Method and system for utilizing givens rotation expressions for asymmetric beamforming matrices in explicit feedback information
View Patent ↗Aspects of a method and system for utilizing Givens rotation expressions for asymmetric beamforming matrices in explicit feedback information are presented. In one aspect of the invention, Givens matrices may be utilized to reduce a quantity of information communicated in explicit feedback information via an uplink RF channel. The explicit feedback information may include specifications for a feedback beamforming matrix that may be utilized when transmitting signals via a corresponding downlink RF channel. The feedback beamforming matrix may represent a rotated version of an un-rotated matrix. The Givens matrices may be utilized to apply one or more Givens rotations to un-rotated matrix. The feedback beamforming matrix may be computed based on a matrix product of a plurality of Givens matrices. The feedback beamforming matrix may be encoded utilizing fewer bits than may be required to encode the un-rotated matrix.
1. A method for processing signals in a MIMO communication system, the method comprising:
in a transmitter in the MIMO communication system:
receiving feedback information from a receiver in said MIMO communication system via an uplink RF channel, the feedback information including feedback angles representing a beamforming matrix computed by the receiver for a downlink RF channel, the feedback angles including at least one phase shift angle and at least one Givens rotation angle;
reconstructing the beamforming matrix using the feedback angles; and
utilizing the beamforming matrix for communications with the receiver on the downlink RF channel.
2. The method of claim 1 , wherein said at least one phase shift angle represents a phase shift of the beamforming matrix such that elements in an i th column of a residual matrix produced from phase shifting the beamforming matrix are represented by at least one real number.
3. The method of claim 2 , wherein said at least one phase shift angle further represents a phase shift of the residual matrix such that, based on said at least one Givens rotation angle, a value of an element in an I th row and in said i th column of a subsequent residual matrix is equal to 0.
4. The method of claim 3 , wherein said Givens rotation angle represents a Givens (l, i) matrix:
wherein a value of an element in an l th row and in said l th column is equal to cos(ψ ij );
wherein a value of an element in said l th row and in said i th column is equal to −sin(ψ li );
wherein a value of an element in said i th row and in said l th column is equal to sin(ψ li );
wherein a value of an element in said i th row and in said i th column is equal to cos(ψ li );
wherein cos( ) represents a cosine trigonometric function, sin( ) represents a sine trigonometric function, and ψ li represents said Givens rotation angle based on said one or both of said I and said i.
5. The method of claim 4 , wherein said feedback information further includes one or both of an additional Givens rotation angle and an additional phase shift angle.
6. The method of claim 5 , wherein said additional phase shift angle represents a phase shift of the subsequent residual matrix such that elements in an m th column of an additional residual matrix are represented by at least one real number.
7. The method of claim 6 , wherein said additional Givens rotation angle represents a rotation of said additional residual matrix such that a value of an element in an nth row and in said m th column is equal to 0.
8. The method of claim 7 , wherein said additional Givens rotation utilizes a Givens (n, m) matrix:
wherein a value of an element in an n th row and in said n th column is equal to cos(ψ nm );
wherein a value of an element in an nth row and in said m th column is equal to −sin(ψ nm );
wherein a value of an element in an m th row and in said n th column is equal to sin(ψ nm );
wherein a value of an element in an m th row and in said m th column is equal to cos(ψ nm )
wherein cos( ) represents a cosine trigonometric function, sin( ) represents a sine trigonometric function, and ψ nm represents a value for said additional Givens rotation angle based on said one or both of said n and said m.
9. The method of claim 1 , wherein said reconstructing further includes:
using an order of said feedback angles to determine an order of multiplications performed to reconstruct the beamforming matrix.
10. The method of claim 1 , wherein said feedback angles are vectors representing values for each subcarrier on the downlink RF channel.
11. A transmitter for use in a MIMO communication system, the transmitter comprising:
a processor, wherein:
said processor is operable to receive feedback information from a receiver in said MIMO communication system via an uplink RF channel, the feedback information including feedback angles representing a beamforming matrix computed by the receiver for a downlink RF channel, the feedback angles including at least one phase shift angle and at least one Givens rotation angle;
said processor is operable to reconstruct the beamforming matrix using the feedback angles; and
said processor is operable to enable the beamforming matrix to be utilized for communications with the receiver on the downlink RF channel.
12. The transmitter of claim 11 , wherein said at least one phase shift angle represents a phase shift of the beamforming matrix such that elements in an i th column of a residual matrix produced from phase shifting the beamforming matrix are represented by at least one real number.
13. The transmitter of claim 12 , wherein said at least one phase shift angle further represents a phase shift of the residual matrix such that, based on said at least one Givens rotation angle, a value of an element in an I th row and in said i th column of a subsequent residual matrix is equal to 0.
14. The transmitter of claim 13 , wherein said Givens rotation angle represents a Givens (l, i) matrix:
wherein a value of an element in an l th row and in said l th column is equal to cos(ψ ij )
wherein a value of an element in said l th row and in said i th column is equal to −sin(ψ li );
wherein a value of an element in said i th row and in said l th column is equal to sin(ψ ij );
wherein a value of an element in said i th row and in said i th column is equal to cos(ψ li );
wherein cos( ) represents a cosine trigonometric function, sin( ) represents a sine trigonometric function, and ψ li represents said Givens rotation angle based on said one or both of said I and said i.
15. The transmitter of claim 14 , wherein said feedback information further includes one or both of an additional Givens rotation angle and an additional phase shift angle.
16. The transmitter of claim 15 , wherein said additional phase shift angle represents a phase shift of the subsequent residual matrix such that elements in an m th column of an additional residual matrix are represented by at least one real number.
17. The transmitter of claim 16 , wherein said additional Givens rotation angle represents a rotation of said additional residual matrix such that a value of an element in an nth row and in said m th column is equal to 0.
18. The transmitter of claim 17 , wherein said additional Givens rotation utilizes a Givens (n, m) matrix:
wherein a value of an element in an n th row and in said n th column is equal to cos(ψ nm );
wherein a value of an element in an nth row and in said m th column is equal to −sin(ψ nm );
wherein a value of an element in an m th row and in said n th column is equal to sin(ψ nm );
wherein a value of an element in an m th row and in said m th column is equal to cos(ψ nm )
wherein cos( ) represents a cosine trigonometric function, sin( ) represents a sine trigonometric function, and ψ nm represents a value for said additional Givens rotation angle based on said one or both of said n and said m.
19. The transmitter of claim 11 , wherein said processor is further operable to use an order of said feedback angles to determine an order of multiplications to be performed to reconstruct the beamforming matrix.
20. The transmitter of claim 11 , wherein said feedback angles are vectors representing values for each subcarrier on the downlink RF channel.