Satellite beam power backoff

1. A method of operating a non-geosynchronous orbit (NGSO) satellite to comply with equivalent power flux density (EPFD) limits, the method comprising:

for each of a number of selected locations on Earth:

determining a first cumulative distribution function (CDF) of EPFD levels associated with reception of a beam, to be transmitted from the NGSO satellite, at the selected location;

identifying a number of EPFD percentile limits that are violated by the first CDF of EPFD levels;

determining a second CDF of EPFD levels at the selected location based, at least in part, on the number of identified EPFD percentile limits; and

determining a power back-off value for the selected location based, at least in part, on the second CDF of EPFD levels;

compiling the determined power back-off values for the number of selected locations into a power back-off schedule; and

dynamically adjusting a power level of the beam to be transmitted from the NGSO satellite based on the power back-off schedule.

2. The method of claim 1 , wherein the power back-off schedule represents the power back-off values as a function of latitude on Earth.

3. The method of claim 1 , wherein the power back-off schedule comprises a vector including a number of components, each component indicating the power back-off value for a corresponding latitude on Earth.

4. The method of claim 1 , wherein the second CDF of EPFD levels does not violate any of the number of identified EPFD percentile limits.

5. The method of claim 1 , wherein determining the second CDF of EPFD levels comprises:

defining, for each of the number of identified EPFD percentile limits, a corresponding step function; and

modifying the first CDF of EPFD levels to include the defined step functions.

6. The method of claim 5 , wherein each of the defined step functions is to avoid violating a corresponding one of the number of identified EPFD percentile limits, each of the identified EPFD percentile limits associated with a corresponding reference antenna dish size of a geosynchronous (GSO) earth station.

7. The method of claim 5 , further comprising:

defining a number of EPFD intervals for the selected location based, at least in part, on the defined step functions; and

determining the power back-off value for the selected location based, at least in part, on the number of defined EPFD intervals.

8. The method of claim 7 , wherein determining the power back-off value comprises:

simulating an operation of the NGSO satellite for a finite number of time ticks;

detecting violations of the EPFD percentile limits associated with each of the number of defined EPFD intervals; and

calculating the power back-off value based, at least in part, on the detected violations.

9. An apparatus for operating a non-geosynchronous orbit (NGSO) satellite to comply with equivalent power flux density (EPFD) limits, the apparatus comprising:

for each of a number of selected locations on Earth:

means for determining a first cumulative distribution function (CDF) of EPFD levels associated with reception of a beam, to be transmitted from the NGSO satellite, at the selected location;

means for identifying a number of EPFD percentile limits that are violated by the first CDF of EPFD levels;

means for determining a second CDF of EPFD levels at the selected location based, at least in part, on the number of identified EPFD percentile limits; and

means for determining a power back-off value for the selected location based, at least in part, on the second CDF of EPFD levels;

means for compiling the determined power back-off values for the number of selected locations into a power back-off schedule; and

means for dynamically adjusting a power level of the beam to be transmitted from the NGSO satellite based on the power back-off schedule.

10. The apparatus of claim 9 , wherein the power back-off schedule represents the power back-off values as a function of latitude on Earth.

11. The apparatus of claim 9 , wherein the power back-off schedule comprises a vector including a number of components, each component indicating the power back-off value for a corresponding latitude on Earth.

12. The apparatus of claim 9 , wherein the second CDF of EPFD levels does not violate any of the number of identified EPFD percentile limits.

13. The apparatus of claim 9 , wherein the means for determining the second CDF of EPFD levels is to:

define, for each of the number of identified EPFD percentile limits, a corresponding step function; and

modify the first CDF of EPFD levels to include the defined step functions.

14. The apparatus of claim 13 , wherein each of the defined step functions is to avoid violating a corresponding one of the number of identified EPFD percentile limits, each of the identified EPFD percentile limits associated with a corresponding reference antenna dish size of a geosynchronous (GSO) earth station.

15. The apparatus of claim 13 , further comprising:

means for defining a number of EPFD intervals for the selected location based, at least in part, on the defined step functions; and

means for determining the power back-off value for the selected location based, at least in part, on the number of defined EPFD intervals.

16. The apparatus of claim 15 , wherein the means for determining the power back-off value is to:

simulate an operation of the NGSO satellite for a finite number of time ticks;

detect violations of the EPFD percentile limits associated with each of the number of defined EPFD intervals; and

calculate the power back-off value based, at least in part, on the detected violations.

17. An apparatus for operating a non-geosynchronous orbit (NGSO) satellite to comply with equivalent power flux density (EPFD) limits, the apparatus comprising:

one or more processors; and

a memory configured to store instructions that, when executed by the one or more processors, cause the apparatus to:

for each of a number of selected locations on Earth:

determine a first cumulative distribution function (CDF) of EPFD levels associated with reception of a beam, to be transmitted from the NGSO satellite, at the selected location;

identify a number of EPFD percentile limits that are violated by the first CDF of EPFD levels;

determine a second CDF of EPFD levels at the selected location based, at least in part, on the number of identified EPFD percentile limits; and

determine a power back-off value for the selected location based, at least in part, on the second CDF of EPFD levels;

compile the determined power back-off values for the number of selected locations into a power back-off schedule; and

dynamically adjust a power level of the beam to be transmitted from the NGSO satellite based on the power back-off schedule.

18. The apparatus of claim 17 , wherein the power back-off schedule represents the power back-off values as a function of latitude on Earth.

19. The apparatus of claim 17 , wherein the power back-off schedule comprises a vector including a number of components, each component indicating the power back-off value for a corresponding latitude on Earth.

20. The apparatus of claim 17 , wherein execution of the instructions for determining the second CDF of EPFD levels causes the apparatus to:

define, for each of the number of identified EPFD percentile limits, a corresponding step function; and

modify the first CDF of EPFD levels to include the defined step functions.

21. The apparatus of claim 20 , wherein each of the defined step functions is to avoid violating a corresponding one of the number of identified EPFD percentile limits, each of the identified EPFD percentile limits associated with a corresponding reference antenna dish size of a geosynchronous (GSO) earth station.

22. The apparatus of claim 20 , wherein execution of the instructions causes the apparatus to further:

define a number of EPFD intervals for the selected location based, at least in part, on the defined step functions; and

determine the power back-off value for the selected location based, at least in part, on the number of defined EPFD intervals.

23. The apparatus of claim 22 , wherein execution of the instructions for determining the power back-off value causes the apparatus to:

simulate an operation of the NGSO satellite for a finite number of time ticks;

detect violations of the EPFD percentile limits associated with each of the number of defined EPFD intervals; and

calculate the power back-off value based, at least in part, on the detected violations.

24. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors of an apparatus, cause the apparatus to perform operations comprising:

for each of a number of selected locations on Earth:

determining a first cumulative distribution function (CDF) of EPFD levels associated with reception of a beam, to be transmitted from a non-geosynchronous orbit (NGSO) satellite, at the selected location;

identifying a number of EPFD percentile limits that are violated by the first CDF of EPFD levels;

determining a second CDF of EPFD levels at the selected location based, at least in part, on the number of identified EPFD percentile limits; and

determining a power back-off value for the selected location based, at least in part, on the second CDF of EPFD levels;

compiling the determined power back-off values for the number of selected locations into a power back-off schedule; and

dynamically adjusting a power level of the beam to be transmitted from the NGSO satellite based on the power back-off schedule.

25. The non-transitory computer-readable medium of claim 24 , wherein the power back-off schedule represents the power back-off values as a function of latitude on Earth.

26. The non-transitory computer-readable medium of claim 24 , wherein the power back-off schedule comprises a vector including a number of components, each component indicating the power back-off value for a corresponding latitude on Earth.

27. The non-transitory computer-readable medium of claim 24 , wherein execution of the instructions for determining the second CDF of EPFD levels causes the apparatus to perform operations further comprising:

defining, for each of the number of identified EPFD percentile limits, a corresponding step function; and

modifying the first CDF of EPFD levels to include the defined step functions.

28. The non-transitory computer-readable medium of claim 27 , wherein each of the defined step functions is to avoid violating a corresponding one of the number of identified EPFD percentile limits, each of the identified EPFD percentile limits associated with a corresponding reference antenna dish size of a geosynchronous (GSO) earth station.

29. The non-transitory computer-readable medium of claim 27 , wherein execution of the instructions causes the apparatus to perform operations further comprising:

defining a number of EPFD intervals for the selected location based, at least in part, on the defined step functions; and

determining the power back-off value for the selected location based, at least in part, on the number of defined EPFD intervals.

30. The non-transitory computer-readable medium of claim 29 , wherein execution of the instructions for determining the power back-off value causes the apparatus to perform operations further comprising:

simulating an operation of the NGSO satellite for a finite number of time ticks;

detecting violations of the EPFD percentile limits associated with each of the number of defined EPFD intervals; and

calculating the power back-off value based, at least in part, on the detected violations.