Methods and apparatus for sub-block based architecture of cholesky decomposition and channel whitening
View Patent ↗Methods and apparatus for sub-block based architecture of Cholesky decomposition and channel whitening. In an exemplary embodiment, an apparatus is provided that parallel processes sub-block matrices (R 00 , R 10 , and R 11 ) of a covariance matrix (R) to determine a whitening coefficient matrix (W). The apparatus includes a first LDL coefficient calculator that calculates a first whitening matrix W 00 , lower triangle matrix L 00 , and diagonal matrix D 00 from the sub-block matrix R 00 , a first matrix calculator that calculates a lower triangle matrix L 10 from the sub-block matrix R 10 and the matrices L 00 and D 00 , and a second matrix calculator that calculates a matrix X from the matrices D 00 and L 10 . The apparatus also includes a matrix subtractor that calculates a matrix Z from the matrix X and the sub-block matrix R 11 , a second LDL coefficient calculator that calculates a third whitening matrix W 11 , lower triangle matrix L 11 , and a diagonal matrix D 11 from the matrix Z, and a third matrix calculator that calculates a second whitening matrix W 10 from the matrices L 00 , L 10 , L 11 , and D 11 .
1. A method operable by a transceiver at a base station coupling to a communications network for parallel processing sub-block matrices (R 00 , R 10 , and R 11 ) of a covariance matrix (R) to determine a whitening coefficient matrix (W), the transceiver configured to include a whitening coefficient calculator (WCC), the method comprising:
calculating a first whitening matrix W 00 , lower triangle matrix L 00 , and diagonal matrix D 00 from the sub-block matrix R 00 ,
calculating a lower triangle matrix L 10 from the sub-block matrix R 10 and the matrices L 00 and D 00 ;
calculating a matrix X from the matrices D 00 and L 10 ;
calculating a matrix Z from the matrix X and the sub-block matrix R 11 ;
calculating a third whitening matrix W 11 , lower triangle matrix L 11 , and a diagonal matrix D 11 from the matrix Z; and
calculating a second whitening matrix W 10 from the matrices L 00 , L 10 , L 11 , and D 11 .
2. The method of claim 1 , wherein each of the operations of calculating the first whitening matrix and calculating the second whitening matrix comprise receiving a Hermitian input matrix and calculating elements associated with selected diagonal, lower triangle, and whitening matrices.
3. The method of claim 1 , wherein each of the operations of calculating the first whitening matrix and calculating the second whitening matrix comprises calculating diagonal (d 00 , d 11 ) of selected diagonal matrix and a triangle matrix (l 10 ) of a select lower triangle matrix according to:
d
00
=
r
00
d
11
=
r
11
-
r
10
2
r
00
=
r
11
-
(
r
10
·
Re
*
r
10
·
Re
+
r
10
·
Im
*
r
10
·
Im
r
00
)
l
10
=
r
10
r
00
=
r
10
·
Re
+
jr
10
·
Im
r
00
4. The method of claim 1 , wherein each of the operations of calculating the first whitening matrix and calculating the second whitening matrix comprises calculating diagonal (d 00 , d 11 ) of selected diagonal matrix and a triangle matrix (l 10 ) of a select lower triangle matrix according to:
d
00
=
r
00
l
10
=
r
10
·
Re
r
00
+
j
r
10
·
Im
r
00
d
11
=
r
11
-
(
r
10
·
Re
r
00
*
r
10
·
Re
+
r
10
·
Im
r
00
*
r
10
·
Im
)
5. The method of claim 1 , wherein each of the means for calculating the first whitening matrix and the means for calculating the second whitening matrix comprises calculating (W 00 , W 10 , W 11 ) of a selected whitening matrix according to:
W 00 =1/sqrt( d 00 )
W 01 =0
W 10 =−l 10 /sqrt( d 11 )
W 11 =1/sqrt( d 11 ).
6. An apparatus that parallel processes sub-block matrices (R 00 , R 10 , and R 11 ) of a covariance matrix (R) to determine a whitening coefficient matrix (W), the apparatus comprising:
a first lower triangle matrix and diagonal matrix (LDL, coefficient calculator that calculates a first whitening matrix W 00 , lower triangle matrix L 00 , and diagonal matrix D 00 from the sub-block matrix R 00 ;
a first matrix calculator that calculates a lower triangle matrix L 10 from the sub-block matrix R 10 and the matrices L 00 and D 00 ;
a second matrix calculator that calculates a matrix X from the matrices D 00 and L 10 ;
a matrix subtractor that calculates a matrix Z from the matrix X and the sub-block matrix R 11 ;
a second LDL coefficient calculator that calculates a third whitening matrix W 11 , lower triangle matrix L 11 , and a diagonal matrix D 11 from the matrix Z; and
a third matrix calculator that calculates a second whitening matrix W 10 from the matrices L 00 , L 10 , L 11 , and D 11 .
7. The apparatus of claim 6 , further comprising an output combiner that combines the first, second, and third whitening matrices to form a whitening coefficient matrix that is output.
8. The apparatus of claim 6 , wherein the first matrix calculator comprises an inverter and a multiplier, and wherein the inverter received the matrices L00 and D00 and determines an output matrix from (D 00 L 00 H ) −1 and the multiplier multiples the output matrix with the sub-block matrix R 10 to calculate L 10 .
9. The apparatus of claim 6 , wherein the second matrix calculator calculates the matrix X from (L 10 D 00 L 10 H ).
10. The apparatus of claim 6 , wherein the matrix subtractor subtracts the matrix X from the sub-block matrix R 11 to determine the matrix Z.
11. The apparatus of claim 6 , wherein the third matrix calculator calculates W 10 from −D 11 −1/2 (L 11 −1 L 10 L 00 −1 ).
12. The apparatus of claim 6 , wherein each of the first and second LDL coefficient calculators is configured to receive a Hermitian input matrix and calculate elements associated with selected diagonal, lower triangle, and whitening matrices.
13. The apparatus of claim 12 , wherein each of the LDL coefficient calculators comprises a calculator that includes five multipliers, two adders and one function that calculate diagonal (d 00 , d 11 ) of the selected diagonal matrix and a triangle matrix (i 10.RE , i 10.IM ) of the select lower triangle matrix according to:
d
00
=
r
00
d
11
=
r
11
-
r
10
2
r
00
=
r
11
-
(
r
10
·
Re
*
r
10
·
Re
+
r
10
·
Im
*
r
10
·
Im
r
00
)
I
10
=
r
10
r
00
=
r
10
·
Re
+
fr
10
·
Im
r
00
14. The apparatus of claim 12 , wherein each of the LDL coefficient calculators comprises a calculator that includes four multipliers, two adders and one function that calculate diagonal (d 00 , d 11 ) of the selected diagonal matrix and a triangle matrix (i 10.RE , i 10.IM ) of the select lower triangle matrix according to:
d
00
=
r
00
l
10
=
r
10
·
Re
r
00
+
j
r
10
·
Im
r
00
d
11
=
r
11
-
(
r
10
·
Re
r
00
*
r
10
·
Re
+
r
10
·
Im
r
00
*
r
10
·
Im
)
15. The apparatus of claim 12 , wherein each of the LDL coefficient calculators comprises a coefficient calculator that includes two multipliers and two functions that calculate (W 00.Re , W 10.Re , W 10.im , W 11.Re ) of selected whitening matrix according to:
W 00 =1/sqrt( d 00 )
W 01 =0
W 10 =−l 10 /sqrt( d 11 )
W 11 =1/sqrt( d 11 )
where (d 00 , d 11 ) is diagonal matrix and (l 10 ) is a triangle matrix.
16. An apparatus that parallel processes sub-block matrices (R 00 , R 10 , and R 11 ) of a covariance matrix (R) to determine a whitening coefficient matrix (W), the apparatus comprising:
means for calculating a first whitening matrix W 00 , lower triangle matrix L 00 , and diagonal matrix D 00 from the sub-block matrix R 00 ;
means for calculating a lower triangle matrix L 10 from the sub-block matrix R 10 and the matrices L 00 and D 00 ;
means for calculating a matrix X from the matrices D 00 and L 10 ;
means for calculating a matrix Z from the matrix X and the sub-block matrix R 11 ;
means for calculating a third whitening matrix W 11 , lower triangle matrix L 11 , and a diagonal matrix D 11 from the matrix Z; and
means for calculating a second whitening matrix W 10 from the matrices L 00 , L 10 , L 11 , and D 11 .
17. The apparatus of claim 16 , wherein each of the means for calculating the first whitening matrix and the means for calculating the second whitening matrix is configured to receive a Hermitian input matrix and calculate elements associated with selected diagonal, lower triangle, and whitening matrices.
18. The apparatus of claim 16 , wherein each of the means for calculating the first whitening matrix and the means for calculating the second whitening matrix comprises a that includes five multipliers, two adders and one function that calculate diagonal (d 00 , d 11 ) of the selected diagonal matrix and a triangle matrix (i 10.RE , i 10.IM ) of the select lower triangle matrix according to:
d
00
=
r
00
d
11
=
r
11
-
r
10
2
r
00
=
r
11
-
(
r
10
·
Re
*
r
10
·
Re
+
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10
·
Im
*
r
10
·
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r
00
)
l
10
=
r
10
r
00
=
r
10
·
Re
+
jr
10
·
Im
r
00
19. The apparatus of claim 16 , wherein each of the means for calculating the first whitening matrix and the means for calculating the second whitening matrix comprises a calculator that includes four multipliers, two adders and one function that calculate diagonal (d 00 , d 11 ) of the selected diagonal matrix and a triangle matrix (i 10.RE , i 10.IM ) of the select lower triangle matrix according to:
d
00
=
r
00
l
10
=
r
10
·
Re
r
00
+
j
r
10
·
Im
r
00
d
11
=
r
11
-
(
r
10
·
Re
r
00
*
r
10
·
Re
+
r
10
·
Im
r
00
*
r
10
·
Im
)
20. The apparatus of claim 16 , wherein each of the means for calculating the first whitening matrix and the means for calculating the second whitening matrix comprises a coefficient calculator that includes two multipliers and two functions that calculate (W 00 , W 10 , W 11 ) of selected whitening matrix according to:
W 00 =1/sqrt( d 00 )
W 01 =0
W 10 =−l 10 /sqrt( d 11 )
W 11 =1/sqrt( d 11 )
where (d 00 , d 11 ) is diagonal matrix and (l 10 ) is a triangle matrix.