Low complexity beamforming with compressed feedback

1. A method for providing beamforming information in a communication channel, the method comprising:

calculating, at a first communication device, an initial matrix from an estimate of the communication channel;

performing, at the first communication device, a matrix decomposition of the initial matrix to decompose the initial matrix into a plurality of decomposition matrices, wherein performing the matrix decomposition comprises determining angles for rotation operations performed on the initial matrix as part of decomposing the initial matrix, and wherein determining angles for rotation operations performed on the initial matrix comprises:

determining first angles for first rotation operations performed on rows of the initial matrix as part of performing the matrix decomposition, and

determining second angles for second rotation operations performed on columns of the initial matrix as part of performing the matrix decomposition;

determining, at the first communication device, compressed feedback using the angles that were determined as part of decomposing the initial matrix into the plurality of decomposition matrices, including using i) the first angles that were determined as part of decomposing the initial matrix into the beamforming steering matrix, and ii) the second angles that were determined as part of decomposing the initial matrix into the beamforming steering matrix, wherein the compressed feedback is a compressed representation of a beamforming steering matrix corresponding to the estimate of the communication; and

transmitting, by the first communication device, the compressed feedback to a second communication device to enable the second communication device to beamform at least one subsequent transmission to the first communication device.

2. The method of claim 1 , wherein:

the first angles are determined as phase rotations performed on rows of different submatrices of the initial matrix to transform elements of columns of the submatrices to positive real numbers; and

the second angles are determined to correspond to Givens rotations performed on columns of the different submatrices to transform elements of columns of the submatrices to zero.

3. The method of claim 1 , further comprising:

determining, at the first communication device, a channel estimate matrix H corresponding to the estimate of the communication channel; and

calculating, at the first communication device, the initial matrix using H.

4. The method of claim 3 , wherein determining the initial matrix comprises determining a product of H and a Hermitian transpose of H.

5. The method of claim 3 , further comprising:

receiving, at the first communication device, a plurality of training signals from the second communication device via the communication channel; and

determining, at the first communication device, the estimate of the communication channel based on receiving the plurality of training signals.

6. The method of claim 1 , wherein:

performing the matrix decomposition of the initial matrix comprises performing multiple iterations of a matrix decomposition algorithm, the multiple iterations including a last occurring iteration;

each iteration of the matrix decomposition algorithm includes determining a respective set of angles for rotation operations performed on a corresponding matrix during the iteration; and

determining the compressed feedback includes using the set of angles that were determined as part of the last occurring iteration.

7. The method of claim 1 , wherein decomposing the initial matrix comprises performing QR decomposition of the initial matrix to determine an orthogonal Q matrix and an upper triangular R matrix.

8. The method of claim 1 , wherein the matrix decomposition of the initial matrix is performed so that a product of the plurality of decomposition matrices equals the initial matrix.

9. The method of claim 1 , wherein performing the matrix decomposition of the initial matrix comprises:

determining norm values corresponding to columns of submatrices of the initial matrix; and

sorting columns of the submatrices using the norm values.

10. A first communication device, comprising:

a network interface device having one or more integrated circuits (ICs) configured to:

calculate an initial matrix from an estimate of a communication channel,

perform a matrix decomposition of the initial matrix to decompose the initial matrix into a plurality of decomposition matrices, wherein performing the matrix decomposition comprises determining angles for rotation operations performed on the initial matrix as part of decomposing the initial matrix, and wherein determining angles for rotation operations performed on the initial matrix comprises:

determining first angles for first rotation operations performed on rows of the initial matrix as part of performing the matrix decomposition, and

determining second angles for second rotation operations performed on columns of the initial matrix as part of performing the matrix decomposition;

wherein the one or more ICs are further configured to:

determine compressed feedback using the angles that were determined as part of decomposing the initial matrix into the plurality of decomposition matrices, including using i) the first angles that were determined as part of decomposing the initial matrix into the beamforming steering matrix, and ii) the second angles that were determined as part of decomposing the initial matrix into the beamforming steering matrix, wherein the compressed feedback is a compressed representation of a beamforming steering matrix corresponding to the estimate of the communication channel; and

wherein the one or more ICs are further configured to: transmit the compressed feedback to a second communication device to enable the second communication device to beamform at least one subsequent transmission to the first communication device.

11. The first communication device of claim 10 , wherein the one or more ICs are further configured to:

determine the first angles as phase rotations performed on rows of different submatrices of the initial matrix to transform elements of columns of the submatrices to positive real numbers; and

determine the second angles to correspond to Givens rotations performed on columns of the different submatrices to transform elements of columns of the submatrices to zero.

12. The first communication device of claim 10 , wherein the one or more ICs are further configured to:

determining, at the first communication device, a channel estimate matrix H corresponding to the estimate of the communication channel; and

calculating, at the first communication device, the initial matrix using H.

13. The first communication device of claim 12 , wherein the one or more ICs are further configured to:

determine the initial matrix as a product of H and a Hermitian transpose of H.

14. The first communication device of claim 12 , wherein the one or more ICs are further configured to:

receive a plurality of training signals from the second communication device via the communication channel; and

determine the estimate of the communication channel based on receiving the plurality of training signals.

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

the one or more ICs are further configured to perform the matrix decomposition of the initial matrix by performing multiple iterations of a matrix decomposition algorithm, the multiple iterations including a last occurring iteration;

each iteration of the matrix decomposition algorithm includes determining a respective set of angles for rotation operations performed on a corresponding matrix during the iteration; and

the one or more ICs are further configured to determine the compressed feedback using the set of angles that were determined as part of the last occurring iteration.

16. The first communication device of claim 10 , wherein the one or more ICs are further configured to decompose the initial matrix by performing a QR decomposition of the initial matrix to determine an orthogonal Q matrix and an upper triangular R matrix.

17. The first communication device of claim 10 , wherein the one or more ICs are further configured to perform the matrix decomposition of the initial matrix so that a product of the plurality of decomposition matrices equals the initial matrix.

18. The first communication device of claim 10 , wherein the one or more ICs are further configured to, as part of performing the matrix decomposition of the initial matrix:

determine norm values corresponding to columns of submatrices of the initial matrix; and

sort columns of the submatrices using the norm values.

19. The first communication device of claim 10 , wherein the network interface device comprises one or more wireless transceivers implemented on the one or more ICs.

20. The first communication device of claim 19 , further comprising:

one or more antennas coupled to the one or more transceivers.