K P, K i, and q were used in all the following results.

At first, the OSNR was maximized to 43 dB. Results shown later were obtained using piecewise-parabolic interpolator with α = 0.5. Fig. 4 shows the parameter response of digital symbol synchronization when the symbol rate was 10 GSymbol/s. Fig. 4(a) shows the variation of control word (w) that settles to the number of 1. It was the expected value because T I equals to T S in this case. The magnitude of error signal was suppressed after ~250 T in Fig. 4(b). Time interval for the convergence of the parameters was mainly dependent on the number of q in Eq. (3), and q was set to be 50 in all the results. Basepoint index m k and fractional interval µ k is shown in Fig. 4(c) and Fig. 4(d). Basepoint index continuously changed by 1 after the feedback had converged because control word was 1. We observed the value of µ k varied continuously by ~0.5 in the measurement time of 100 µsec. It meant that the clock of PPG was different from the sampling clock of the oscilloscope by ~2.5 × 10-7 in the ratio. Feedback loop was stable over the measurement time, though Fig. 4 shows the results in relatively small time interval to reveal the transient behavior of the parameters clearly.

 

Fig. 4. Parameter response in digital symbol synchronization at 10.0 GSymbol/s, OSNR = 43 dB, T I=T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval.

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When the feedback loop operated, we found that the output signal samples of the interpolator at even basepoint index were pulled to the time of data transition of the symbols. The average amplitude of the signal samples at even basepoint was less than that at odd basepoint, because there was intensity dip at the time of even basepoint. Therefore, the decision was done with the samples at odd basepoint index. After decision, the bit error was measured and there was no error detected in the case.

The sampling rate of 20 GSymbol/s was fixed at the oscilloscope, therefore we changed the symbol rate by changing the output of PPG. Fig. 5 shows the results of symbol synchronization when the symbol rate is 10.1 GSymbol/s. In Fig. 5(a), control word was settled to 0.99 because T I = 0.99T S at 10.1 GSymbol/s. The magnitude of error signal in Fig. 5(b) was nearly the same as that of Fig. 4(b). The parameters in Fig. 5(c) and Fig. 5(d) show repetitive responses, and the period was ~100 T I that agrees with T I = 0.99T S. There was no error detected after the feedback had converged.

 

Fig. 5. Parameter response in digital symbol synchronization at 10.1 GSymbol/s, OSNR = 43 dB, T I=T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval

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Fig. 6. Parameter response in digital symbol synchronization at 10.1 GSymbol/s, OSNR = 10 dB, T I=T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval

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We decreased the OSNR to 10 dB to check the impact of noises in the processing. Fig. 6 shows the results when the symbol rate is 10.1 GSymbol/s. Control word converged to 0.99 in average with some fluctuations in Fig. 6(a), although the magnitude of error signal in Fig. 6(b) was increased compared with Fig. 5(b). The parameters in Fig. 6(c) and Fig. 6(d) were varied repetitively with the period of ~100 T I after they had settled. The convergence time was increased to ~500T. The convergence time could be reduced by decreasing the parameter of q or optimally guessing the initial conditions. Moreover, convergence time of ~500 T was short enough compared with the time for stabilizing commercial optical transceivers. Bit error rate was 2.2×10-2 in this measurement. The results demonstrated that the algorithm of digital symbol synchronization worked well even at high bit error rate with OSNR of 10 dB.

The timing error feedback algorithm operated well even when the symbol rate was changed more. Fig. 7 shows the measured bit error rate when the symbol rate was changed from 9.7 to 10.3 GSymbol/s with a step of 0.1 GSymbol/s. OSNR was 10 dB in the case. Three kinds of interpolators were applied in sequence to the same measurement data. It showed that there was no considerable performance degradation within the range of the symbol rate when the digital symbol synchronization was applied. The bit error rate was the lowest when piecewise-parabolic interpolator was used, which agreed with the calculated results in [11]. The feedback loop was stable in the range with all kinds of the interpolator. Successful results could be obtained even outside of the range in Fig. 7, e.g. at the symbol rate of 10.9 GSymbol/s. However, outside of the range, the convergence of feedback loop was dependent on the initial conditions of the parameters, and constants of Eq. (3). It will be investigated to widen the range of symbol rate in the near future.

 

Fig. 7. Measured bit error rate at OSNR = 10 dB with the change of symbol rate. Measurement time is 100 µsec.

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4. Conclusions

In conclusion, the algorithm of timing error feedback is proposed and digital symbol synchronization in optical coherent intradyne reception is experimentally demonstrated. The feedback loop is stable over the range of the symbol rate, 9.7~10.3 GSymbol/s with fixed sampling rate of 20 GSample/s. The experiments are done with optical BPSK signals, however, it is reasonable to consider that the algorithm is applicable to any optical M-ary PSK signals, because it is based on general property of optical PSK signals. Moreover, it can be incorporated with other techniques of signal processing to enhance the integratability of the digital optical receivers.

Acknowledgments

This work was supported by the IT R&D program of MKE/IITA. [2008-F017-01, 100Gbps Ethernet and optical transmission technology development]

References and links

1. H. Sun, K. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16, 873–879 (2008).

2. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15, 2120–2126 (2007). [CrossRef]   [PubMed]  

3. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008). [CrossRef]   [PubMed]  

4. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008). [CrossRef]   [PubMed]  

5. K. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22, 779–783 (2004). [CrossRef]  

6. K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000 km 20 Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Express 16, 889–896 (2008). [CrossRef]   [PubMed]  

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

8. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noe, “Coherent optical communication: towards realtime systems at 40Gbit/s and beyond,” Opt. Express 16, 866–872 (2008). [CrossRef]   [PubMed]  

9. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).

10. F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Trans. Commun. 41, 501–507 (1993). [CrossRef]  

11. L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993). [CrossRef]  

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

13. W. R. Leeb, “Realization of 90- and 180 degree hybrids for optical frequencies,” Arch. Elek. Ubertragung 37, 203–206 (1983).

14. L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987). [CrossRef]  

15. D. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24, 12–21 (2006). [CrossRef]  

References

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  1. H. Sun, K. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16, 873–879 (2008).
  2. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15, 2120–2126 (2007).
    [Crossref] [PubMed]
  3. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
    [Crossref] [PubMed]
  4. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008).
    [Crossref] [PubMed]
  5. K. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22, 779–783 (2004).
    [Crossref]
  6. K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000 km 20 Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Express 16, 889–896 (2008).
    [Crossref] [PubMed]
  7. A. Leven, N. Kaneda, U. Koc, and K. Chen, “Frequency estimation in intradyne reception,” IEEE Photon. Technol. Lett. 19, 366–368 (2007).
    [Crossref]
  8. T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, and R. Noe, “Coherent optical communication: towards realtime systems at 40Gbit/s and beyond,” Opt. Express 16, 866–872 (2008).
    [Crossref] [PubMed]
  9. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).
  10. F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Trans. Commun. 41, 501–507 (1993).
    [Crossref]
  11. L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
    [Crossref]
  12. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keying transmission,” J. Lightwave Technol. 23, 115–130 (2005).
    [Crossref]
  13. W. R. Leeb, “Realization of 90- and 180 degree hybrids for optical frequencies,” Arch. Elek. Ubertragung 37, 203–206 (1983).
  14. L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
    [Crossref]
  15. D. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24, 12–21 (2006).
    [Crossref]

2008 (5)

2007 (2)

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15, 2120–2126 (2007).
[Crossref] [PubMed]

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

2006 (1)

2005 (1)

2004 (1)

1993 (2)

F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Trans. Commun. 41, 501–507 (1993).
[Crossref]

L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
[Crossref]

1987 (1)

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

1983 (1)

W. R. Leeb, “Realization of 90- and 180 degree hybrids for optical frequencies,” Arch. Elek. Ubertragung 37, 203–206 (1983).

Adamczyk, O.

Barros, D. J. F.

Bayvel, P.

Chen, K.

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

Cheung, N. K.

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

Curtis, L.

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

Erup, L.

L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
[Crossref]

Fechtel, S. A.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).

Gardner, F. M.

F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Trans. Commun. 41, 501–507 (1993).
[Crossref]

L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
[Crossref]

Gavioli, G.

Gnauck, A. H.

Harris, R. A.

L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
[Crossref]

Herath, V.

Ho, K.

Hoffmann, S.

Ip, E.

Kahn, J. M.

Kaneda, N.

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

Katoh, K.

Kazovsky, L. G.

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

Kikuchi, K.

Killey, R. I.

Koc, U.

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

Lau, A. P. T.

Leeb, W. R.

W. R. Leeb, “Realization of 90- and 180 degree hybrids for optical frequencies,” Arch. Elek. Ubertragung 37, 203–206 (1983).

Leven, A.

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

Ly-Gagnon, D.

Meyr, H.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).

Moeneclaey, M.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).

Noe, R.

Peveling, R.

Pfau, T.

Porrmann, M.

Roberts, K.

Savory, S. J.

Sun, H.

Tsukamoto, S.

Winzer, P. J.

Wu, K.

Young, W. C.

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

App. Optics (1)

L. G. Kazovsky, L. Curtis, W. C. Young, and N. K. Cheung, “All-fiber 90o optical hybrid for coherent communications,” App. Optics 26, 437–439 (1987).
[Crossref]

Arch. Elek. Ubertragung (1)

W. R. Leeb, “Realization of 90- and 180 degree hybrids for optical frequencies,” Arch. Elek. Ubertragung 37, 203–206 (1983).

IEEE Photon. Technol. Lett. (1)

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

IEEE Trans. Commun. (2)

F. M. Gardner, “Interpolation in digital modems-part I: fundamentals,” IEEE Trans. Commun. 41, 501–507 (1993).
[Crossref]

L. Erup, F. M. Gardner, and R. A. Harris, “Interpolation in digital modems-part II: implementation and performance,” IEEE Trans. Commun. 41, 998–1008 (1993).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (6)

Other (1)

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital communication receivers (John Wiley & Sons Inc,1998).

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Figures (7)

Fig. 1.
Fig. 1.

Block diagram of digital symbol synchronization in optical coherent intradyne reception.

Fig. 2.
Fig. 2.

Explanation of timing parameters in Eq. (1). Mapping of k T I +ε I T I onto m k T s +µ k T S is shown.

Fig. 3.
Fig. 3.

Experimental set-up. PPG: pulse pattern generator, MZM: mach-zehnder modulator, 3 dB: 3 dB coupler, PC: polarization controller, PBS: polarization beam splitter, LO: local oscillator.

Fig. 4.
Fig. 4.

Parameter response in digital symbol synchronization at 10.0 GSymbol/s, OSNR = 43 dB, T I =T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval.

Fig. 5.
Fig. 5.

Parameter response in digital symbol synchronization at 10.1 GSymbol/s, OSNR = 43 dB, T I =T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval

Fig. 6.
Fig. 6.

Parameter response in digital symbol synchronization at 10.1 GSymbol/s, OSNR = 10 dB, T I =T/2. T : symbol interval. (a) control word (b) error signal of loop filter (c) basepoint index difference (d) fractional interval

Fig. 7.
Fig. 7.

Measured bit error rate at OSNR = 10 dB with the change of symbol rate. Measurement time is 100 µsec.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

y ( k T I + ε I T I ) = y ( m k T s + μ k T s ) = n = I 1 I 2 x ( ( m k n ) T s ) h n ( μ )
e ( m k ) = Re { y ( m k T s + μ k T s ) y * ˙ ( m k T s + μ k T s ) }
Re { y ( m k T s + μ k T s ) [ y * ( ( m k + 1 ) T s + μ k T s ) y * ( ( m k 1 ) T s + μ k T s ) ] }
e loop ( m 2 n ) = K p e ( m 2 n ) + K i k = n q + 1 n e ( m 2 k )
w ( m 2 n ) = w ( m 2 ( n 1 ) ) + e loop ( m 2 ( n 1 ) )
m k + 1 = m k + floor [ μ k + w ( m k ) ]
μ k + 1 = [ μ k + w ( m k ) ] mod 1

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