Antenna beam forming systems/methods using unconstrained phase response
View Patent ↗Beamforming methods for operating a transceiver including an antenna having a plurality of antenna feed elements include defining a plurality of real valued antenna gain constraint values associated with a plurality of geographic constraint points within a geographic region, and generating complex valued antenna feed element weights that result in complex antenna gain values at the geographic constraint points based on the corresponding real valued antenna gain constraint values. An antenna beam is formed from the antenna to the geographic region using the complex valued antenna feed element weights, and information is transmitted over the antenna beam.
1. A method of operating a transceiver including an antenna having a plurality of antenna feed elements, comprising:
defining a plurality of real valued antenna gain constraint values associated with a plurality of geographic constraint points within a geographic region;
generating complex valued antenna feed element weights that result in complex antenna gain values at the geographic constraint points based on the corresponding real valued antenna gain constraint values;
forming an antenna beam from the antenna to the geographic region using the complex valued antenna feed element weights; and
transmitting information over the antenna beam.
2. The method of claim 1 , wherein the complex antenna gain values at the geographic constraint points having real components that are equal to the corresponding real valued antenna gain constraint values.
3. The method of claim 1 , wherein generating the complex valued antenna feed element weights comprises:
defining a constraint function that relates the real valued antenna gain constraint values to the complex valued antenna feed element weights.
4. The method of claim 3 , further comprising:
forming a cost function that is related to a total received power; and
evaluating the constraint function to find a set of complex valued antenna feed element weights that reduces the cost function.
5. The method of claim 4 , wherein the cost function comprises:
W H Ryw =MIN
wherein w is a vector of M feed element weights, Ry is an M×M covariance matrix for the M feed elements, and MIN is a scalar value.
6. The method of claim 4 , wherein the constraint function comprises:
C H w=f
wherein w is a vector of M feed element weights, C is an M×K constant matrix containing responses of the M feed elements at K constraint points and f is a desired response vector at the K constraint points.
7. The method of claim 4 , wherein evaluating the constraint function to find a set of complex valued antenna feed element weights that reduces the cost function comprises:
forming a combined expression for the constraint function and the cost function using Lagrange multipliers;
differentiating the combined expression with respect to the complex valued antenna feed element weights;
setting the differentiated combined expression equal to zero and obtaining the complex valued antenna feed element weights in terms of the Lagrange multipliers; and
substituting the complex valued antenna feed element weights into the constraint function.
8. The method of claim 1 , further comprising measuring a complex antenna gain value;
transmitting the measured complex antenna gain values to the transceiver; and
adjusting the complex valued antenna feed element weights in response to the measured complex antenna gain value.
9. The method of claim 1 , wherein generating the complex valued antenna feed element weights comprises:
evaluating a cost function that comprises squared differences between real components of the complex antenna gain values and the real valued antenna gain constraint values.
10. The method of claim 9 , wherein the real valued antenna gain constraint values comprise soft constraint values.
11. The method of claim 10 , wherein the cost function comprises:
∑
n
=
1
N
y
n
′
y
n
′
*
+
∑
p
=
1
P
(
Re
{
y
p
″
}
-
f
p
)
2
=
MIN
wherein y′ n denotes composite amplitude response values at N geographic constraint points having zero amplitude antenna gain constraint values, y″ p denotes composite amplitude response values at P geographic constraint points having non-zero amplitude antenna gain constraint values, and f p denotes desired real amplitude components at the P geographic constraint points.
12. The method of claim 11 , further comprising weighting composite amplitude response values to emphasize respective geographic constraint points based on their relative geographic importance.
13. The method of claim 12 , wherein the cost function comprises:
∑
n
=
1
N
c
n
′
y
n
′
y
n
′
*
+
∑
p
=
1
P
c
p
″
(
Re
{
y
p
″
}
-
f
p
)
2
=
MIN
wherein c′ n and c″ n comprise user-defined weighting vectors.
14. The method of claim 9 comprising generating a set of complex antenna feed element weights that reduces the cost function.
15. A transceiver, comprising:
an antenna having a plurality of antenna feed elements; and
an electronics system including a beam former configured to generate complex valued antenna feed element weights that result in complex antenna gain values associated with a plurality of geographic constraint points within a geographic region of the antenna based on corresponding real valued antenna gain constraint values defined for the plurality of geographic constraint points, and to form an antenna beam from the antenna to the geographic region using the complex valued antenna feed element weights.
16. The transceiver of claim 15 , wherein the complex antenna gain values at the geographic constraint points have real components that are equal to the corresponding real valued antenna gain constraint values.
17. The transceiver of claim 15 , wherein the beam former is further configured to evaluate a constraint function that relates the real valued antenna gain constraint values to the complex valued antenna feed element weights.
18. The transceiver of claim 17 , wherein the beam former is further configured to form a cost function that is related to a total received power, and to evaluate the constraint function to find a set of complex valued antenna feed element weights that reduces the cost function.
19. The transceiver of claim 18 , wherein the cost function comprises:
w H Ryw =MIN
wherein w is a vector of M feed element weights, Ry is an M×M covariance matrix for the M feed elements, and MIN is a scalar value.
20. The transceiver of claim 18 , wherein the constraint function comprises:
C H w=f
wherein w is a vector of M feed element weights, C is an M×K constant matrix containing responses of the M feed elements at K constraint points and f is a desired response vector at the K constraint points.
21. The transceiver of claim 18 , wherein the beam former is further configured to evaluate the constraint function to find a set of complex valued antenna feed element weights that reduces the cost function by forming a combined expression for the constraint function and the cost function using Lagrange multipliers, differentiating the combined expression with respect to the complex valued antenna feed element weights, setting the differentiated combined expression equal to zero and obtaining the complex valued antenna feed element weights in terms of the Lagrange multipliers, and substituting the complex valued antenna feed element weights into the constraint function.
22. The transceiver of claim 15 , wherein the beam former is further configured to receive a measured complex antenna gain value to the transceiver, and to adjust the complex valued antenna feed element weights in response to the measured complex antenna gain value.
23. The transceiver of claim 15 , wherein the beam former is configured to generate the complex valued antenna feed element weights by evaluating a cost function that comprises squared differences between real components of the complex antenna gain values and the real valued antenna gain constraint values.
24. The transceiver of claim 23 , wherein the real valued antenna gain constraint values comprise soft constraint values.
25. The transceiver of claim 24 , wherein the cost function comprises:
∑
n
=
1
N
y
n
′
y
n
′
*
+
∑
p
=
1
P
(
Re
{
y
p
″
}
-
f
p
)
2
=
MIN
wherein y′ n denotes composite amplitude response values at N geographic constraint points having zero amplitude antenna gain constraint values, y″ p denotes composite amplitude response values at P geographic constraint points having non-zero amplitude antenna gain constraint values, and f p denotes desired real amplitude components at the P geographic constraint points.
26. The transceiver of claim 25 , wherein the beam former is further configured to weight composite amplitude response values to emphasize respective geographic constraint points based on their relative geographic importance.
27. The transceiver of claim 26 , wherein the cost function comprises:
∑
n
=
1
N
c
n
′
y
n
′
y
n
′
*
+
∑
p
=
1
P
c
p
″
(
Re
{
y
p
″
}
-
f
p
)
2
=
MIN
wherein c′ n and c″ n comprise user-defined weighting vectors.
28. The transceiver of claim 23 , wherein the beam former is configured to generate a set of complex antenna feed element weights that reduces the cost function.
29. A communications satellite, comprising:
an antenna having a plurality of antenna feed elements; and
an electronics system including a beam former configured to generate complex valued antenna feed element weights that result in complex antenna gain values associated with a plurality of geographic constraint points within a geographic region of the antenna based on corresponding real valued antenna gain constraint values defined for the plurality of geographic constraint points, and to form an antenna beam from the antenna to the geographic region using the complex valued antenna feed element weights.
30. A satellite gateway, comprising:
an electronics system including a beam former configured to generate complex valued antenna feed element weights for antenna feed elements of an antenna of a remote satellite that result in complex antenna gain values associated with a plurality of geographic constraint points within a geographic region of the satellite antenna based on corresponding real valued antenna gain constraint values defined for the plurality of geographic constraint points, 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.