Recursive reduction of channel state feedback
A method and a system that multiplies a beamforming matrix by a unitary matrix that does not change the subspace of the beamforming matrix for form a converted matrix having a lower left triangle of zeros. A first column vector having a fewest number of elements of the converted matrix is quantized using a codebook and represented by a first codebook index. A Householder matrix is determined from the quantized first column vector and the converted matrix is multiplied by the Householder matrix. Quantizing, determining a Householder matrix from further column vectors of the converted matrix using a codebook and representing each respective column vector by further corresponding codebook index, and multiplying the converted matrix on the left by the determined Householder matrix for each respective column vector are recursively repeated. The first codebook index and further codebook indices are transmitted to a remote station for use in beamforming.
1. A method, comprising:
receiving a plurality of codebook indices from a remote station having a plurality of antennas, the plurality of codebook indices representing a plurality of quantized column vectors of the same dimensionality, each quantized column vector corresponding to a column of a beamforming matrix, each column of the beamforming matrix being quantized by the remote station in an ordered sequence from a left-most column vector of the beamforming matrix to a right-most column vector of the beamforming matrix;
determining a Householder matrix from a quantized column vector of the plurality of quantized column vectors corresponding to the right-most column vector of the beamforming matrix, the determining a Householder matrix comprising:
indexing into a codebook using one of the plurality of codebook indices to yield a quantized column vector; and
calculating the Householder matrix as a function of the quantized column vector; and
recursively determining a Householder matrix for a next quantized column vector of the plurality of quantized column vectors to generate a beamforming matrix, the next quantized column vector for each recursive determination of the Householder matrix corresponding to a column vector of the beamforming matrix being immediately to the left of the column vector corresponding to the most recently determined Householder matrix.
2. The method of claim 1 , wherein determining a Householder matrix further comprises indexing into a different codebook with each of the plurality of codebook indices.
3. The method of claim 1 , wherein determining a Householder matrix further comprises indexing into the same codebook with each of the plurality of codebook indices.
4. The method of claim 1 , wherein recursively determining yields a matrix with a lower left triangle of zeros.
5. An electronic system, comprising:
N antennas;
a processor coupled to the N antennas; and
a physical radio interface (PHY) operable to receive a plurality of codebook indices representing a plurality of quantized column vectors of the same dimensionality, each quantized column vector corresponding to a column of a beamforming matrix, each column of the beamforming matrix being quantized by the remote station in an ordered sequence from a left-most column vector of the beamforming matrix to a right-most column vector of the beamforming matrix, the physical radio interface further operable to determine a Householder matrix from a quantized column vector of the plurality of quantized column vectors corresponding to the right-most column vector of the beamforming matrix, the determining a Householder matrix comprising indexing into a codebook using the plurality of codebook indices to yield the plurality of quantized column vectors, and calculating the Householder matrix as a function of the plurality of quantized column vectors, and operable to recursively determine a Householder matrix for a next quantized column vector of the plurality of quantized column vectors to generate a beamforming matrix, the next quantized column vector for each recursive determination of the Householder matrix corresponding to a column vector of the beamforming matrix being immediately to the left of the column vector corresponding to the most recently determined Householder matrix.
6. The electronic system of claim 5 , wherein the dimensionality of the plurality of quantized column vectors is equal to n−k+1, wherein n is the number of rows in the beamforming matrix, and k is a number of spatial channels.