Iterative antenna beam forming systems/methods

• US 8,193,975 B2
• Filed: 10/22/2009
• Issued: 06/05/2012
• Est. Priority Date: 11/12/2008
• Status: Active Grant

• Current Assignee: ATC Technology Corporation (FedEx Corporation)
• Original Assignee: ATC Technology Corporation (FedEx Corporation)
• Inventors: Zheng, Dunmin
• Primary Examiner(s): Issing, Gregory C
• Application Number:
  US12/603,911
• Publication Number:
  US 20100117903A1
• Time in Patent Office: 957 Days
• Field of Search: 342/354, 342/377
• US Class Current: 342/354
• CPC Class Codes: H01Q 3/2605 Array of radiating elements provided with a feedback control over the element weights, e.g. adaptive arrays
• CPC Class Codes: H04B 7/0617 for beam forming
• CPC Class Codes: H04B 7/086 using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming

Abstract

Methods of operating a transceiver including an antenna having a plurality of antenna feed elements are presented. The methods include defining a plurality of antenna gain constraint values g_k associated with K geographic constraint points within a geographic region, iteratively generating M antenna feed element weights w_M that result in antenna response values f_K at the K geographic constraint points based on the corresponding antenna gain constraint values g_K, forming an antenna beam from the antenna to the geographic region using the antenna feed element weights w_M, and communicating information over the antenna beam. Related transceivers, satellites, and satellite gateways are also disclosed.

Claims

1. A method of operating a transceiver including an antenna having a plurality of antenna feed elements, the method comprising:

defining a plurality of antenna gain constraint values g_k associated with K geographic constraint points within a geographic region;

iteratively generating M antenna feed element weights w_M in an antenna feed element weight vector wε

C<sup>M×

1</sup> that result in antenna response values f_K at the K geographic constraint points such that beam gain response values |f_k| converge on the corresponding antenna gain constraint values g_K;

forming an antenna beam from the antenna to the geographic region using the antenna feed element weights w_M; and

communicating information over the antenna beam;

wherein iteratively generating the antenna feed element weight vector w comprises;

defining a cost function that relates the antenna beam gain constraint values g_K to the antenna feed element weights w_M;

specifying an initial vector w¹ of the antenna feed element weights w_M;

evaluating the cost function using the initial vector w¹ of the antenna feed element weights w_M;

generating a gradient of the cost function, and

iteratively modifying the antenna feed element weight vector w and evaluating the cost function using the antenna feed element weight vector w while the value of the cost function is decreasing, wherein iteratively modifying the antenna feed element weight vector w comprises adjusting the antenna feed element weight vector w in the direction of the gradient of the cost function.

2. The method of claim 1, further comprising iteratively generating the M antenna feed element weights w_M that result in antenna response values f_K at the K geographic constraint points based on the corresponding antenna gain constraint values g_K until the antenna feed element weights w_M converge.

3. The method of claim 1, further comprising selecting a vector of the antenna feed element weights in response to the value of the cost function converging.

4. The method of claim 1 further comprising selecting a vector of the antenna feed element weights in response to the value of the cost function no longer decreasing in response to modifying the antenna weights.

5. The method of claim 1, wherein the initial weight vector comprises a conjugate of a beam steering center.

6. The method of claim 1, wherein adjusting the antenna weights comprises adjusting the weights by a fixed step size in the direction of the gradient of the cost function.

7. The method of claim 1, wherein the cost function comprises a sum of squared differences between the antenna gain constraint values g_k and the antenna response values f_k at the K geographic constraint points.

8. The method of claim 7, further comprising weighting the squared differences between the antenna gain constraint values g_k and the antenna response values f_k using weighting factors.

9. The method of claim 1, wherein iteratively modifying the antenna weights comprises adjusting the weights by a weight shift vector Δ

w.

10. The method of claim 9, further comprising generating the weight shift vector Δ

w based on a set of linearized equations representing the antenna response values f_k at the K geographic constraint points.

11. The method of claim 10, further comprising:

generating a residual error vector in terms of the weight shift vector Δ

w;

generating a matrix Q that represents partial derivatives of the K antenna beam gain responses with respect to the M feed element weights in response to the residual error vector;

forming a vector Δ

g that represents differences between the actual and desired beam gain responses at each of the K locations of interest;

evaluating the cost function using the matrix Q and the vector Δ

g to form a set of linear equations that relate the vector Δ

g to the weight shift vector Δ

w; and

solving the set of linear equations to find the weight shift vector Δ

w.

12. The method of claim 11, wherein the cost function comprises a sum of squared differences between the antenna gain constraint values g_k and the antenna response values f_k at the K geographic constraint points.

13. The method of claim 12, further comprising weighting the squared differences between the antenna gain constraint values g_k and the antenna response values f_k using weighting factors.

14. A transceiver, comprising:

an antenna having a plurality of antenna feed elements; and

an electronics system including a beam former configured to iteratively generate M antenna feed element weights w_M in an antenna feed element weight vector wε

C<sup>M×

1</sup> that result in antenna response values f_K at K geographic constraint points based on corresponding antenna gain constraint values g_K, and to form an antenna beam from the antenna to the geographic region using the antenna feed element weights;

wherein the beam former is further configured to define a cost function that relates the beam gain constraint values g_K to the antenna feed element weights w_M, to specify an initial vector w¹ of the antenna feed element weights w_M, to evaluate the cost function using the initial vector w¹ of the antenna feed element weights w_M, to iteratively modify the antenna feed element weight vector w and evaluate the cost function using the antenna feed element weight vector w while the value of the cost function is decreasing such that beam gain response values |f_k| converge towards the beam gain constraint values g_k; and

wherein the beam former is further configured to generate a gradient of the cost function and to adjust the antenna feed element weight vector w in the direction of the gradient of the cost function.

15. The transceiver of claim 14, wherein the beam former is configured to iteratively generate M antenna feed element weights w_M that result in antenna response values f_K at K geographic constraint points based on corresponding antenna gain constraint values g_K until the antenna feed element weights w_M converge.

16. The transceiver of claim 14, wherein the beam former is further configured to select a vector of the antenna feed element weights in response to the value of the cost function converging.

17. The transceiver of claim 14, wherein the beam former is further configured to select a vector of the antenna feed element weights in response to the value of the cost function no longer decreasing in response to modifying the antenna weights.

18. The transceiver of claim 14, wherein the initial weight vector comprises a conjugate of a beam steering center.

19. The transceiver of claim 14, wherein the beam former is further configured adjust the antenna weights by a fixed step size in the direction of the gradient of the cost function.

20. The transceiver of claim 14, wherein the cost function comprises a sum of squared differences between the antenna gain constraint values g_k and the antenna response values f_k at the K geographic constraint points.

21. The transceiver of claim 20, wherein the beam former is further configured to weight the squared differences between the antenna gain constraint values g_k and the antenna response values f_k using weighting factors.

22. The transceiver of claim 14, wherein the beam former is further configured to modify the antenna weights by adjusting the weights by a weight shift vector Δ

w.

23. The transceiver of claim 22, wherein the beam former is further configured to generate the weight shift vector Δ

w based on a set of linearized equations representing the antenna response values f_k at the K geographic constraint points.

24. The transceiver of claim 23, wherein the beam former is further configured to:

generate a residual error vector in terms of the weight shift vector Δ

w;

generate a matrix Q that represents partial derivatives of the K antenna beam gain responses with respect to the M feed element weights in response to the residual error vector;

form a vector Δ

g that represents differences between the actual and desired beam gain responses at each of the K locations of interest;

evaluate the cost function using the matrix Q and the vector Δ

g to form a set of linear equations that relate the vector Δ

g to the weight shift vector Δ

w; and

solve the set of linear equations to find the weight shift vector Δ

w.

25. The transceiver of claim 24, wherein the cost function comprises a sum of squared differences between the antenna gain constraint values g_k and the antenna response values f_k at the K geographic constraint points.

26. The transceiver of claim 25, wherein the beam former is further configured to weight the squared differences between the antenna gain constraint values g_k and the antenna response values f_k using weighting factors.

27. A communications satellite, comprising:

an antenna having a plurality of antenna feed elements; and

an electronics system including a beam former configured to iteratively generate M antenna feed element weights w_M in an antenna feed element weight vector wε

C<sup>M×

1</sup> that result in antenna response values f_K at K geographic constraint points based on corresponding antenna gain constraint values g_K, and to form an antenna beam from the antenna to the geographic region using the antenna feed element weights;

wherein the beam former is further configured to define a cost function that relates the beam gain constraint values g_K to the antenna feed element weights w_M, to specify an initial vector w¹ of the antenna feed element weights w_M, to evaluate the cost function using the initial vector w¹ of the antenna feed element weights w_M, to iteratively modify the antenna feed element weight vector w and evaluate the cost function using the antenna feed element weight vector w while the value of the cost function is decreasing such that beam gain response values |f_k| converge towards the beam gain constraint values g_k; and

wherein the beam former is further configured to generate a gradient of the cost function and to adjust the antenna feed element weight vector w in the direction of the gradient of the cost function.

28. A satellite gateway, comprising:

an electronics system including a beam former configured to iteratively generate M antenna feed element weights w_M in an antenna feed element weight vector wε

C<sup>M×

1</sup> for antenna feed elements of an antenna of a remote satellite that result in antenna response values f_K at K geographic constraint points based on corresponding antenna gain constraint values g_K, and to transmit the complex valued antenna feed element weights to the satellite for use in forming an antenna beam from the satellite antenna to the geographic region; and

wherein the beam former is further configured to define a cost function that relates the beam gain constraint values g_K to the antenna feed element weights w_M, to specify an initial vector w¹ of the antenna feed element weights w_M, to evaluate the cost function using the initial vector w¹ of the antenna feed element weights w_M, to iteratively modify the antenna feed element weight vector w and evaluate the cost function using the antenna feed element weight vector w while the value of the cost function is decreasing such that beam gain response values |f_k| converge towards the beam gain constraint values g_k; and

wherein the beam former is further configured to generate a gradient of the cost function and to adjust the antenna feed element weight vector w in the direction of the gradient of the cost function.