Interpolation in channel state feedback
Feedback bandwidth may be reduced in a closed loop MIMO system by Householder transformations, vector quantization using codebooks, and down-sampling in the frequency domain. A column of a beamforming matrix is quantized using a codebook, a Householder reflection is performed on the beamforming matrix to reduce the dimensionality of the beamforming matrix, and the quantizing and performing of Householder reflection on the previously dimensionality reduced beamforming matrix is recursively repeated to obtain a further reduction of dimensionality of the beamforming matrix. These actions are performed for a subset of orthogonal frequency divisional multiplexing (OFDM) carriers, and quantized column vectors for the subset of OFDM carriers are transmitted.
1. A method performed by a wireless station in a closed loop multiple-input-multiple-output (MIMO) wireless network, the method comprising:
quantizing a column of a beamforming matrix using a codebook;
performing a Householder reflection on the beamforming matrix to reduce the dimensionality of the beamforming matrix;
recursively repeating the quantizing and performing of Householder reflection on the previously dimensionality-reduced beamforming matrix in order to obtain a further reduction of dimensionality of the beamforming matrix;
performing the preceding actions for each carrier of a subset of OFDM carriers to obtain quantized column vectors for the subset of OFDM carriers; and
transmitting the quantized column vectors for the subset of OFDM carriers.
2. The method of claim 1 wherein recursively repeating the quantizing results in a plurality of quantized column vectors, and each of the plurality of quantized column vectors is quantized using a different codebook.
3. The method of claim 2 wherein a size of the codebook for each recursion is smaller than a size of a codebook for a previous recursion.
4. The method of claim 1 wherein the beamforming matrix comprises three columns, and recursively repeating the quantizing comprises quantizing a first column using six bits, a second column using five bits, and a third column using four bits.
5. The method of claim 1 wherein the beamforming matrix comprises three columns, and recursively repeating the quantizing comprises quantizing a first column using five bits, a second column using four bits, and a third column using three bits.
6. The method of claim 1 further comprising:
quantizing a small matrix using a codebook having entries that represent small matrices.
7. The method of claim 1 wherein performing a Householder reflection on the beamforming matrix comprises performing the Householder reflection as a function of the column vector.
8. The method of claim 1 wherein performing a Householder reflection on the beamforming matrix comprises performing the Householder reflection as a function of a column vector selected from a codebook.
9. A computer-readable medium having instructions stored thereon that when accessed result in a wireless station in a closed loop multiple-input-multiple-output (MIMO) wireless network performing:
quantizing a column of a beamforming matrix using a codebook;
performing a Householder reflection on the beamforming matrix to reduce the dimensionality of the beamforming matrix;
recursively repeating the quantizing and performing of Householder reflection on the previously dimensionality-reduced beamforming matrix in order to obtain a further reduction of dimensionality of the beamforming matrix;
performing the preceding actions for each carrier of a subset of OFDM carriers to obtain quantized column vectors for the subset of OFDM carriers; and
transmitting the quantized column vectors for the subset of OFDM carriers.
10. The article of claim 9 wherein recursively repeating the quantizing results in a plurality of quantized column vectors, and each of the plurality of quantized column vectors is quantized using a different codebook.
11. The article of claim 10 wherein a size of the codebook for each recursion is smaller than a size of a codebook for a previous recursion.
12. The article of claim 9 wherein the beamforming matrix comprises three columns, and recursively repeating the quantizing comprises quantizing a first column using six bits, a second column using five bits, and a third column using four bits.