Fiber input power selection for probabilistically shaped signals in optical networks

1. A method for setting fiber input power in an optical transport network, comprising:

determining, dependent on a target distance for an optical transmission path in the optical transport network, an initial modulation format for the optical transmission path, the initial modulation format representing a uniform distribution quadrature amplitude modulation (QAM) format selected from among a plurality of QAM modulation formats supported in the optical transport network, the initial modulation format being associated with a first fiber input power and a first spectral efficiency;

configuring one or more optical transponders to apply probabilistic shaping to the initial modulation format when transmitting traffic over the optical transmission path, the traffic comprising probabilistically shaped signals associated with a second spectral efficiency;

determining, dependent on the second spectral efficiency, a second fiber input power different from the first fiber input power; and

configuring one or more optical amplifiers along the optical transmission path to transmit the traffic comprising the probabilistically shaped signals over the optical transmission path using the second fiber input power.

2. The method of claim 1 , wherein the first fiber input power is dependent on one or more of a measure of fiber nonlinearity in the optical transmission path and a link configuration along the optical transmission path.

3. The method of claim 1 , wherein determining the second fiber input power comprises:

determining a first difference between the second spectral efficiency and a third spectral efficiency associated with a first reference modulation format, the third spectral efficiency being less than the second spectral efficiency, and the first reference modulation format being a uniform distribution QAM modulation format associated with a third fiber input power;

determining a second difference between the second spectral efficiency and a fourth spectral efficiency associated with a second reference modulation format, the fourth spectral efficiency being greater than the second spectral efficiency, the second reference modulation format being a next higher order uniform distribution QAM modulation format than the first reference modulation format, and the second reference modulation format being associated with a fourth fiber input power;

determining that the first difference is less than the second difference; and

in response to determining that the first difference is less than the second difference, determining the second fiber input power by reducing the third fiber input power by an amount dependent on the difference between the third fiber input power and the fourth fiber input power.

4. The method of claim 1 , wherein determining the second fiber input power comprises:

determining a first difference between the second spectral efficiency and a third spectral efficiency associated with a first reference modulation format, the third spectral efficiency being less than the second spectral efficiency, and the first reference modulation format being a uniform distribution QAM modulation format associated with a third fiber input power;

determining a second difference between the second spectral efficiency and a fourth spectral efficiency associated with a second reference modulation format, the fourth spectral efficiency being greater than the second spectral efficiency, the second reference modulation format being a next higher order uniform distribution QAM modulation format than the first reference modulation format, and the second reference modulation format being associated with a fourth fiber input power;

determining that the first difference is greater than the second difference; and

in response to determining that the first difference is greater than the second difference, setting the second fiber input power to an amount equal to the fourth fiber input power.

5. The method of claim 1 , wherein configuring the one or more optical transponders to apply probabilistic shaping to the initial modulation format comprises:

determining, dependent on the initial modulation format, a maximum signal-to-noise ratio (SNR) for the optical transmission path and a corresponding fiber input power associated with the maximum SNR;

determining, dependent on the maximum SNR, a maximum achievable information rate (AIR) and a corresponding shaping factor to be applied to the initial modulation format;

determining an entropy for the probabilistic shaping dependent on the maximum AIR and the corresponding shaping factor, the entropy being indicative of the second spectral efficiency; and

configuring the one or more optical transponders to apply probabilistic shaping to the initial modulation format in accordance with the determined entropy.

6. The method of claim 5 , wherein determining the second fiber input power comprises:

monitoring SNR performance of the optical transmission path; and

calculating the second fiber input power dependent on the monitoring.

7. The method of claim 5 , wherein determining the second fiber input power comprises calculating, using an enhanced Gaussian noise model, the second fiber input power dependent on the maximum SNR.

8. The method of claim 5 , wherein determining the second fiber input power comprises:

modifying kurtosis of a probability distribution associated with the shaping factor; and

adjusting fiber input power dependent on increased tolerance to fiber nonlinearity caused by modifying the probability distribution.

9. The method of claim 5 , wherein determining the maximum SNR comprises computing the maximum SNR using an enhanced Gaussian noise model.

10. The method of claim 5 , further comprising:

repeating said determining a maximum SNR to determine a modified maximum SNR;

repeating said determining a maximum AIR and a corresponding shaping factor to determine a modified maximum AIR and a modified shaping factor;

repeating said determining an entropy to determine a modified entropy, the modified entropy being indicative of a modified spectral efficiency;

determining a third fiber input power for the probabilistically shaped signals dependent on the modified spectral efficiency; and

configuring the one or more optical amplifiers along the optical transmission path to transmit the traffic comprising the probabilistically shaped signals over the optical transmission path using the second fiber input power.

11. The method of claim 1 , wherein determining the second fiber input power comprises selecting, dependent on an SNR margin for the optical transport network, a process for determining the second fiber input power from among a plurality of processes for determining the second fiber input power, the plurality of processes including a coarse method for estimating an optimum fiber input power in which an optimum fiber input power for a reference modulation format is incrementally increased or decreased dependent on the second spectral efficiency, and an adaptive process in which selection of the second fiber input power is dependent on measured performance, enhanced Gaussian nose modeling, or modification of a shaping distribution associated with the probabilistically shaped signals.

12. An optical transport network for constellation shaping of quadrature amplitude modulation (QAM) formats, the optical transport network comprising:

an optical transmission path;

a plurality of transponders, each operable to apply probabilistic shaping to QAM modulation formats;

one or more optical amplifiers along the optical transmission path; and

a network management system configured to:

determine, dependent on a target distance for the optical transmission path, an initial modulation format for the optical transmission path, the initial modulation format representing a uniform distribution QAM modulation format selected from among a plurality of QAM modulation formats supported in the optical transport network, the initial modulation format being associated with a first fiber input power and a first spectral efficiency;

configure the one or more optical transponders to apply probabilistic shaping to the initial modulation format when transmitting traffic over the optical transmission path, the traffic comprising probabilistically shaped signals associated with a second spectral efficiency;

determine, dependent on the second spectral efficiency, a second fiber input power different from the first fiber input power; and

configure the one or more optical amplifiers along the optical transmission path to transmit the traffic comprising the probabilistically shaped signals over the optical transmission path using the second fiber input power.

13. The optical transport network of claim 12 , wherein the first fiber input power is dependent on one or more of a measure of fiber nonlinearity in the optical transmission path and a link configuration along the optical transmission path.

14. The optical transport network of claim 12 , wherein to determine the second fiber input power, the network management system is configured to:

determine a first difference between the second spectral efficiency and a third spectral efficiency associated with a first reference modulation format, the third spectral efficiency being less than the second spectral efficiency, and the first reference modulation format being a uniform distribution QAM modulation format associated with a third fiber input power;

determine a second difference between the second spectral efficiency and a fourth spectral efficiency associated with a second reference modulation format, the fourth spectral efficiency being greater than the second spectral efficiency, the second reference modulation format being a next higher order uniform distribution QAM modulation format than the first reference modulation format, and the second reference modulation format being associated with a fourth fiber input power;

determine whether the first difference is less than the second difference;

in response to a determination that the first difference is less than the second difference, determine the second fiber input power by reducing the third fiber input power by an amount dependent on the difference between the third fiber input power and the fourth fiber input power; and

in response to a determination that that the first difference is not less than the second difference, set the second fiber input power to an amount equal to the fourth fiber input power.

15. The optical transport network of claim 12 , wherein to configure the one or more optical transponders to apply probabilistic shaping to the initial modulation format, the network management system is configured to:

determine, dependent on the initial modulation format, a maximum signal-to-noise ratio (SNR) for the optical transmission path and a corresponding fiber input power associated with the maximum SNR;

determine, dependent on the maximum SNR, a maximum achievable information rate (AIR) and a corresponding shaping factor to be applied to the initial modulation format;

determine an entropy for the probabilistic shaping dependent on the maximum AIR and the corresponding shaping factor, the entropy being indicative of the second spectral efficiency; and

configure the one or more optical transponders to apply probabilistic shaping to the initial modulation format in accordance with the determined entropy.

16. The optical transport network of claim 15 , wherein to determine the second fiber input power, the network management system is configured to:

monitor SNR performance of the optical transmission path; and

calculate the second fiber input power dependent on the monitoring.

17. The optical transport network of claim 15 , wherein to determine the second fiber input power, the network management system is configured to calculate, using an enhanced Gaussian noise model, the second fiber input power dependent on the maximum SNR.

18. The optical transport network of claim 15 , wherein to determine the second fiber input power, the network management system is configured to:

modify kurtosis of a probability distribution associated with the shaping factor; and

adjust fiber input power dependent on increased tolerance to fiber nonlinearity caused by modification of the probability distribution.

19. The optical transport network of claim 15 , wherein to determine the maximum SNR, the network management system is configured to compute the maximum SNR using an enhanced Gaussian noise model.

20. The optical transport network of claim 15 , wherein the network management system is further configured to:

determine a modified maximum SNR for the optical transmission path;

determine a modified maximum AIR and a modified shaping factor for the optical transmission path;

determine a modified entropy for the optical transmission path, the modified entropy being indicative of a modified spectral efficiency for the probabilistically shaped signals;

determine a third fiber input power for the probabilistically shaped signals dependent on the modified spectral efficiency; and

configure the one or more optical amplifiers along the optical transmission path to transmit the traffic comprising the probabilistically shaped signals over the optical transmission path using the third fiber input power.