Method and apparatus for sub-sampling of a codebook in LTE-A system
View Patent ↗The embodiments of the present invention disclose a method and an apparatus for sub-sampling of a codebook in the LTE-A system where a precoding matrix W is a product of two matrices W 1 and W 2 , i.e. W=W 1 W 2 , codebooks for W, W 1 and W 2 are denoted as C, C 1 and C 2 respectively, and r indicates a rank. The method includes sub-sampling the codebook C such that the sub-sampled codebook C has a size of equal to or less than 4 bits. In the sub-sampling, codewords evenly distributed in the codebook C are extracted, where some or all of the codewords are in a form of discrete Fourier transform (DFT) vector to be suitable for evenly linear arrays, and the other codewords are suitable for cross-polarized linear arrays.
1. A method for sub-sampling of a codebook in a LTE-A system, the method comprising:
receiving at a base station a precoding matrix W as a product of two matrices W 1 and W 2 , wherein W=W 1 W 2 , and codebooks for W, W 1 and W 2 are denoted as C, C 1 and C 2 respectively, and r indicates a rank;
the base station sub-sampling the codebook C by applying the following equations under the following circumstances such that the sub-sampled codebook C has a size of equal to or less than 4 bits, wherein when the received codebook has an r=1 or 2, C 1 has the size of 4 bits and for a given codeword in C 1 , one codeword in C 2 corresponds;
wherein when the received codebook has a value of r=3 or 4, C 1 has a size of 2 bits and C 2 is subsampled as:
C
2
=
{
1
2
[
Y
1
Y
2
Y
1
-
Y
2
]
}
for
r
=
3
(
Y
1
,
Y
2
)
∈
{
(
e
1
,
[
e
1
,
e
5
]
)
,
(
e
2
,
[
e
2
,
e
6
]
)
,
(
e
3
,
[
e
3
,
e
7
]
)
,
(
e
4
,
[
e
4
,
e
8
]
)
}
;
(
1
)
C
2
=
{
1
2
[
Y
Y
Y
-
Y
]
}
for
r
=
4
Y
∈
{
[
e
1
,
e
5
]
,
[
e
2
,
e
6
]
,
[
e
3
,
e
7
]
,
[
e
4
,
e
8
]
}
;
(
2
)
Yε{[e 1 ,e 5 ],[e 2 ,e 6 ],[e 3 ,e 7 ],[e 4 ,e 8 ]} where e k indicates an 8×1 selection vector for which the k-th element has a value of 1 and the other elements are zero, and the sub-sampled rank 3 codebook and rank 4 codebook have a nesting property; and
wherein when the received codebook has a value of r=1 or 2, and C 2 is sub-sampled to 1 bit, C 1 is sub-sampled to 3 bits, wherein the sub-sampled C 1 is C 1 ={W 1 (0) , W 1 (2) , W 1 (4) , . . . , W 1 (14) } such that
the sampled C 2 is
C
2
=
{
[
e
1
e
1
]
,
[
e
1
j
e
1
]
}
for
r
=
1
,
and
the sampled C 2 is
C
2
=
{
[
e
1
e
1
e
1
-
e
1
]
,
[
e
1
e
1
j
e
1
-
j
e
1
]
}
for
r
=
2.
2. The method of claim 1 , wherein when the received codebook has a value of r=1 or 2, C 1 is sub-sampled to 4 bits, and C 2 is defined as:
the sub-sampled C 2 is
C
2
=
{
[
e
1
e
2
]
}
for
r
=
1
,
and
the sub-sampled C 2 is
C
2
=
{
[
e
1
e
1
e
1
-
e
1
]
}
for
r
=
2
,
wherein e 1 indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and the sub-sampled rank 1 codebook, rank 2 codebook and the corresponding rank 3 code-book and rank 4 codebook have a nesting property.
3. The method of claim 1 , wherein,
when the received codebook has a value of r=1, for a codeword W 1 (4k+l) in C 1 , k=0, 1, 2, 3, l=0, 1, 2, 3,
a codeword
1
2
[
e
1
α
l
e
1
]
in C 2 is extracted to correspond thereto, wherein e 1 indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and α 0 =1, α 1 =j, α 2 =−1 and α 3 =−j; and
when the received codebook has a value of r=2, for a codeword W 1 (2k+l) in C 1 , k=0, 1, . . . , 7, l=0, 1,
a codeword
1
2
[
e
1
e
1
α
l
e
1
-
α
l
e
1
]
in C 2 is extracted to correspond thereto, wherein α 0 =1, α 1 =j.
4. An apparatus for sub-sampling of a codebook in a LTE-A system where a precoding matrix W is a product of two matrices W 1 and W 2 , wherein W=W 1 W 2 , codebooks for W, W 1 and W 2 are denoted as C, C 1 and C 2 respectively, and r indicates a rank, the apparatus comprising:
a processor configured to sub-sample the received codebook C, the received sub-sampled codebook C has a size of equal to or less than 4 bits; and
a receiver configured to receive the sub-sampled codebook C for precoding in an LTE advanced base station and/or user equipment,
wherein when r=1 or 2, C 1 has the size of 4 bits and for a given codeword in C 1 , one codeword in C 2 corresponds thereto;
wherein r=3 or 4 C 1 has a size of 2 bits and the processor sub-samples C 2 as:
C
2
=
{
1
2
[
Y
1
Y
2
Y
1
-
Y
2
]
}
for
r
=
3
(
Y
1
,
Y
2
)
∈
{
(
e
1
,
[
e
1
,
e
5
]
)
,
(
e
2
,
[
e
2
,
e
6
]
)
,
(
e
3
,
[
e
3
,
e
7
]
)
,
(
e
4
,
[
e
4
,
e
8
]
)
}
;
(
1
)
C
2
=
{
1
2
[
Y
Y
Y
-
Y
]
}
for
r
=
4
Y
∈
{
[
e
1
,
e
5
]
,
[
e
2
,
e
6
]
,
[
e
3
,
e
7
]
,
[
e
4
,
e
8
]
}
;
(
2
)
wherein e k indicates an 8×1 selection vector for which the k-th element has a value of 1 and the other elements are zero, and the sub-sampled rank 3 codebook and rank 4 codebook have a nesting property; and
wherein when r=1 or 2, the processor is configured to sub-sample C 1 and C 2 respectively, and C 2 is sub-sampled to 1 bit, C 1 is sub-sampled respectively to 3 bits, wherein the processor sub-samples C 1 as C 1 ={W 1 (0) , W 1 (2) , W 1 (4) , . . . , W 1 (14) } such that the processor samples C 2 as
C
2
=
{
[
e
1
e
1
]
,
[
e
1
j
e
1
]
}
for
r
=
1
,
and the processor samples C 2 as
C
2
=
{
[
e
1
e
1
e
1
-
e
1
]
,
[
e
1
e
1
j
e
1
-
j
e
1
]
}
for
r
=
2.
5. The apparatus of claim 4 , wherein when r=1 or 2, C 1 is sub-sampled to 4 bits, and the processor is configured to define C 2 as:
C
2
=
{
[
e
1
e
1
]
}
for
r
=
1
,
and
C
2
=
{
[
e
1
e
1
e
1
-
e
1
]
}
for
r
=
2
,
wherein e 1 indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and the sub-sampled rank 1 codebook, rank 2 codebook and the corresponding rank 3 code book and rank 4 codebook have a nesting property.
6. The apparatus of claim 4 , wherein
when r=1, for a codeword W 1 (4k+l) in C 1 , k=0, 1, 2, 3, l=0, 1, 2, 3,
the processor extracts a codeword
1
2
[
e
1
α
l
e
1
]
in C 2 to correspond thereto, wherein e 1 indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and α 0 =1, α 1 =j, α 2 =−1 and α 3 =−j; and
when r=2, for a codeword W 2 (2k+l) in C 1 , k=0, 1, . . . , 7, l=0, 1, the processor extracts a codeword
1
2
[
e
1
e
1
α
l
e
1
-
α
l
e
1
]
in C 2 to correspond thereto, wherein α 0 =1, α 1 =j.