Symbol timing recovery in polarization division multiplexed coherent optical transmission system

1. A method in a receiver for recovering clock timing of a polarization division multiplexed (PDM) signal having two linear polarization states, each having an in-phase and quadrature-phase component, wherein complex signals X and Y represent sampled in-phase and quadrature-phase components for each orthogonal linear polarization state of the PDM signal, comprising the steps of:

processing each of the complex signals X and Y using at least one or more reference frequencies associated with a spectrum of the sampled PDM signal to obtain co-polarization and cross-polarization terms for each orthogonal linear polarization state of the one or more reference frequencies; and

determining a phase of a determinant of a two-by-two matrix, from said terms, the two-by-two matrix having the co-polarization and cross-polarization terms as elements therein, said phase value being indicative of clock timing offset of the PDM signal.

2. The method of claim 1 , further comprising:

providing the phase of the determinant to one or more units adapted to recover the clock timing of the PDM signal using the phase of the determinant.

3. The method of claim 2 , wherein the one or more units adapted to recover the clock timing of the PDM signal are interpolators.

4. The method of claim 2 , wherein the phase of the determinant is provided to the one or more units in a feedforward manner or as feedback.

5. The method of claim 1 , wherein the PDM signal is a wavelength division multiplexed (WDM) signal.

6. The method of claim 1 , wherein said sampling comprises oversampling at a sampling rate greater than a symbol rate of the PDM signal.

7. The method of claim 6 , wherein the sampling rate is two times the symbol rate of the PDM signal.

8. The method of claim 1 , wherein the steps of the method are performed automatically by said receiver.

9. The method of claim 8 , wherein said receiver comprises a digital signal processor adapted to perform the steps of the method.

10. The method of claim 1 , wherein said PDM signal is an optical signal.

11. The method of claim 1 , wherein the steps of the method are performed by a unit, the unit being disposed between one or more chromic dispersion correctors and one or more equalizers.

12. The method of claim 1 , wherein processing each of the complex signals X and Y to obtain the co-polarization and cross-polarization terms for each orthogonal linear polarization state comprises:

processing each of the complex signals X and Y by a Fourier transform operation to form respective frequency domain signals TX and TY;

separating each of the frequency domain signals TX and TY into upper and lower sideband components; and

multiplying the upper sideband components of TX and TY by complex conjugates of the lower sideband components of TX and TY to obtain thereby the co-polarization and cross-polarization terms for each orthogonal linear polarization state.

13. The method of claim 12 , wherein said multiplying further comprises:

averaging the obtained co-polarization and cross-polarization terms over multiple frequencies.

14. The method of claim 12 , wherein said multiplying further comprises:

time-averaging the obtained co-polarization and cross-polarization terms over multiple sample periods.

15. The method of claim 12 , wherein said separating comprises computing upper sideband components and lower sideband components separated by the symbol rate.

16. An apparatus for recovering the clock timing of a polarization division multiplexed (PDM) signal having two orthogonal linear polarization states, each having an in-phase and quadrature-phase component, wherein complex signals X and Y represent sampled in-phase and quadrature-phase components for each orthogonal linear polarization state of the PDM signal, comprising:

means for processing each of the complex signals X and Y using at least one or more reference frequencies associated with a spectrum of the sampled PDM signal to obtain co-polarization and cross-polarization terms for each orthogonal linear polarization state of the one or more reference frequencies; and

means for determining a phase of a determinant of a two-by-two matrix, from said terms, the two-by-two matrix having the co-polarization and cross-polarization terms as elements therein, said phase value being indicative of clock timing offset of the PDM signal.

17. The apparatus of claim 16 , wherein the PDM signal is a wavelength division multiplexed (WDM) signal.

18. The apparatus of claim 16 , wherein said PDM signal is an optical signal.

19. The apparatus of claim 16 , wherein said means for processing each of the complex signals X and Y to obtain the co-polarization and cross-polarization terms for each orthogonal linear polarization state comprises:

means for processing each of the complex signals X and Y by a Fourier transform operation to form respective frequency domain signals TX and TY;

means for separating each of the frequency domain signals TX and TY into upper and lower sideband components; and

means for multiplying the upper sideband components of TX and TY by complex conjugates of the lower sideband components of TX and TY to obtain thereby the co-polarization and cross-polarization terms for each orthogonal linear polarization state.

20. The apparatus of claim 19 , wherein said multiplying means further comprises:

means for averaging the obtained co-polarization and cross-polarization terms over multiple frequencies.

21. The apparatus of claim 19 , wherein said multiplying means further comprises:

means for time-averaging the obtained co-polarization and cross-polarization terms over multiple sample periods.

22. The apparatus of claim 19 , wherein said separating means further comprises:

means for computing upper sideband components and lower sideband components separated by the symbol rate.

23. The apparatus of claim 16 , further comprising:

means for providing the phase of the determinant to one or more units adapted to recover the clock timing of the PDM signal using the phase of the determinant.

24. The apparatus of claim 23 , wherein the means for providing the phase of the determinant to the one or more units comprises:

mean for providing the phase of the determinant to the one or more units in a feedforward manner or as feedback.

25. The apparatus of claim 23 , wherein the one or more units adapted to recover the clock timing of the PDM signal are interpolators.

26. The apparatus of claim 16 , wherein the means for determining the phase of the determinant is configured to be disposed between one or more chromic dispersion correctors and one or more equalizers.

27. A receiver for receiving a polarization division multiplexed (PDM) signal having two orthogonal linear polarization states, each having an in-phase and quadrature-phase component, adapted to recover the clock timing of the PDM signal, comprising:

at least one analog to digital converter for sampling the PDM signal to obtain thereby complex signals X and Y representing sampled in-phase and quadrature phase components for each orthogonal linear polarization state of the PDM signal; and

a digital signal processor adapted to:

process each of the complex signals X and Y using at least one or more reference frequencies associated with a spectrum of the sampled PDM signal to obtain co-polarization and cross-polarization terms for each orthogonal linear polarization state of the one or more reference frequencies; and

determine a phase of a determinant of a two-by-two matrix, from said terms, the two-by-two matrix having the co-polarization and cross-polarization terms as elements therein, said phase value being indicative of clock timing offset of the PDM signal.

28. A system for coherent optical communication, comprising:

at least one transmitter for transmitting a polarization division multiplexed (PDM) signal having two orthogonal linear polarization states, each having an in-phase and quadrature-phase component; and

at least one receiver for receiving the PDM signal and adapted to recover the clock timing of the PDM signal, comprising:

at least one analog to digital converter for sampling the PDM signal to obtain thereby complex signals X and Y representing sampled in-phase and quadrature phase components for each orthogonal linear polarization state of the PDM signal; and

a digital signal processor adapted to:

process each of the complex signals X and Y using at least one or more reference frequencies associated with a spectrum of the sampled PDM signal to obtain co-polarization and cross-polarization terms for each orthogonal linear polarization state of the one or more reference frequencies; and

determine a phase of a determinant of a two-by-two matrix, from said terms, the two-by-two matrix having the co-polarization and cross-polarization terms as elements therein, said phase value being indicative of clock timing offset of the PDM signal.

29. An apparatus for recovering clock timing of a polarization division multiplexed (PDM) signal having two linear polarization states, each having an in-phase and quadrature-phase component, wherein complex signals X and Y represent sampled in-phase and quadrature-phase components for each orthogonal linear polarization state of the PDM signal, the apparatus comprising:

a digital signal processor configured to:

process each of the complex signals X and Y using at least one or more reference frequencies associated with a spectrum of the sampled PDM signal to obtain co-polarization and cross-polarization terms for each orthogonal linear polarization state of the one or more reference frequencies; and

determine a phase of a determinant of a two-by-two matrix, from said terms, the two-by-two matrix having the co-polarization and cross-polarization terms as elements therein, said phase value being indicative of clock timing offset of the PDM signal.

30. The apparatus of claim 29 , the digital signal processor configured to:

provide the phase of the determinant to one or more units adapted to recover the clock timing of the PDM signal using the phase of the determinant.

31. The apparatus of claim 30 , the digital signal processor configured to provide the phase of the determinant to the one or more units in a feedforward manner or as feedback.

32. The apparatus of claim 30 , wherein the one or more units adapted to recover the clock timing of the PDM signal are interpolators.

33. The apparatus of claim 29 , the apparatus comprising at least one chromatic dispersion corrector and at least one equalizer, the digital signal processor configured to determine the phase of the determinant after chromic dispersion correction by the at least one chromatic dispersion corrector and before equalization by the at least one equalizer.

34. The apparatus of claim 29 , further comprising:

at least one hybrid optical detector configured to produce the sampled versions of the respective in-phase and quadrature-phase components of the orthogonal linear polarization states.