Minimum variance carrier recovery with increased phase noise tolerance

1. In a coherent receiver of an optical communications system, a method of data symbol recovery comprising:

periodically computing, by a frequency error estimator, a local slope representative of at least a frequency offset between a local oscillator of the receiver and a transmitter laser;

computing, by a phase noise estimator, probabilistic phase error estimates based on the computed local slope and data symbol estimates detected from a received optical signal, the probabilistic phase error estimates being representative of a phase error of each data symbol estimate and a probability that each data symbol estimate is in a correct decision region of a symbol constellation; and

computing by a phase rotator a phase rotation by applying a predetermined filter function to a plurality of the probabilistic phase error estimates, and applying the computed phase rotation to at least one data symbol estimate to generate a corresponding rotated symbol estimate.

2. The method of claim 1 , wherein the probabilistic phase error is proportional to a magnitude of a symbol estimate, and proportional to a phase error of the symbol estimate for values of the phase error close to zero, and zero at a boundary between adjacent decision regions of the symbol constellation.

3. The method of claim 1 , wherein computing the probabilistic phase error comprises calculating an expected value of phase noise using a selected operator on a conditional probability density function, the conditional probability density function being conditioned on phase and magnitude of at least one data symbol estimate.

4. The method of claim 3 , wherein the selected operator is any one of an L 1 norm, an L 2 norm and an L ∞ norm.

5. The method of claim 3 , wherein the conditional probability density function models an asymmetry of the symbol constellation.

6. The method of claim 1 , wherein computing the probabilistic phase error estimates comprises, for each data symbol estimate:

calculating respective polar coordinate symbol phase and magnitude values of the data symbol estimate;

calculating a phase error of the data symbol estimate, based on the calculated symbol phase; and

calculating the respective probabilistic phase error based on the calculated phase error and the symbol magnitude.

7. The method of claim 6 , wherein calculating the phase error comprises:

adjusting the detected symbol phase using the local slope to compensate frequency offset between a transmit laser and a local oscillator of the coherent receiver, to generate a corrected symbol phase; and

calculating the phase error between the corrected symbol phase and a nearest symbol of the symbol constellation.

8. The method of claim 1 , wherein computing a respective phase rotation comprises:

filtering minimum variance phase error estimates calculated for a time series of successive data symbol estimates to obtain a minimum variance phase error; and

calculating a minimum variance phase rotation using the minimum variance phase error.

9. The method of claim 8 , wherein filtering the phase error estimates comprises any one or more of:

applying a Wiener filter to the phase error estimates; and

computing a running average over the probabilistic phase error estimates.

10. The method of claim 8 , wherein computing the minimum variance phase rotation comprises accumulating, for each successive data symbol estimate, a corresponding incremental phase rotation corresponding to μ 1 Ψ+μ 2 Δφ(n+1), where μ 1 and μ 2 are a scaling factors defining a phase adjustment step size for each successive data symbol estimate; Ψ is a phase slope indicative of unbounded phase error due to frequency offset; and Δφ(n+1) is the minimum variance phase error.

11. The method of claim 8 , wherein filtering the phase error estimates comprises the operation of emphasis of a subset of the phase error estimate values being filtered.

12. A coherent receiver of an optical communications system, the coherent receiver comprising:

a frequency error estimator configured to periodically compute a local slope representative of at least a frequency offset between a local oscillator of the receiver and a transmitter laser;

a phase noise estimator configured to compute probabilistic phase error estimates based on the computed local slope and data symbol estimates detected from a received optical signal, the probabilistic phase error estimates being representative of a phase error of each data symbol estimate and a probability that each data symbol estimate is in a correct decision region; and

a phase rotator configured to compute a phase rotation by applying a predetermined filter function to a plurality of the probabilistic phase error estimates, and to apply the computed phase rotation to at least one data symbol estimate to generate a corresponding rotated symbol estimate.

13. The coherent receiver of claim 12 , wherein the phase noise estimator comprises:

a converter configured to calculate respective polar coordinate symbol phase and magnitude values of each data symbol estimate;

a phase detector configured to calculate a phase error of each data symbol estimate, based on the symbol phase; and

a Minimum Mean Square Error processor configured to calculate the phase error estimate based on the calculated phase error and the symbol magnitude.

14. The coherent receiver of claim 13 , wherein the Minimum Mean Square Error processor comprises a look-up-table.

15. The coherent receiver of claim 13 , further comprising a frequency correction block configured to adjust the symbol phase to compensate frequency offset between a transmit laser and a local oscillator of the coherent receiver, to generate a corrected symbol phase, and wherein the phase detector is configured to calculate the phase error between the corrected symbol phase and a nearest symbol of the symbol constellation.

16. The coherent receiver of claim 13 further comprising a filter block configured to filter phase error estimates calculated for a time series of successive data symbol estimates to obtain a minimum variance phase error estimate.

17. The coherent receiver of claim 16 , wherein the phase rotator is configured to calculate a minimum variance phase rotation using the minimum variance phase error estimate.

18. The coherent receiver of claim 17 , wherein the phase rotator is configured to compute the minimum variance phase rotation by accumulating, for each successive data symbol estimate, a corresponding incremental phase rotation corresponding to μ 1 Ψ+μ 2 Δφ(n+1), where μ 1 and μ 2 are a scaling factors defining a phase adjustment step size for each successive symbol estimate; Ψ is a phase slope indicative of unbounded phase error due to frequency offset; and Δφ(n+1) is the minimum variance phase error estimate.

19. The coherent receiver of claim 16 , wherein the filter block comprises any one or more of:

a Wiener filter; and

an averaging circuit configured to compute a running average over the phase error estimates.

20. The coherent receiver of claim 12 , wherein the phase noise estimator is configured to compute the probabilistic phase error by calculating an expected value of phase noise using a selected operator on a conditional probability density function, the conditional probability density function being conditioned on phase and magnitude of at least one data symbol estimate.