Method and device for transmitting/receiving information in closed-loop multi-antenna system
The present invention discloses a method for transmitting information in a closed loop multiple antenna system. The method includes that: a transmission apparatus receives information transmitted from a reception apparatus, wherein the information includes codeword index information; the transmission apparatus selects a corresponding codeword from a double-layer-structure-based codebook according to the codeword index information; the transmission apparatus generates a precoding matrix according to the selected codeword; the transmission apparatus performs precoding for data to be transmitted according to the precoding matrix; the transmission apparatus transmits the precoded data to the reception apparatus. The present invention can enable a formed and used codebook to match channel distribution characteristic of a dual-polarized antenna as much as possible, and minimize performance loss brought by codebook quantization, thereby performance of a precoding system can be effectively improved.
1. A method for transmitting information in a closed-loop multi-antenna system, comprising:
receiving, by a transmitting device, information comprising codeword index information transmitted from a receiving device;
selecting, by the transmitting device, a corresponding codeword from a codebook in a two-stage structure according to the codeword index information;
generating, by the transmitting device, a pre-coding matrix from the selected codeword;
pre-coding, by the transmitting device, data to be transmitted according to the pre-coding matrix; and
transmitting, by the transmitting device, the pre-coded data to the receiving device;
wherein a codeword c n r in the codebook in the two-stage structure satisfies the following relationship:
c
n
r
=
[
Φ
k
r
(
:
,
1
)
⊗
w
m
r
(
:
,
1
)
Φ
k
r
(
:
,
2
)
⊗
w
m
r
(
:
,
2
)
…
Φ
k
r
(
:
,
r
)
⊗
w
m
r
(
:
,
r
)
]
=
[
Φ
k
r
(
1
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
1
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
1
,
r
)
w
m
r
(
:
,
r
)
Φ
k
r
(
2
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
2
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
2
,
r
)
w
m
r
(
:
,
r
)
]
,
wherein Φ k r is a 2×r-dimension matrix, k=0, 1, . . . , K−1, w m r is a N T /2×r-dimension matrix, m=0, 1, . . . , M r −1, r is the number of Ranks, N T is the number of transmitting antennas, X(:,l) represents the l th column of a matrix X, X(l 1 ,l 2 ) represents an element in the l 1 th row and in the l 2 th column of the matrix X, and represents a direct product of matrices; and a set consists of a number K r of Φ k r is a transformation codebook of the codebook in the two-stage structure, and a set consists of a number M r of w m r is a basic codebook of the codebook in the two-stage structure.
2. The method for transmitting information in a closed-loop multi-antenna system according to claim 1 , wherein a column vector of the matrix w m r is a truncated 2 K -DFT vector, and wherein 2 K ≧N T /2 and K is a natural number; and if c n r is a codeword with a unitary characteristic, column vectors of the codeword w m r of the basic codebook, corresponding to mutually non-orthogonal columns of the codeword Φ k r in the transformation codebook, are mutually orthogonal.
3. The method for transmitting information in a closed-loop multi-antenna system according to claim 2 , wherein with N T =8, the matrix Φ k r takes its values selected from all or a part of matrices in Table 1 below or first r columns in all or a part of matrices in Table 2 below, and the matrix w m r takes its values selected from all or a part of matrices in Table 3 below or first r columns in all or a part of matrices in Table 4 below:
Table 1 is:
Rank3 transformation
Rank4 transformation
Index k
codebook Φ k 3
codebook Φ k 4
0
[
1
1
1
1
1
-
1
]
[
1
1
1
1
1
-
1
1
-
1
]
1
[
1
2
0
1
0
2
]
[
1
0
1
0
0
1
0
1
]
,
Table 2 is:
Index
Φ k
0
Φ
0
=
[
1
1
1
1
1
-
1
1
-
1
]
1
Φ
1
=
[
1
1
1
1
-
1
1
-
1
1
]
2
Φ
2
=
[
1
1
1
1
j
-
j
j
-
j
]
3
Φ
3
=
[
1
1
1
1
-
j
j
-
j
j
]
4
Φ
4
=
[
1
1
1
1
1
+
j
2
-
1
+
j
2
1
+
j
2
-
1
+
j
2
]
5
Φ
5
=
[
1
1
1
1
-
1
+
j
2
1
+
j
2
-
1
+
j
2
1
+
j
2
]
6
Φ
6
=
[
1
1
1
1
-
1
+
j
2
1
-
j
2
-
1
+
j
2
1
-
j
2
]
7
Φ
7
=
[
1
1
1
1
1
-
j
2
-
1
+
j
2
1
-
j
2
-
1
+
j
2
]
,
Table 3 is:
Rank3 basic
Rank4 basic
Index
codebook w m 3
codebook w m 4
0
[v 0 v 6 v 6 ]
[v 0 v 0 v 6 v 6 ]
1
[v 1 v 7 v 7 ]
[v 1 v 1 v 7 v 7 ]
2
[v 2 v 0 v 0 ]
[v 2 v 2 v 0 v 0 ]
3
[v 3 v 1 v 1 ]
[v 3 v 3 v 1 v 1 ]
4
[v 4 v 2 v 2 ]
[v 4 v 4 v 2 v 2 ]
5
[v 5 v 3 v 3 ]
[v 5 v 5 v 3 v 3 ]
6
[v 6 v 4 v 4 ]
[v 6 v 6 v 4 v 4 ]
7
[v 7 v 5 v 5 ]
[v 7 v 7 v 5 v 5 ],
and Table 4 is:
Index
w m
0
w 0 = [v 0 v 1 v 2 v 3 ]
1
w 1 = [v 1 v 2 v 3 v 4 ]
2
w 2 = [v 2 v 3 v 4 v 5 ]
3
w 3 = [v 3 v 4 v 5 v 6 ]
4
w 4 = [v 4 v 5 v 6 v 7 ]
5
w 5 = [v 5 v 6 v 7 v 0 ]
6
w 6 = [v 6 v 7 v 0 v 1 ]
7
w 7 = [v 7 v 0 v 1 v 2 ],
wherein:
Index
v n
0
v 0 = [1 1 1 1] T
1
v 1 = [1 (1 − j)/{square root over (2)} −j (−1 − j)/{square root over (2)}] T
2
v 2 = [1 −j −1 j] T
3
v 3 = [1 (−1 − j)/{square root over (2)} j (1 − j)/{square root over (2)}] T
4
v 4 = [1 −1 1 −1] T
5
v 5 = [1 (−1 + j)/{square root over (2)} −j (1 + j)/{square root over (2)}] T
6
v 6 = [1 j −1 −j] T
7
v 7 = [1 (1 + j)/{square root over (2)} j (−1 + j)/{square root over (2)}] T .
4. The method for transmitting information in a closed-loop multi-antenna system according to claim 1 , wherein the codebook in the two-stage structure comprises a codebook resulting from column exchange.
5. A method for receiving information in a closed-loop multi-antenna system, comprising:
receiving, by a receiving device, information transmitted from a transmitting device;
estimating, by the receiving device, channel state information according to the information;
selecting, by the receiving device, a corresponding codeword from a codebook in a two-stage structure according to the channel state information;
generating, by the receiving device, codeword index information of the selected codeword; and
transmitting, by the receiving device, the codeword index information of the codeword to the transmitting device;
wherein a codeword c n r in the codebook in the two-stage structure satisfies the following relationship:
c
n
r
=
[
Φ
k
r
(
:
,
1
)
⊗
w
m
r
(
:
,
1
)
Φ
k
r
(
:
,
2
)
⊗
w
m
r
(
:
,
2
)
…
Φ
k
r
(
:
,
r
)
⊗
w
m
r
(
:
,
r
)
]
=
[
Φ
k
r
(
1
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
1
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
1
,
r
)
w
m
r
(
:
,
r
)
Φ
k
r
(
2
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
2
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
2
,
r
)
w
m
r
(
:
,
r
)
]
,
wherein Φ k r is a 2×r-dimension matrix, k=0, 1, . . . , K−1, w m r is a N T /2×r-dimension matrix, m=0, 1, . . . , M r −1, r is the number of Ranks, N T is the number of transmitting antennas, X(:,l) represents the l th column of a matrix X, X(l 1 ,l 2 ) represents an element in the l 1 th row and in the l 2 th column of the matrix X, and represents a direct product of matrices, and a set consists of a number K r of Φ k r is a transformation codebook of the codebook in the two-stage structure, and a set consists of a number M r of w m r is a basic codebook of the codebook in the two-stage structure.
6. The method for receiving information in a closed-loop multi-antenna system according to claim 5 , wherein a column vector of the matrix w m r is a truncated 2 K -DFT vector, and wherein 2 K ≧N T /2 and K is a natural number; and if c n r is a codeword with a unitary characteristic, column vectors of the codeword w m r of the basic codebook, corresponding to mutually non-orthogonal columns of the codeword Φ k r in the transformation codebook, are mutually orthogonal.
7. The method for receiving information in a closed-loop multi-antenna system according to claim 6 , wherein with N T =8, the matrix Φ k r takes its values selected from all or a part of matrices in Table 1 below or first r columns in all or a part of matrices in Table 2 below, and the matrix w m r takes its values selected from all or a part of matrices in Table 3 below or first r columns in all or a part of matrices in Table 4 below:
Table 1 is:
Rank3 transformation
Rank4 transformation
Index k
codebook Φ k 3
codebook Φ k 4
0
[
1
1
1
1
1
-
1
]
[
1
1
1
1
1
-
1
1
-
1
]
1
[
1
2
0
1
0
2
]
[
1
0
1
0
0
1
0
1
]
,
Table 2 is:
Index
Φ k
0
Φ
0
=
[
1
1
1
1
1
-
1
1
-
1
]
1
Φ
1
=
[
1
1
1
1
-
1
1
-
1
1
]
2
Φ
2
=
[
1
1
1
1
j
-
j
j
-
j
]
3
Φ
3
=
[
1
1
1
1
-
j
j
-
j
j
]
4
Φ
4
=
[
1
1
1
1
1
+
j
2
-
1
+
j
2
1
+
j
2
-
1
+
j
2
]
5
Φ
5
=
[
1
1
1
1
-
1
+
j
2
1
+
j
2
-
1
+
j
2
1
+
j
2
]
6
Φ
6
=
[
1
1
1
1
-
1
+
j
2
1
-
j
2
-
1
+
j
2
1
-
j
2
]
7
Φ
7
=
[
1
1
1
1
1
-
j
2
-
1
+
j
2
1
-
j
2
-
1
+
j
2
]
,
Table 3 is:
Rank3 basic
Rank4 basic
Index
codebook w m 3
codebook w m 4
0
[v 0 v 6 v 6 ]
[v 0 v 0 v 6 v 6 ]
1
[v 1 v 7 v 7 ]
[v 1 v 1 v 7 v 7 ]
2
[v 2 v 0 v 0 ]
[v 2 v 2 v 0 v 0 ]
3
[v 3 v 1 v 1 ]
[v 3 v 3 v 1 v 1 ]
4
[v 4 v 2 v 2 ]
[v 4 v 4 v 2 v 2 ]
5
[v 5 v 3 v 3 ]
[v 5 v 5 v 3 v 3 ]
6
[v 6 v 4 v 4 ]
[v 6 v 6 v 4 v 4 ]
7
[v 7 v 5 v 5 ]
[v 7 v 7 v 5 v 5 ],
and Table 4 is:
Index
w m
0
w 0 = [v 0 v 1 v 2 v 3 ]
1
w 1 = [v 1 v 2 v 3 v 4 ]
2
w 2 = [v 2 v 3 v 4 v 5 ]
3
w 3 = [v 3 v 4 v 5 v 6 ]
4
w 4 = [v 4 v 5 v 6 v 7 ]
5
w 5 = [v 5 v 6 v 7 v 0 ]
6
w 6 = [v 6 v 7 v 0 v 1 ]
7
w 7 = [v 7 v 0 v 1 v 2 ],
wherein:
Index
v n
0
v 0 = [1 1 1 1] T
1
v 1 = [1 (1 − j)/{square root over (2)} −j (−1 − j)/{square root over (2)}] T
2
v 2 = [1 −j −1 j] T
3
v 3 = [1 (−1 − j)/{square root over (2)} j (1 − j)/{square root over (2)}] T
4
v 4 = [1 −1 1 −1] T
5
v 5 = [1 (−1 + j)/{square root over (2)} −j (1 + j)/{square root over (2)}] T
6
v 6 = [1 j −1 −j] T
7
v 7 = [1 (1 + j)/{square root over (2)} j (−1 + j)/{square root over (2)}] T .
8. The method for receiving information in a closed-loop multi-antenna system according to claim 5 , wherein the codebook in the two-stage structure comprises a codebook resulting from column exchange.
9. A transmitting device, comprising a receiving module, a codeword determining module, a pre-coding matrix calculating module, a pre-coding module and a transmitting module, wherein:
the receiving module is configured to receive information comprising codeword index information transmitted from a receiving device;
the codeword determining module is configured to select a corresponding codeword from a codebook in a two-stage structure according to the codeword index information;
the pre-coding matrix calculating module is configured to generate a pre-coding matrix according to the selected codeword;
the pre-coding module is configured to pre-code data to be transmitted according to the pre-coding matrix; and
the transmitting module is configured to transmit the pre-coded data to the receiving device;
wherein a codeword c n r in the codebook in the two-stage structure satisfies the following relationship:
c
n
r
=
[
Φ
k
r
(
:
,
1
)
⊗
w
m
r
(
:
,
1
)
Φ
k
r
(
:
,
2
)
⊗
w
m
r
(
:
,
2
)
…
Φ
k
r
(
:
,
r
)
⊗
w
m
r
(
:
,
r
)
]
=
[
Φ
k
r
(
1
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
1
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
1
,
r
)
w
m
r
(
:
,
r
)
Φ
k
r
(
2
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
2
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
2
,
r
)
w
m
r
(
:
,
r
)
]
,
wherein Φ k r is a 2×r-dimension matrix, k=0, 1, . . . , K r −1, w m r is a N T /2×r-dimension matrix, m=0, 1, . . . , M r −1, r is the number of Ranks, N T is the number of transmitting antennas, X(:,l) represents the l th column of a matrix X, X(l 1 ,l 2 ) represents an element in the l 1 th row and in the l 2 th column of the matrix X, and represents a direct product of matrices, and a set consists of a number K r of Φ k r is a transformation codebook of the codebook in the two-stage structure, and a set consists of a number M r of w m r is a basic codebook of the codebook in the two-stage structure.
10. The transmitting device according to claim 9 , wherein a column vector of the matrix w m r is a truncated 2 K -DFT vector, and wherein 2 K ≧N T /2 and K is a natural number; and if c n r is a codeword with a unitary characteristic, column vectors of the codeword w m r of the basic codebook, corresponding to mutually non-orthogonal columns of the codeword Φ k r in the transformation codebook, are mutually orthogonal.
11. The transmitting device according to claim 10 , wherein with N T =8, the matrix Φ k r takes its values selected from all or a part of matrices in Table 1 below or first r columns in all or a part of matrices in Table 2 below, and the matrix w m r takes its values selected from all or a part of matrices in Table 3 below or first r columns in all or a part of matrices in Table 4 below:
Table 1 is:
Rank3 transformation
Rank4 transformation
Index k
codebook Φ 3 k
codebook Φ 4 k
0
[
1
1
1
1
1
-
1
]
[
1
1
1
1
1
-
1
1
-
1
]
1
[
1
2
0
1
0
2
]
[
1
0
1
0
0
1
0
1
]
,
Table 2 is:
Index
Φ k
0
Φ
0
=
[
1
1
1
1
1
-
1
1
-
1
]
1
Φ
1
=
[
1
1
1
1
-
1
1
-
1
1
]
2
Φ
2
=
[
1
1
1
1
j
-
j
j
-
j
]
3
Φ
3
=
[
1
1
1
1
-
j
j
-
j
j
]
4
Φ
4
=
[
1
1
1
1
1
+
j
2
-
1
+
j
2
1
+
j
2
-
1
+
j
2
]
5
Φ
5
=
[
1
1
1
1
-
1
+
j
2
1
+
j
2
-
1
+
j
2
1
+
j
2
]
6
Φ
6
=
[
1
1
1
1
-
1
+
j
2
1
-
j
2
-
1
+
j
2
1
-
j
2
]
7
Φ
7
=
[
1
1
1
1
1
-
j
2
-
1
+
j
2
1
-
j
2
-
1
+
j
2
]
,
Table 3 is:
Rank3 basic
Rank4 basic
Index
codebook w m 3
codebook w m 4
0
[v 0 v 6 v 6 ]
[v 0 v 0 v 6 v 6 ]
1
[v 1 v 7 v 7 ]
[v 1 v 1 v 7 v 7 ]
2
[v 2 v 0 v 0 ]
[v 2 v 2 v 0 v 0 ]
3
[v 3 v 1 v 1 ]
[v 3 v 3 v 1 v 1 ]
4
[v 4 v 2 v 2 ]
[v 4 v 4 v 2 v 2 ]
5
[v 5 v 3 v 3 ]
[v 5 v 5 v 3 v 3 ]
6
[v 6 v 4 v 4 ]
[v 6 v 6 v 4 v 4 ]
7
[v 7 v 5 v 5 ]
[v 7 v 7 v 5 v 5 ],
and Table 4 is:
Index
w m
0
w 0 = [v 0 v 1 v 2 v 3 ]
1
w 1 = [v 1 v 2 v 3 v 4 ]
2
w 2 = [v 2 v 3 v 4 v 5 ]
3
w 3 = [v 3 v 4 v 5 v 6 ]
4
w 4 = [v 4 v 5 v 6 v 7 ]
5
w 5 = [v 5 v 6 v 7 v 0 ]
6
w 6 = [v 6 v 7 v 0 v 1 ]
7
w 7 = [v 7 v 0 v 1 v 2 ],
wherein:
Index
v n
0
v 0 = [1 1 1 1] T
1
v 1 = [1 (1 − j)/{square root over (2)} −j (−1 − j)/{square root over (2)}] T
2
v 2 = [1 −j −1 j] T
3
v 3 = [1 (−1 − j)/{square root over (2)} j (1 − j)/{square root over (2)}] T
4
v 4 = [1 −1 1 −1] T
5
v 5 = [1 (−1 + j)/{square root over (2)} −j (1 + j)/{square root over (2)}] T
6
v 6 = [1 j −1 −j] T
7
v 7 = [1 (1 + j)/{square root over (2)} j (−1 + j)/{square root over (2)}] T .
12. The transmitting device according to claim 9 , wherein the codebook in the two-stage structure comprises a codebook resulting from column exchange.
13. A receiving device, comprising a receiving module, a channel estimating module, a codeword selecting module, a codeword index information generating module and a transmitting module, wherein:
the receiving module is configured to receive information transmitted from a transmitting device;
the channel estimating module is configured to estimate channel state information according to the information;
the codeword selecting module is configured to select a corresponding codeword from a codebook in a two-stage structure according to the channel state information;
the codeword index information generating module is configured to generate codeword index information of the selected codeword; and
the transmitting module is configured to transmit the codeword index information of the codeword to the transmitting device;
wherein a codeword c n r in the codebook in the two-stage structure satisfies the following relationship:
c
n
r
=
[
Φ
k
r
(
:
,
1
)
⊗
w
m
r
(
:
,
1
)
Φ
k
r
(
:
,
2
)
⊗
w
m
r
(
:
,
2
)
…
Φ
k
r
(
:
,
r
)
⊗
w
m
r
(
:
,
r
)
]
=
[
Φ
k
r
(
1
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
1
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
1
,
r
)
w
m
r
(
:
,
r
)
Φ
k
r
(
2
,
1
)
w
m
r
(
:
,
1
)
Φ
k
r
(
2
,
2
)
w
m
r
(
:
,
2
)
…
Φ
k
r
(
2
,
r
)
w
m
r
(
:
,
r
)
,
]
wherein Φ k r is a 2×r-dimension matrix, k=0, 1, . . . , K r −1, w m r is a N T /2×r-dimension matrix, m=0, 1, . . . , M r −1, r is the number of Ranks, N T is the number of transmitting antennas, X(:,l) represents the l th column of a matrix X, X(l 1 ,l 2 ) represents an element in the l 1 th row and in the l 2 th column of the matrix X, and represents a direct product of matrices, and a set consists of a number K r of Φ k r is a transformation codebook of the codebook in the two-stage structure, and a set consists of a number M r of w m r is a basic codebook of the codebook in the two-stage structure.
14. The receiving device according to claim 13 , wherein a column vector of the matrix w m r is a truncated 2 K -DFT vector, and wherein 2 K ≧N T /2 and K is a natural number; and if c n r is a codeword with a unitary characteristic, column vectors of the codeword w m r of the basic codebook, corresponding to mutually non-orthogonal columns of the codeword Φ k r in the transformation codebook, are mutually orthogonal.
15. The receiving device according to claim 14 , wherein with N T =8 the matrix Φ k r takes its values selected from all or a part of matrices in Table 1 below or first r columns in all or a part of matrices in Table 2 below, and the matrix w m r takes its values selected from all or a part of matrices in Table 3 below or first r columns in all or a part of matrices in Table 4 below:
Table 1 is:
Rank3 transformation
Rank4 transformation
Index k
codebook Φ
codebook Φ
0
[
1
1
1
1
1
-
1
]
[
1
1
1
1
1
-
1
1
-
1
]
1
[
1
2
0
1
0
2
]
[
1
0
1
0
0
1
0
1
]
,
Table 2 is:
Index
Φ k
0
Φ
0
=
[
1
1
1
1
1
-
1
1
-
1
]
1
Φ
1
=
[
1
1
1
1
-
1
1
-
1
1
]
2
Φ
2
=
[
1
1
1
1
j
-
j
j
-
j
]
3
Φ
3
=
[
1
1
1
1
-
j
j
-
j
j
]
4
Φ
4
=
[
1
1
1
1
1
+
j
2
-
1
+
j
2
1
+
j
2
-
1
+
j
2
]
5
Φ
5
=
[
1
1
1
1
-
1
+
j
2
1
+
j
2
-
1
+
j
2
1
+
j
2
]
6
Φ
6
=
[
1
1
1
1
-
1
+
j
2
1
-
j
2
-
1
+
j
2
1
-
j
2
]
7
Φ
7
=
[
1
1
1
1
1
-
j
2
-
1
+
j
2
1
-
j
2
-
1
+
j
2
]
,
Table 3 is:
Rank3 basic
Rank4 basic
Index
codebook w m 3
codebook w m 4
0
[v 0 v 6 v 6 ]
[v 0 v 0 v 6 v 6 ]
1
[v 1 v 7 v 7 ]
[v 1 v 1 v 7 v 7 ]
2
[v 2 v 0 v 0 ]
[v 2 v 2 v 0 v 0 ]
3
[v 3 v 1 v 1 ]
[v 3 v 3 v 1 v 1 ]
4
[v 4 v 2 v 2 ]
[v 4 v 4 v 2 v 2 ]
5
[v 5 v 3 v 3 ]
[v 5 v 5 v 3 v 3 ]
6
[v 6 v 4 v 4 ]
[v 6 v 6 v 4 v 4 ]
7
[v 7 v 5 v 5 ]
[v 7 v 7 v 5 v 5 ],
and Table 4 is:
Index
w m
0
w 0 = [v 0 v 1 v 2 v 3 ]
1
w 1 = [v 1 v 2 v 3 v 4 ]
2
w 2 = [v 2 v 3 v 4 v 5 ]
3
w 3 = [v 3 v 4 v 5 v 6 ]
4
w 4 = [v 4 v 5 v 6 v 7 ]
5
w 5 = [v 5 v 6 v 7 v 0 ]
6
w 6 = [v 6 v 7 v 0 v 1 ]
7
w 7 = [v 7 v 0 v 1 v 2 ],
wherein:
Index
v n
0
v 0 = [1 1 1 1] T
1
v 1 = [1 (1 − j)/{square root over (2)} −j (−1 − j)/{square root over (2)}] T
2
v 2 = [1 −j −1 j] T
3
v 3 = [1 (−1 − j)/{square root over (2)} j (1 − j)/{square root over (2)}] T
4
v 4 = [1 −1 1 −1] T
5
v 5 = [1 (−1 + j)/{square root over (2)} −j (1 + j)/{square root over (2)}] T
6
v 6 = [1 j −1 −j] T
7
v 7 = [1 (1 + j)/{square root over (2)} j (−1 + j)/{square root over (2)}] T .
16. The receiving device according to claim 13 , wherein the codebook in the two-stage structure comprises a codebook resulting from column exchange.