Power allocation method for MIMO transmit beamforming
A transmit power allocation method for computing a transmit beamforming W matrix for a N streams of data, the method has a first step of measuring a receive channel characteristic H matrix, a second step of decomposing the H matrix into a U matrix which is formed from the left eigenvectors of the H matrix, an Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix and re-ordered by strength, and a V T matrix with rows comprising the right eigenvectors of H, such that UΣV T =H. The transmit beamforming W matrix is then formed from the re-ordered V matrix of the previous decomposition. Optional waterfilling methods for a plurality of subcarriers may then be done using either a minimum mean square error, an optimal signal to noise ratio, or any other waterfilling method which optimizes a desired metric, such as signal to noise ratio or minimum mean square error.
1. A method for computing a transmit beamforming W matrix for a plurality M streams of data over N subcarriers, the method comprising:
a first step of measuring a receive channel characteristic H matrix;
a second step of a transmit beamformer decomposing said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, an Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix, and a V T matrix with rows comprising the right eigenvectors of H, such that UΣV T =H;
where said transmit beamforming W matrix is derived from said V matrix by swapping the strongest column of said V matrix with a different column of said V matrix when a first said eigenvalue associated with said strongest column is greater than a second said eigenvalue corresponding to said different column, said V matrix containing at least two non-zero columns.
2. The method of claim 1 where deriving said W matrix includes waterfilling at least one said subcarrier.
3. The method of claim 1 where deriving said W matrix includes waterfilling each subcarrier using a minimum mean square error for each said subcarrier.
4. The method of claim 3 where said waterfilling using a minimum mean square error comprises computing a power contribution for each k subcarriers and each of m streams according to:
ϕ
k
,
m
2
=
(
u
(
v
/
λ
k
,
m
)
1
/
2
-
v
/
λ
k
,
m
)
∑
ϕ
k
,
m
2
=
N
subcarriers
where Nsubcarriers is equal to said N.
5. The method of claim 1 where said transmit beamforming W matrix is derived from said V matrix by sorting said eigenvalues for each said subcarrier.
6. The method of claim 1 where said second step includes selecting the strongest two eigenvalues for each subcarrier and using the columns of V T associated with said strongest two eigenvalues to form said W matrix.
7. A method for forming a beamforming matrix W from a channel characterization matrix H, each said W and said H having a value for each of N subcarriers, the method having the steps:
a first step of a transmit beamformer decomposing, for each said subcarrier, said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, a Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix, and a V T matrix with rows comprising the right eigenvectors of H, such that UΣV T =H;
a second step of sorting said eigenvalues in descending order for each said subcarrier;
a third step of arranging the columns of said V T matrix such that each column associated with a particular eigenvalue is ordered according to the order of said eigenvalues for each said subcarrier;
a fourth step of arranging the relative strength of each subcarrier using a waterpouring subcarrier equalization method.
8. The method of claim 7 where said waterpouring subcarrier equalization method operates over all eigenmodes and subcarriers.
9. The method of claim 7 where said waterpouring subcarrier equalization method is minimum square error constrained by:
Φ m 2 =(μ(ν/λ m ) 1/2 −ν/λ m )
where:
λ m is the m th eigenvalue,
ν is the noise variance,
μ is the waterline and is selected based on the power constraint
∑
ϕ
m
2
=
1.
10. A method for forming a beamforming matrix W from a channel characterization matrix H, each said W and said H having a first stream value and a second stream value for each of N subcarriers, the method having the steps:
a first step of decomposing, for each said subcarrier, said H matrix into a U matrix which is formed from the left eigenvectors of said H matrix, a Σ matrix which is a diagonal matrix formed from the square roots of the eigenvalues of said H matrix and re-ordered by strength, and a V T matrix with rows comprising the right eigenvectors of H, such that UΣV T =H;
a second step of initializing a first accumulator value to the eigenvalue for a first stream, a second accumulator value to the eigenvalue for a second stream, and a subcarrier iteration variable k to a first value;
iterate over all said subcarriers using said variable k, where:
if said first accumulator value is greater than said second accumulator value, swapping said kth columns associated with a first stream and a second stream of said V matrix;
incrementing said k and adding an eigenvalue for a first stream to said first accumulator value, and adding an eigenvalue for a second stream to said second accumulator value;
thereafter waterfilling each subcarrier W matrix value.
11. The method of claim 10 where deriving said W matrix includes waterfilling each subcarrier using a minimum mean square error for each said subcarrier.
12. The method of claim 10 where said waterfilling using a minimum mean square error comprises computing a power contribution for each k subcarriers and each of m streams according to:
ϕ
k
,
m
2
=
(
u
(
v
/
λ
k
,
m
)
1
/
2
-
v
/
λ
k
,
m
)
∑
ϕ
k
,
m
2
=
N
subcarriers
where Nsubcarriers is equal to said N.
13. The method of claim 10 where said transmit beamforming W matrix is derived from said V matrix by sorting said eigenvalues for each said subcarrier.
14. The method of claim 10 where said second step includes selecting the strongest two eigenvalues and using the columns of V T associated with said strongest two eigenvalues to form said W matrix.