Efficient feedback of channel information in a closed loop beamforming wireless communication system

1. A method for feeding back transmitter beamforming information from a receiving wireless communication device to a transmitting wireless communication device, the method comprising:

the receiving wireless communication device receiving a preamble sequence from the transmitting wireless device;

the receiving wireless device estimating a channel response based upon the preamble sequence;

the receiving wireless device determining an estimated transmitter beamforming unitary matrix (V) based upon the channel response and a receiver beamforming unitary matrix (U);

the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information; and

the receiving wireless device wirelessly sending the transmitter beamforming information to the transmitting wireless device.

2. The method of claim 1 wherein the receiving wireless device determining an estimated transmitter beamforming unitary matrix (V) based upon the channel response and a receiver beamforming unitary matrix (U) comprises:

the receiving wireless device producing the estimated transmitter beamforming unitary matrix (V) in Cartesian coordinates; and

the receiving wireless device converting the estimated transmitter beamforming unitary matrix (V) to polar coordinates.

3. The method of claim 1 wherein the channel response (H), estimated transmitter beamforming unitary matrix (V), and the receiver beamforming unitary matrix (U) are related by the equation:

H=UDV*

where, D is a diagonal matrix.

4. The method of claim 3 , wherein the receiving wireless device determining an estimated transmitter beamforming unitary matrix (V) based upon the channel response and a receiver beamforming unitary matrix (U) comprises performing a Singular Value Decomposition (SVD) operation.

5. The method of claim 1 , wherein the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information comprises the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) using a QR decomposition technique.

6. The method of claim 5 , wherein the QR decomposition technique comprises a Givens Rotation operation performed according to the equation:

V

=

∏

i

=

1

M

⁢

⁢

[

D

i

⁡

(

1

i

-

1

⁢

ⅇ

j

⁢

⁢

ϕ

ii

⁢

⁢

…

⁢

⁢

ⅇ

j

⁢

⁢

ϕ

iN

)

⁢

∏

j

=

i

N

-

1

⁢

⁢

G

j

⁡

(

ψ

i

,

j

)

]

×

I

~

N

×

M

Where:

D i is an N×N diagonal matrix with diagonal components in arguments;

I N×M is an N×M identity matrix, where (I) ii =1 for i=1, . . . , min(M,N); and

wherein the transmitter beamforming information includes angles corresponding to elements of the diagonal matrix D and elements of the Givens Rotation, wherein N is a number of transmit antennas, M is a number of receive antennas, and wherein i and j are each integers.

7. The method of claim 1 , wherein:

the transmitting wireless device transmits on N antennas; and

the receiving wireless device receives on M antennas.

8. The method of claim 1 , wherein at least one of the transmitting wireless device and the receiving wireless device supports Multiple Input Multiple Output (MIMO) operations.

9. A wireless communication device comprising:

a plurality of Radio Frequency (RF) components operable to receive an RF signal and to convert the RF signal to a baseband signal; and

a baseband processing module operable to:

receive a preamble sequence carried by the baseband signal;

estimate a channel response based upon the preamble sequence;

determine an estimated transmitter beamforming unitary matrix (V) based upon the channel response and a receiver beamforming unitary matrix (U);

decompose the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information; and

form a baseband signal employed by the plurality of RF components to wirelessly send the transmitter beamforming information to the transmitting wireless device.

10. The wireless communication device of claim 9 , wherein in determining an estimated transmitter beamforming unitary matrix (V) based upon the channel response and a receiver beamforming unitary matrix (U), the baseband processing module is operable to:

produce the estimated transmitter beamforming unitary matrix (V) in Cartesian coordinates; and

convert the estimated transmitter beamforming unitary matrix (V) to polar coordinates.

11. The wireless communication device of claim 9 , wherein the channel response (H), estimated transmitter beamforming unitary matrix (V), and the receiver beamforming unitary matrix (U) are related by the equation:

H=UDV*

where, D is a diagonal matrix.

12. The wireless communication device of claim 9 , wherein in determining the estimated transmitter beamforming unitary matrix (V) based upon the channel response and the receiver beamforming unitary matrix (U), the baseband processing module performs Singular Value Decomposition (SVD) operations.

13. The wireless communication device of claim 9 , wherein in decomposing the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information, the baseband processing module decomposes the estimated transmitter beamforming unitary matrix (V) using a QR decomposition technique.

14. The wireless communication device of claim 13 , wherein the QR decomposition technique comprises a Givens Rotation operation performed according to the equation:

V

=

∏

i

=

1

M

⁢

⁢

[

D

i

⁡

(

1

i

-

1

⁢

ⅇ

j

⁢

⁢

ϕ

ii

⁢

⁢

…

⁢

⁢

ⅇ

j

⁢

⁢

ϕ

iN

)

⁢

∏

j

=

i

N

-

1

⁢

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G

j

⁡

(

ψ

i

,

j

)

]

×

I

~

N

×

M

Where:

D i is an N×N diagonal matrix with diagonal components in arguments;

I N×M is an N×M identity matrix, where (I) ii =1 for i=1, . . . , min(M,N); and

wherein the transmitter beamforming information includes angles corresponding to elements of the diagonal matrix D and elements of the Givens Rotation, wherein N is a number of transmit antennas, M is a number of receive antennas, and wherein i and j are each integers.

15. The wireless communication device of claim 10 , wherein:

the transmitting wireless device transmits on N antennas; and

the wireless communication device includes M antennas.

16. The wireless communication device of claim 10 , wherein the wireless communication device supports Multiple Input Multiple Output (MIMO) operations.

17. A method for feeding back transmitter beamforming information from a receiving wireless communication device to a transmitting wireless communication device, the method comprising:

the receiving wireless communication device receiving a preamble sequence from the transmitting wireless device;

the receiving wireless device estimating a channel response based upon the preamble sequence;

the receiving wireless device decomposing the channel response based upon the channel response and a receiver beamforming unitary matrix (U) to produce an estimated transmitter beamforming unitary matrix (V);

the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information; and

the receiving wireless device wirelessly sending the transmitter beamforming information to the transmitting wireless device.

18. The method of claim 17 , wherein the receiving wireless device decomposing the channel response based upon the channel response and a receiver beamforming unitary matrix (U) to produce an estimated transmitter beamforming unitary matrix (V) includes performing a Singular Value Decomposition (SVD) operation.

19. The method of claim 17 , wherein the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) to produce the transmitter beamforming information comprises the receiving wireless device decomposing the estimated transmitter beamforming unitary matrix (V) using a Givens Rotation operation performed according to the equation:

V

=

∏

i

=

1

M

⁢

⁢

[

D

i

⁡

(

1

i

-

1

⁢

ⅇ

j

⁢

⁢

ϕ

ii

⁢

⁢

…

⁢

⁢

ⅇ

j

⁢

⁢

ϕ

iN

)

⁢

∏

j

=

i

N

-

1

⁢

⁢

G

j

⁡

(

ψ

i

,

j

)

]

×

I

~

N

×

M

Where:

D i is an N×N diagonal matrix with diagonal components in arguments;

I N×M is an N×M identity matrix, where (I) ii =1 for i=1, . . . , min(M,N); and

wherein the transmitter beamforming information includes angles corresponding to elements of the diagonal matrix D and elements of the Givens Rotation, wherein N is a number of transmit antennas, M is a number of receive antennas, and wherein i and j are each integers.

20. The method of claim 19 , wherein the transmitter beamforming information comprises element values of the diagonal matrix D and element values of the Givens Rotation matrix.