Placement of calibration earth stations for ground based beam forming in a satellite system
A system and method for estimating calibration parameters and locating a Calibration Earth Station (CES) is described. The method may be performed offline. The method includes: providing L×M pilot signal measurements in a matrix R from L CESs and the M feed elements, wherein the matrix R comprises a set of channel coefficients c={c1, c2, . . . , cM}, and k={k1, k2, . . . , kL} perturbations; linking a subset of channel coefficients {c1, c2, . . . , cM} using each of the L CESs; and estimating a relative estimate of the k={k1, k2, . . . , kL} pertubations across the L CESs by using each of the L CESs as a bridging element. In the method, the bridging element provides a strong pilot signal for at least two of the L CESs. A set of criteria for determining locations of CESs have been described. A set of desirable properties for the solution set of L CESs have been disclosed. A combination of inner loop and outer loop methods for determining the final set of optimal locations have been described.
1. A method for estimating calibration parameters and locating a Calibration Earth Station (CES) receiving a signal from an antenna array with M feed elements, the method comprising:
providing L×M pilot signal measurements in a matrix R from L CESs and the M feed elements, wherein the matrix R comprises a set of channel coefficients c={c1, c2, . . . , cM}, and k={k1, k2, . . . , kL} perturbations;
linking a subset of channel coefficients {c1, c2, . . . , cM} using each of the L CESs;
estimating a relative estimate of the k={k1, k2, . . . , kL} perturbations across the L CESs by using one of the M feed elements as a bridging element;
performing the estimating for a plurality of sets of L locations;
calculating a residual calibration error for each set of the plurality of sets of L locations; and
selecting a set from the plurality of sets of L locations having a lowest residual calibration error,
wherein the bridging element provides a strong pilot signal measurement for at least two of the L CESs.
2. The method of claim 1 , the method further comprising: providing criterion comprising specifying that each of the one or more bridging elements has at least L k CES sites (where k=1, 2, . . . , K) within ζ k A dB in power degradation relative to a peak of a feeder beam.
3. The method of claim 1 , the method further comprising: providing criterion comprising specifying geographical preferences and constraints.
4. The method of claim 1 , the method further comprising: providing criterion comprising specifying that each of the one or more bridging elements has connectivity to least M j feeds (j=1, . . . , J) where a j th feed is visible at a CES no less than ζ j B dB suppressed in power relative to a peak of a secondary beam.
5. The method of claim 1 , the method further comprising: minimizing L by selecting the location for each of the L CESs such that each of the one or more bridging elements is allotted about an equal number of feed elements of the M feed elements.
6. The method of claim 1 , the method further comprising: selecting the location for each of the L CESs such that each of the one or more bridging elements meets a priority specification.
7. The method of claim 1 , the method further comprising: selecting the location for each of the L CESs such that variations of footprints of elemental secondary patterns of a satellite at the selected locations are minimized.
8. The method of claim 1 , wherein the determining comprises generating locations of the L CESs at random, performing the estimating for the L CESs, monitoring a performance of the estimating, and incrementing a count of the L CESs locations based on the performance of the estimating.
9. The method of claim 1 , further comprising: performing simulated annealing with each of the L CESs and at least two neighboring feeds to search for locations of the L CESs.
10. A system to estimate calibration parameters and locate a Calibration Earth Station (CES) receiving a signal from an antenna array with M feed elements, the system comprising:
a matrix R to provide L×M pilot signal measurements from L CESs and the M feed elements, wherein the matrix R comprises a set of channel coefficients c={c1, c2, . . . , cM}, and k={k1, k2, . . . , kL} perturbations; and
a signal processor
to link a subset of channel coefficients {c1, c2, . . . , cM} using each of the L CESs, and
to estimate a relative estimate of the k={k1, k2, . . . , kL} perturbations across the L CESs by using one of the M feed elements as a bridging element,
wherein the bridging element provides a strong pilot signal measurement for at least two of the L CESs and
wherein the signal processor performs the estimating for a plurality of sets of L locations, calculates a residual calibration error for each set of the plurality of sets of L locations, and selects a set from the plurality of sets of L locations having a lowest residual calibration error.
11. The system of claim 10 , the system further comprising: a criterion specifying that each of the one or more bridging elements has at least L k CES sites (where k=1, 2, . . . , K) within ζ k A dB in power degradation relative to a peak of a feeder beam.
12. The system of claim 10 , the system further comprising: a criterion specifying that each of the one or more bridging elements has connectivity to least M j feeds (j=1, . . . , J) where a j th feed is visible at a CES no less than ζ j B dB suppressed in power relative to a peak of a secondary beam.
13. The system of claim 10 , wherein the signal processor minimizes L by selecting the location for each of the L CESs such that each of the one or more bridging elements is allotted about an equal number of feed elements of the M feed elements.
14. The system of claim 10 , wherein the signal processor selects the location for each of the L CESs such that each of the one or more bridging elements meets a priority specification.
15. The system of claim 10 , wherein the signal processor selects the location for each of the L CESs such that variations of footprints of elemental secondary patterns of a satellite at the selected locations are minimized.
16. The system of claim 10 , wherein the signal processor generates locations of the L CESs at random, performs the estimating for the L CESs, monitors a performance of the estimating, and increments a count of the L CESs locations based on the performance of the estimating.
17. A method for locating a set of Calibration Earth Stations (CES), the method comprising:
providing pilot signal measurements matrix R from L CESs and M feed elements, wherein R comprises a set of channel coefficients c={c1, c2, . . . , cM}, {k=k1, k2, . . . , kL} perturbations, and a noise component N;
ensuring that each column of matrix R includes a plurality of strong secondary pattern connections;
ensuring that each row of R includes the plurality of strong secondary pattern connections;
bridging two neighboring CESs of the L CESs with at least two neighboring feeds, and two neighboring feeds of the M feed elements with at least one CES;
performing simulated annealing with the at least one CES and the at least two neighboring feeds to search for locations of the L CESs;
calculating a residual calibration error for each of the locations of the L CESs, and
selecting locations having a lowest residual calibration error,
wherein the bridging comprises a plurality of bridge CESs.
18. The method of claim 17 , further comprising minimizing a count of the plurality of bridge CESs.
19. The method of claim 17 , further comprising searching for locations of the plurality of bridge CESs within a geographic region, wherein the geographic region is a subset of a satellite coverage region.