Low complexity beamforming with compressed feedback
A first communication device receives a plurality of training signals from a second communication device via a communication channel. The first communication device determines, based on the plurality of training signals, a channel matrix corresponding to the communication channel, and determines, based the channel matrix and without decomposing a steering matrix, compressed feedback to be provided to the second communication device. The first communication device transmits the compressed feedback to the second communication device to enable the second communication device to steer at least one subsequent transmission to the first communication device.
1. A method for providing beamforming feedback in a communication channel, the method comprising:
receiving, at a first communication device, a plurality of training signals from a second communication device via the communication channel;
determining, at the first communication device based on the plurality of training signals, a channel matrix corresponding to the communication channel;
deriving, at the first communication device, an intermediate matrix from the channel matrix;
determining, at the first communication device based on the channel matrix, compressed feedback to be provided to the second communication device, wherein determining the compressed feedback i) does not include decomposing a steering matrix and ii) includes performing QR decomposition of the intermediate matrix to determine a Q matrix and an R matrix, including, for each of one or more stages of the QR decomposition:
determining norm values corresponding to columns of a sub-matrix to be processed in the stage of the QR decomposition, and
prior to performing QR decomposition of the sub-matrix, sorting columns of the sub-matrix such that a column corresponding to a highest norm value among the determined norm values is the first column of the sub-matrix; and
transmitting the compressed feedback from the first communication device to the second communication device to enable the second communication device to steer at least one subsequent transmission to the first communication device.
2. The method of claim 1 , wherein deriving the intermediate matrix comprises determining a product of the channel matrix and a Hermitian transpose of the channel matrix.
3. The method of claim 1 , wherein deriving the intermediate matrix comprises performing an initial QR decomposition of the channel matrix to obtain an initial Q matrix and an initial R matrix, wherein a conjugate transpose of the intermediate matrix is the initial R matrix.
4. The method of claim 1 , wherein determining norm values for a second stage of the QR decomposition comprises updating norm values previously determined for a first stage of the QR decomposition, wherein the first stage of the QR decomposition is performed prior to the second stage of the QR decomposition.
5. The method of claim 1 , further comprising, for each of one or more stages of the QR decomposition, dynamically scaling elements of a sub-matrix of the R matrix to be processed in the stage of the QR decomposition, including one of i) dynamically scaling the elements based on an absolute value of a largest one of a) real parts and b) imaginary parts of the elements of the sub-matrix such that a leading bit of the absolute value is a logic 1 and ii) dynamically scaling the elements based on a largest norm value among norm values corresponding to columns of the sub-matrix such that a leading bit of the largest norm value is a logic 1.
6. The method of claim 1 , wherein determining the compressed feedback includes performing multiple iterations of QR decomposition, including performing an initial iteration of the multiple iterations on the intermediate matrix.
7. The method of claim 6 , further comprising, for each of one or more iterations of QR decomposition subsequent to the initial iteration of QR decomposition, determining a product of the intermediate matrix and a Q matrix resulting from a previous iteration of QR decomposition, including determining the product by applying QR decomposition directly to a scaled intermediate matrix determined during the previous iteration of QR decomposition.
8. A first communication device, comprising:
a network interface device having one or more integrated circuits configured to
receive a plurality of training signals from a second communication device via a communication channel,
determine, based on the plurality of training signals, a channel matrix corresponding to the communication channel,
derive an intermediate matrix from the channel matrix,
determine, based on the channel matrix, compressed feedback to be provided to the second communication device that represents the steering matrix, wherein determining the compressed feedback i) does not include decomposing a steering matrix and ii) includes performing QR decomposition of the intermediate matrix to determine a Q matrix and an R matrix, the one or more integrated circuits being configured to, for each of one or more stages of the QR decomposition:
determine norm values corresponding to columns of a sub-matrix being processed in the stage of the QR decomposition, and
prior to performing QR decomposition of the sub-matrix, sort columns of the sub-matrix such that a column with a highest norm value among the determined norm values is the first column of the sub-matrix, and
transmit the compressed feedback to the second communication device to enable the second communication device to steer at least one subsequent transmission to the first communication device.
9. The first communication device of claim 8 , wherein the one or more integrated circuits are configured to derive the intermediate matrix at least by determining a product of the channel matrix and a Hermitian transpose of the channel matrix.
10. The first communication device of claim 8 , wherein the one or more integrated circuits are configured to derive the intermediate matrix at least by performing an initial QR decomposition of the channel matrix to obtain an initial Q matrix and an initial R matrix, wherein a conjugate transpose of the intermediate matrix is the initial R matrix.
11. The first communication device of claim 8 , wherein the one or more integrated circuits are configured to determine norm values for a second stage of the QR decomposition at least by updating norm values previously determined for a first stage of the QR decomposition, wherein the first stage of the QR decomposition is performed prior to the second stage of the QR decomposition.
12. The first communication device of claim 8 , wherein the one or more integrated circuits are further configured to, for each of one or more stages of the QR decomposition, dynamically scale elements of a sub-matrix of the R matrix to be processed in the stage of the QR decomposition, including one of i) dynamically scaling the elements based on an absolute value of a largest one of a) real parts and b) imaginary parts of the elements of the sub-matrix such that a leading bit of the absolute value is a logic 1 and ii) dynamically scaling the elements based on a largest norm value among norm values corresponding to columns of the sub-matrix such that a leading bit of the largest norm value is a logic 1.
13. The first communication device of claim 8 , wherein the one or more integrated circuits are configured to determine the compressed feedback at least by performing multiple iterations of QR decomposition, including performing an initial iteration of the multiple iterations on the intermediate matrix.
14. The first communication device of claim 13 , wherein the one or more integrated circuits are further configured to, for each of one or more iterations of QR decomposition subsequent to the initial iteration of QR decomposition, determine a product of the intermediate matrix and a Q matrix resulting from a previous iteration of QR decomposition, including determining the product by applying QR decomposition directly to a scaled intermediate matrix determined during the previous iteration of QR decomposition.
15. A method for providing beamforming feedback in a communication channel, the method comprising:
receiving, at a first communication device, a plurality of training signals from a second communication device via the communication channel;
determining, at the first communication device based on the plurality of training signals, a channel matrix corresponding to the communication channel;
deriving, at the first communication device, an intermediate matrix from the channel matrix;
determining, at the first communication device based on the channel matrix, compressed feedback to be provided to the second communication device, wherein determining the compressed feedback i) does not include decomposing a steering matrix and ii) includes performing QR decomposition of the intermediate matrix to determine a Q matrix and an R matrix, including, for each of one or more stages of the QR decomposition, dynamically scaling elements of a sub-matrix of the R matrix to be processed in the stage of the QR decomposition, including one of i) dynamically scaling the elements based on an absolute value of a largest one of a) real parts and b) imaginary parts of the elements of the sub-matrix such that a leading bit of the absolute value is a logic 1 and ii) dynamically scaling the elements based on a largest norm value among norm values corresponding to columns of the sub-matrix such that a leading bit of the largest norm value is a logic 1, and
transmitting the compressed feedback from the first communication device to the second communication device to enable the second communication device to steer at least one subsequent transmission to the first communication device.
16. A first communication device, comprising:
a network interface device having one or more integrated circuits configured to
receive a plurality of training signals from a second communication device via a communication channel,
determine, based on the plurality of training signals, a channel matrix corresponding to the communication channel,
derive an intermediate matrix from the channel matrix,
determine, based on the channel matrix, compressed feedback to be provided to the second communication device, wherein determining the compressed feedback i) does not include decomposing a steering matrix and ii) includes performing QR decomposition of the intermediate matrix to determine a Q matrix and an R matrix, the one or more integrated circuits being configured to, for each of one or more stages of the QR decomposition, dynamically scale elements of a sub-matrix of the R matrix to be processed in the stage of the QR decomposition, including one of i) dynamically scaling the elements based on an absolute value of a largest one of a) real parts and b) imaginary parts of the elements of the sub-matrix such that a leading bit of the absolute value is a logic 1 and ii) dynamically scaling the elements based on a largest norm value among norm values corresponding to columns of the sub-matrix such that a leading bit of the largest norm value is a logic 1, and
transmit the compressed feedback to the second communication device to enable the second communication device to steer at least one subsequent transmission to the first communication device.