Method and apparatus for singular value decomposition of a channel matrix
First Claim
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 DH matrix such that H=UDHVH using a singular value decomposition (SVD), DH 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 HHH and HHH, 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 DA matrices such that A=QDAQH, DA being a diagonal matrix obtained by SVD on the matrix A; and
(d) calculating the U matrix, the V matrix and the DH matrix from the Q matrix and the DA matrix.
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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=HHH or A=HHH is created. A Jacobi process is cyclically performed on the matrix A to obtain Q and DA matrixes such that A=QDAQH. DA 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 DH matrixes of H matrix are then calculated from the Q and DA matrices. DH is a diagonal matrix comprising singular values of the H matrix.
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Citations
9 Claims
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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 DH matrix such that H=UDHVH using a singular value decomposition (SVD), DH being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the method comprising:
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(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 HHH and HHH, 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 DA matrices such that A=QDAQH, DA being a diagonal matrix obtained by SVD on the matrix A; and
(d) calculating the U matrix, the V matrix and the DH matrix from the Q matrix and the DA matrix. - View Dependent Claims (2, 3, 4)
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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 DH matrix such that H=UDHVH using a singular value decomposition (SVD), DH being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the apparatus comprising:
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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 HHH and HHH, 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 DA matrices such that A=QDAQH, DA being a diagonal matrix obtained by SVD on the A matrix; and
calculate the U matrix, the V matrix and the DH matrix from the Q matrix and the DA matrix. - View Dependent Claims (6, 7, 8)
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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 DH matrix such that H=UDHVH using a singular value decomposition (SVD), DH being a diagonal matrix comprising singular values of the matrix H, the superscript H denoting a Hermitian transpose, the IC comprising:
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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 HHH and HHH, 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 DA matrices such that A=QDAQH, DA being a diagonal matrix obtained by SVD on the A matrix; and
calculate the U matrix, the V matrix and the DH matrix from the Q matrix and the DA matrix.
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Specification