Method and apparatus for singular value decomposition of a channel matrix

• US 20060245513A1
• Filed: 03/29/2006
• Published: 11/02/2006
• Est. Priority Date: 04/01/2005
• Status: Active Grant

• Current Assignee: Interdigital Technology Corporation (InterDigital, Inc.)
• Original Assignee: Interdigital Technology Corporation (InterDigital, Inc.)
• Inventors: Olesen, Robert Lind, Koo, Chang-Soo
• Granted Patent: US 7,602,855 B2
• Time in Patent Office: Days
• US Class Current: 375/267
• CPC Class Codes: G06F 17/16 Matrix or vector computation , e.g. matrix-matrix or matrix-vector multiplication, matrix factorization matrix transposition G06F7/78
• CPC Class Codes: H04B 7/0408 using two or more beams, i.e. beam diversity
• CPC Class Codes: H04B 7/0417 Feedback systems
• CPC Class Codes: H04B 7/0617 for beam forming
• CPC Class Codes: H04B 7/0634 Antenna weights or vector/matrix coefficients
• CPC Class Codes: H04B 7/0663 using vector or matrix manipulations
• CPC Class Codes: H04L 25/0204 of multiple channels
• CPC Class Codes: H04L 25/0248 Eigen-space methods
• CPC Class Codes: H04L 27/2647 Arrangements specific to the receiver only equalisation H04L27/01

Abstract

A method and apparatus for decomposing a channel matrix in a wireless communication system are disclosed. A channel matrix H is generated for channels between transmit antennas and receive antennas. A Hermitian matrix A=H^HH or A=HH^H is created. A Jacobi process is cyclically performed on the matrix A to obtain Q and D_A matrixes such that A=QD_AQ^H. D_A is a diagonal matrix obtained by singular value decomposition (SVD) on the A matrix. In each Jacobi transformation, real part diagonalization is performed to annihilate real parts of off-diagonal elements of the matrix and imaginary part diagonalization is performed to annihilate imaginary parts of off-diagonal elements of the matrix after the real part diagonalization. U, V and D_H matrixes of H matrix are then calculated from the Q and D_A matrices. D_H is a diagonal matrix comprising singular values of the H matrix.

Claims

1. In a wireless communication system including a transmitter having a plurality of transmit antennas and a receiver having a plurality of receive antennas, a method of decomposing a channel matrix H into a U matrix, a V matrix and a D_H matrix such that H=UD_HV^H using a singular value decomposition (SVD), D_H being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the method comprising:

(a) generating a channel matrix H for channels between the transmit antennas and the receive antennas;

(b) creating a Hermitian matrix A, the matrix A being defined as one of H^HH and HH^H, depending on the dimensions of the channel matrix H;

(c) cyclically performing at least one sweep of a Jacobi process on the matrix A to obtain Q and D_A matrices such that A=QD_AQ^H, D_A being a diagonal matrix obtained by SVD on the matrix A; and

(d) calculating the U matrix, the V matrix and the D_H matrix from the Q matrix and the D_A matrix.

2. The method of claim 1 wherein the step (c) comprises:

(c1) selecting a 2×

2 matrix

$\mathrm{symW}=<br><br>\begin{array}{cc}{a}_{\mathrm{ii}}& a_{\mathrm{ij}}\\ a_{\mathrm{ji}}& a_{\mathrm{jj}}\end{array}<br><br>$

 

from the matrix A for Jacobi transformation;

(c2) performing real part diagonalization to annihilate real parts of off-diagonal elements of the matrix symW; and

(c3) performing imaginary part diagonalization to annihilate imaginary parts of off-diagonal elements of the matrix symW after the real part diagonalization to generate a diagonal matrix D_A; and

(c4) combining transformation matrices for the real part diagonalization and imaginary part diagonalization to calculate the Q matrix.

3. The method of claim 2 further comprising:

at each sweep of the Jacobi process, calculating a square sum of off-diagonal elements of a matrix obtained at each sweep of the Jacobi process;

comparing the square sum with a threshold; and

performing a next step of Jacobi transformation only if the square sum is greater than the threshold.

4. The method of claim 3 wherein the threshold is a machine dependent small number.

5. In a wireless communication system including a transmitter having a plurality of transmit antennas and a receiver having a plurality of receive antennas, an apparatus for decomposing a channel matrix H into a U matrix, a V matrix and a D_H matrix such that H=UD_HV^H using a singular value decomposition (SVD), D_H being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the apparatus comprising:

a channel estimator for generating a channel matrix H for channels between the transmit antennas and the receive antennas; and

a matrix decomposition and channel correlation matrix unit configured to create a Hermitian matrix A, the matrix A being defined as one of H^HH and HH^H, depending on the dimensions of the channel matrix H;

cyclically perform at least one sweep of a Jacobi process on the matrix A to obtain Q and D_A matrices such that A=QD_AQ^H, D_A being a diagonal matrix obtained by SVD on the A matrix; and

calculate the U matrix, the V matrix and the D_H matrix from the Q matrix and the D_A matrix.

6. The apparatus of claim 5 wherein the matrix decomposition and channel correlation matrix unit is configured to, during each Jacobi transformation of one sweep the matrix decomposition and channel correlation matrix unit, select a 2×

2 matrix

$\mathrm{symW}=<br><br>\begin{array}{cc}{a}_{\mathrm{ii}}& a_{\mathrm{ij}}\\ a_{\mathrm{ji}}& a_{\mathrm{jj}}\end{array}<br><br>$

from the matrix A for Jacobi transformation;

perform real part diagonalization to annihilate real parts of off-diagonal elements of the matrix symW;

perform imaginary part diagonalization to annihilate imaginary parts of off-diagonal elements of the matrix symW after the real part diagonalization to generate a diagonal matrix D_A; and

combine transformation matrices for the real part diagonalization and imaginary part diagonalization to calculate the Q matrix.

7. The apparatus of claim 6 wherein the matrix decomposition and channel correlation matrix unit, at each sweep of the Jacobi process, is configured to calculate a square sum of off-diagonal elements of a matrix obtained at each sweep of the Jacobi process, compare the square sum with a threshold and perform a next step of Jacobi transformation only if the square sum is greater than the threshold.

8. The apparatus of claim 6 wherein the threshold is a machine dependent small number.

9. In a wireless communication system including a transmitter having a plurality of transmit antennas and a receiver having a plurality of receive antennas, an integrated circuit (IC) for decomposing a channel matrix H into a U matrix, a V matrix and a D_H matrix such that H=UD_HV^H using a singular value decomposition (SVD), D_H being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the IC comprising:

a channel estimator for generating a channel matrix H for channels between the transmit antennas and the receive antennas; and

a matrix decomposition and channel correlation matrix unit configured to create a Hermitian matrix A, the matrix A being defined as one of H^HH and HH^H, depending on the dimensions of the channel matrix H;

cyclically perform at least one sweep of a Jacobi process on the matrix A to obtain Q and D_A matrices such that A=QD_AQ^H, D_A being a diagonal matrix obtained by SVD on the A matrix; and

calculate the U matrix, the V matrix and the D_H matrix from the Q matrix and the D_A matrix.