Method for transmitting 4-antenna precoding matrix, user equipment and base station

1. A method, comprising:

determining a rank used for indicating a number of transmission layers;

determining a first precoding matrix in a codebook set corresponding to the rank, wherein precoding matrices comprised in the codebook set are represented by a first codebook index and a second codebook index;

determining a second precoding matrix indicator (PMI) for indicating the first precoding matrix, wherein the second PMI and the second codebook index have a first correspondence, and for a given first codebook index, a value range of the second codebook index corresponding to a value range of the second PMI is a proper subset of a value range of the second codebook index; and

sending the second PMI used for indicating the first precoding matrix to a base station, wherein:

the precoding matrices (W) comprised in the codebook set satisfy the following equation:

W=W 1 ×W 2 , wherein

W

1

=

[

X

n

0

0

X

n

]

,

X

n

=

[

1

1

1

1

q

1

n

q

1

n

+

8

q

1

n

+

16

q

1

n

+

24

]

,

q 1 =e j2π/32 , and n=0, 1, . . . , 15;

wherein the first codebook index corresponds to one value of n, and a value range of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; and

wherein when the rank is determined to be 2, in precoding matrix sets that are determined according to the first codebook index and the second codebook index corresponding to the value range of the second PMI, a first precoding matrix set corresponding to a first codebook index i 1,a and a second precoding matrix set corresponding to a first codebook index i 1,a+8 are mutually exclusive, wherein the first codebook index i 1,a represents a first codebook index corresponding to n whose value is a, the first codebook index i 1,a+8 represents a first codebook index corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

2. The method according to claim 1 , wherein when the rank is determined to be 1, W 2 satisfies the following equation:

W

2

∈

{

1

A

⁡

[

Y

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

α

⁢

⁢

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

}

,

wherein Yε{e 1 ,e 2 ,e 3 ,e 4 }, α(i)=q 1 2(i-1) ; when Y is e 1 , α(i) is α(1); when Y is e 2 , α(i) is α(2); when Y is e 3 , α(i) is α(3); when Y is e 4 , α(i) is α(4); wherein e i represents a column vector with a dimension of 4×1, wherein an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein A is a constant.

3. The method according to claim 2 , wherein when the rank is determined to be 2, W 2 satisfies the following equation:

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

,

(

e

1

,

e

2

)

,

(

e

2

,

e

3

)

,

(

e

1

,

e

4

)

,

(

e

2

,

e

4

)

}

;

⁢

or

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

-

Y

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

2

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

2

-

Y

1

]

,

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

3

)

,

(

e

2

,

e

4

)

,

(

e

3

,

e

1

)

,

(

e

4

,

e

2

)

}

wherein e i represents a column vector with a dimension of 4×1, an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein B is a constant.

4. The method according to claim 3 , wherein when the rank is determined to be 2, mutual relationships between the second PMI, the first codebook index, and the second codebook index are determined according to Table F1 or F2:

TABLE F1

I PMI2

i 1

i 2

0-3

0-7 

2 × I PMI2

8-15

2 × I PMI2 + 1

TABLE F2

I PMI2

i 1

i 2

0-3

0-7

2 × I PMI2

8-15

2 × I PMI2 + 8

wherein I PMI2 represents the second PMI, i 1 represents the first codebook index, and i 2 represents the second codebook index.

5. The method according to claim 1 , wherein when the rank is determined to be 3 or 4, the precoding matrices comprised in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G

Codebook

RI

Index

u n

1

2

3

4

0

u 0 = [1 −1 −1 −1] T

W 0 {1}

W 0 {14} /{square root over (2)}

W 0 {124} /{square root over (3)}

W 0 {1234} /2

1

u 1 = [1 −j 1 j] T

W 1 {1}

W 1 {12} /{square root over (2)}

W 1 {123} /{square root over (3)}

W 1 {1234} /2

2

u 2 = [1 1 −1 1] T

W 2 {1}

W 2 {12} /{square root over (2)}

W 2 {123} /{square root over (3)}

W 2 { 3214} /2

3

u 3 = [1 j 1 −j] T

W 3 {1}

W 3 {12} /{square root over (2)}

W 3 {123} /{square root over (3)}

W 3 { 3214} /2

4

u 4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}] T

W 4 {1}

W 4 {14} /{square root over (2)}

W 4 {124} /{square root over (3)}

W 4 {1234} /2

5

u 5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}] T

W 5 {1}

W 5 {14} /{square root over (2)}

W 5 {124} /{square root over (3)}

W 5 {1234} /2

6

u 6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}] T

W 6 {1}

W 6 {13} /{square root over (2)}

W 6 {134} /{square root over (3)}

W 6 {1324} /2

7

u 7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}] T

W 7 {1}

W 7 {13} /{square root over (2)}

W 7 {134} /{square root over (3)}

W 7 {1324} /2

8

u 8 = [1 −1 1 1] T

W 8 {1}

W 8 {12} /{square root over (2)}

W 8 {124} /{square root over (3)}

W 8 {1234} /2

9

u 9 = [1 −j −1 −j] T

W 9 {1}

W 9 {14} /{square root over (2)}

W 9 {134} /{square root over (3)}

W 9 {1234} /2

10

u 10 = [1 1 1 −1] T

W 10 {1}

W 10 {13} /{square root over (2)}

W 10 {123} /{square root over (3)}

W 10 {1324} /2

11

u 11 = [1 j −1 j] T

W 11 {1}

W 11 {13} /{square root over (2)}

W 11 {134} /{square root over (3)}

W 11 {1324} /2

12

u 12 = [1 −1 −1 1] T

W 12 {1}

W 12 {12} /{square root over (2)}

W 12 {123} /{square root over (3)}

W 12 {1234} /2

13

u 13 = [1 −1 1 −1] T

W 13 {1}

W 13 {13} /{square root over (2)}

W 13 {123} /{square root over (3)}

W 13 {1324} /2

14

u 14 = [1 1 −1 −1] T

W 14 {1}

W 14 {13} /{square root over (2)}

W 14 {123} /{square root over (3)}

W 14 { 3214} /2

15

u 15 = [1 1 1 1] T

W 15 {1}

W 15 {12} /{square root over (2)}

W 15 {123} /{square root over (3)}

W 15 {1234} /2

wherein W n {s} represents a matrix formed by a column set {s} of a matrix W n =I−2u n u n H /u n H u n , and I is a 4×4 identity matrix.

6. A method, comprising:

receiving a second precoding matrix indicator PMI, a first codebook index, and a rank used for indicating a number of transmission layers that are sent by a user equipment; and

determining a first precoding matrix in a codebook set corresponding to the rank according to the second PMI and the first codebook index, wherein precoding matrices comprised in the codebook set are represented by the first codebook index and a second codebook index, the second PMI and the second codebook index have a first correspondence, and for a given first codebook index, a value range of the second codebook index corresponding to a value range of the second PMI is a proper subset of a value range of the second codebook index;

wherein the precoding matrices W comprised in the codebook set satisfy the following equation:

W=W 1 ×W 2 , wherein

W

1

=

[

X

n

0

0

X

n

]

,

X

n

=

[

1

1

1

1

q

1

n

q

1

n

+

8

q

1

n

+

16

q

1

n

+

24

]

,

q 1 =e j2π/32 , and n=0, 1, . . . , 15;

wherein the first codebook index corresponds to one value of n, and a value range of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; and

wherein when the received rank is 2, in precoding matrix sets that are determined according to the first codebook index and the second codebook index corresponding to the value range of the second PMI, a first precoding matrix set corresponding to a first codebook index i 1,a and a second precoding matrix set corresponding to a first codebook index i 1,a+8 are mutually exclusive, wherein the first codebook index i 1,a represents a first codebook index corresponding to n whose value is a, and the first codebook index i 1,a+8 represents a first codebook index corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

7. The method according to claim 6 , wherein the received rank is 1, and W 2 satisfies the following equation:

W

2

∈

{

1

A

⁡

[

Y

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

α

⁢

⁢

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

}

,

wherein Yε{e 1 ,e 2 ,e 3 ,e 4 }, α(i)=q 1 2(i-1) ; when Y is e 1 , α(i) is α(1); when Y is e 2 , α(i) is α(2); when Y is e 3 , α(i) is α(3); when Y is e 4 , α(i) is α(4); wherein e i represents a column vector with a dimension of 4×1, wherein an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein A is a constant.

8. The method according to claim 7 , wherein the received rank is 2, and W 2 satisfies the following equation:

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

,

(

e

1

,

e

2

)

,

(

e

2

,

e

3

)

,

(

e

1

,

e

4

)

,

(

e

2

,

e

4

)

}

;

⁢

or

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

-

Y

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

2

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

2

-

Y

1

]

,

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

3

)

,

(

e

2

,

e

4

)

,

(

e

3

,

e

1

)

,

(

e

4

,

e

2

)

}

wherein e i represents a column vector with a dimension of 4×1, an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; B is a constant.

9. The method according to claim 8 , wherein mutual relationships between the second PMI, the first codebook index, and the second codebook index are determined according to Table F1 or F2:

TABLE F1

I PMI2

i 1

i 2

0-3

0-7 

2 × I PMI2

8-15

2 × I PMI2 + 1

TABLE F2

I PMI2

i 1

i 2

0-3

0-7

2 × I PMI2

8-15

2 × I PMI2 + 8

wherein I PMI2 represents the second PMI, i 1 represents the first codebook index, and i 2 represents the second codebook index.

10. The method according to claim 6 , wherein the received rank is 3 or 4, and the precoding matrices comprised in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G

Codebook

RI

Index

u n

1

2

3

4

0

u 0 = [1 −1 −1 −1] T

W 0 {1}

W 0 {14} /{square root over (2)}

W 0 {124} /{square root over (3)}

W 0 {1234} /2

1

u 1 = [1 −j 1 j] T

W 1 {1}

W 1 {12} /{square root over (2)}

W 1 {123} /{square root over (3)}

W 1 {1234} /2

2

u 2 = [1 1 −1 1] T

W 2 {1}

W 2 {12} /{square root over (2)}

W 2 {123} /{square root over (3)}

W 2 { 3214} /2

3

u 3 = [1 j 1 −j] T

W 3 {1}

W 3 {12} /{square root over (2)}

W 3 {123} /{square root over (3)}

W 3 { 3214} /2

4

u 4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}] T

W 4 {1}

W 4 {14} /{square root over (2)}

W 4 {124} /{square root over (3)}

W 4 {1234} /2

5

u 5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}] T

W 5 {1}

W 5 {14} /{square root over (2)}

W 5 {124} /{square root over (3)}

W 5 {1234} /2

6

u 6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}] T

W 6 {1}

W 6 {13} /{square root over (2)}

W 6 {134} /{square root over (3)}

W 6 {1324} /2

7

u 7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}] T

W 7 {1}

W 7 {13} /{square root over (2)}

W 7 {134} /{square root over (3)}

W 7 {1324} /2

8

u 8 = [1 −1 1 1] T

W 8 {1}

W 8 {12} /{square root over (2)}

W 8 {124} /{square root over (3)}

W 8 {1234} /2

9

u 9 = [1 −j −1 −j] T

W 9 {1}

W 9 {14} /{square root over (2)}

W 9 {134} /{square root over (3)}

W 9 {1234} /2

10

u 10 = [1 1 1 −1] T

W 10 {1}

W 10 {13} /{square root over (2)}

W 10 {123} /{square root over (3)}

W 10 {1324} /2

11

u 11 = [1 j −1 j] T

W 11 {1}

W 11 {13} /{square root over (2)}

W 11 {134} /{square root over (3)}

W 11 {1324} /2

12

u 12 = [1 −1 −1 1] T

W 12 {1}

W 12 {12} /{square root over (2)}

W 12 {123} /{square root over (3)}

W 12 {1234} /2

13

u 13 = [1 −1 1 −1] T

W 13 {1}

W 13 {13} /{square root over (2)}

W 13 {123} /{square root over (3)}

W 13 {1324} /2

14

u 14 = [1 1 −1 −1] T

W 14 {1}

W 14 {13} /{square root over (2)}

W 14 {123} /{square root over (3)}

W 14 { 3214} /2

15

u 15 = [1 1 1 1] T

W 15 {1}

W 15 {12} /{square root over (2)}

W 15 {123} /{square root over (3)}

W 15 {1234} /2

wherein W n {s} represents a matrix formed by a column set {s} of a matrix W n =I−2u n u n H /u n H u n , and I is a 4×4 identity matrix.

11. A user equipment, comprising:

a processor, configured to:

determine a rank used for indicating a number of transmission layers;

determine a first precoding matrix in a codebook set corresponding to the rank, wherein precoding matrices comprised in the codebook set are represented by a first codebook index and a second codebook index;

determine a second precoding matrix indicator (PMI) for indicating the first precoding matrix, wherein the second PMI and the second codebook index have a first correspondence, and for a given first codebook index, a value range of the second codebook index corresponding to a value range of the second PMI is a proper subset of a value range of the second codebook index; and

a transmitter, configured to send, to a base station, the second PMI for indicating the first precoding matrix;

wherein the precoding matrices W comprised in the codebook set satisfy the following equation:

W=W 1 ×W 2 , wherein

W

1

=

[

X

n

0

0

X

n

]

,

X

n

=

[

1

1

1

1

q

1

n

q

1

n

+

8

q

1

n

+

16

q

1

n

+

24

]

,

q 1 =e j2π/32 , and n=0, 1, . . . , 15;

wherein the first codebook index corresponds to one value of n, and a value range of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; and

wherein when the rank determined by the processor is 2, in precoding matrix sets that are determined according to the first codebook index and the second codebook index corresponding to the value range of the second PMI, a first precoding matrix set corresponding to a first codebook index i 1,a and a second precoding matrix set corresponding to a first codebook index i 1,a+8 are mutually exclusive, wherein the first codebook index i 1,a represents a first codebook index corresponding to n whose value is a, the first codebook index i 1,a+8 represents a first codebook index corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

12. The user equipment according to claim 11 , wherein the rank determined by the processor is 1, and W 2 satisfies the following equation:

W

2

∈

{

1

A

⁡

[

Y

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

α

⁢

⁢

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

}

,

wherein Yε{e 1 ,e 2 ,e 3 ,e 4 }, α(i)=q 1 2(i-1) ; when Y is e 1 , α(i) is α(1); when Y is e 2 , α(i) is α(2); when Y is e 3 , α(i) is α(3); when Y is e 4 , α(i) is α(4); wherein e i represents a column vector with a dimension of 4×1, wherein an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein A is a constant.

13. The user equipment according to claim 11 , wherein the rank determined by the processor is 2, and W 2 satisfies the following equation:

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

,

(

e

1

,

e

2

)

,

(

e

2

,

e

3

)

,

(

e

1

,

e

4

)

,

(

e

2

,

e

4

)

}

;

⁢

or

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

-

Y

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

2

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

2

-

Y

1

]

,

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

3

)

,

(

e

2

,

e

4

)

,

(

e

3

,

e

1

)

,

(

e

4

,

e

2

)

}

wherein e i represents a column vector with a dimension of 4×1, an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein B is a constant.

14. The user equipment according to claim 13 , wherein the rank determined by the processor is 2, and mutual relationships between the second PMI, the first codebook index, and the second codebook index are determined according to Table F1 or F2:

TABLE F1

I PMI2

i 1

i 2

0-3

0-7 

2 × I PMI2

8-15

2 × I PMI2 + 1

TABLE F2

I PMI2

i 1

i 2

0-3

0-7

2 × I PMI2

8-15

2 × I PMI2 + 8

wherein I PMI2 represents the second PMI, i 1 represents the first codebook index, and i 2 represents the second codebook index.

15. The user equipment according to claim 11 , wherein the rank determined by the processor is 3 or 4, and the precoding matrices comprised in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G;

TABLE G

Codebook

RI

Index

u n

1

2

3

4

0

u 0 = [1 −1 −1 −1] T

W 0 {1}

W 0 {14} /{square root over (2)}

W 0 {124} /{square root over (3)}

W 0 {1234} /2

1

u 1 = [1 −j 1 j] T

W 1 {1}

W 1 {12} /{square root over (2)}

W 1 {123} /{square root over (3)}

W 1 {1234} /2

2

u 2 = [1 1 −1 1] T

W 2 {1}

W 2 {12} /{square root over (2)}

W 2 {123} /{square root over (3)}

W 2 { 3214} /2

3

u 3 = [1 j 1 −j] T

W 3 {1}

W 3 {12} /{square root over (2)}

W 3 {123} /{square root over (3)}

W 3 { 3214} /2

4

u 4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}] T

W 4 {1}

W 4 {14} /{square root over (2)}

W 4 {124} /{square root over (3)}

W 4 {1234} /2

5

u 5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}] T

W 5 {1}

W 5 {14} /{square root over (2)}

W 5 {124} /{square root over (3)}

W 5 {1234} /2

6

u 6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}] T

W 6 {1}

W 6 {13} /{square root over (2)}

W 6 {134} /{square root over (3)}

W 6 {1324} /2

7

u 7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}] T

W 7 {1}

W 7 {13} /{square root over (2)}

W 7 {134} /{square root over (3)}

W 7 {1324} /2

8

u 8 = [1 −1 1 1] T

W 8 {1}

W 8 {12} /{square root over (2)}

W 8 {124} /{square root over (3)}

W 8 {1234} /2

9

u 9 = [1 −j −1 −j] T

W 9 {1}

W 9 {14} /{square root over (2)}

W 9 {134} /{square root over (3)}

W 9 {1234} /2

10

u 10 = [1 1 1 −1] T

W 10 {1}

W 10 {13} /{square root over (2)}

W 10 {123} /{square root over (3)}

W 10 {1324} /2

11

u 11 = [1 j −1 j] T

W 11 {1}

W 11 {13} /{square root over (2)}

W 11 {134} /{square root over (3)}

W 11 {1324} /2

12

u 12 = [1 −1 −1 1] T

W 12 {1}

W 12 {12} /{square root over (2)}

W 12 {123} /{square root over (3)}

W 12 {1234} /2

13

u 13 = [1 −1 1 −1] T

W 13 {1}

W 13 {13} /{square root over (2)}

W 13 {123} /{square root over (3)}

W 13 {1324} /2

14

u 14 = [1 1 −1 −1] T

W 14 {1}

W 14 {13} /{square root over (2)}

W 14 {123} /{square root over (3)}

W 14 { 3214} /2

15

u 15 = [1 1 1 1] T

W 15 {1}

W 15 {12} /{square root over (2)}

W 15 {123} /{square root over (3)}

W 15 {1234} /2

wherein W n {s} represents a matrix formed by a column set {s} of a matrix W n =I−2u n u n H /u n H u n , and I is a 4×4 identity matrix.

16. A base station, comprising:

a receiver, configured to receive a second precoding matrix indicator (PMI), a first codebook index, and a rank used for indicating the number of transmission layers that are sent by a user equipment;

a processor, configured to determine, according to the second PMI and the first codebook index received by the receiver, a first precoding matrix in a codebook set corresponding to the rank received by the receiver, wherein precoding matrices comprised in the codebook set are represented by the first codebook index and a second codebook index, the second PMI and the second codebook index have a first correspondence, and for a given first codebook index, a value range of the second codebook index corresponding to a value range of the second PMI is a proper subset of a value range of the second codebook index;

wherein the precoding matrices (W) comprised in the codebook set satisfy the following equation:

W=W 1 ×W 2 , wherein

W

1

=

[

X

n

0

0

X

n

]

,

X

n

=

[

1

1

1

1

q

1

n

q

1

n

+

8

q

1

n

+

16

q

1

n

+

24

]

,

q 1 =e j2π/32 , and n=0, 1, . . . , 15;

wherein the first codebook index corresponds to one value of n, and a value range of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; and

wherein when the received rank is 2, in precoding matrix sets that are determined according to the first codebook index and the second codebook index corresponding to the value range of the second PMI, a first precoding matrix set corresponding to a first codebook index i 1,a and a second precoding matrix set corresponding to a first codebook index i 1,a+8 are mutually exclusive, wherein the first codebook index i 1,a represents a first codebook index corresponding to n whose value is a, the first codebook index i 1,a+8 represents a first codebook index corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

17. The base station according to claim 16 , wherein the rank received by the receiver is 1, and W 2 satisfies the following equation:

W

2

∈

{

1

A

⁡

[

Y

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

α

⁢

⁢

(

i

)

⁢

Y

]

,

1

A

⁡

[

Y

-

j

⁢

⁢

α

⁡

(

i

)

⁢

Y

]

}

,

wherein Yε{e 1 ,e 2 ,e 3 ,e 4 }, α(i)=q 1 2(i-1) ; when Y is e 1 , α(i) is α(1); when Y is e 2 , α(i) is α(2); when Y is e 3 , α(i) is α(3); when Y is e 4 , α(i) is α(4); wherein e i represents a column vector with a dimension of 4×1, wherein an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein A is a constant.

18. The base station according to claim 16 , wherein the rank received by the receiver is 2, and W 2 satisfies the following equation:

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

,

(

e

1

,

e

2

)

,

(

e

2

,

e

3

)

,

(

e

1

,

e

4

)

,

(

e

2

,

e

4

)

}

;

⁢

or

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

-

Y

1

-

Y

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

2

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

1

-

Y

2

]

,

1

B

⁡

[

Y

1

Y

2

jY

1

-

jY

2

]

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

1

)

,

(

e

2

,

e

2

)

,

(

e

3

,

e

3

)

,

(

e

4

,

e

4

)

}

⁢

⁢

W

2

∈

{

1

B

⁡

[

Y

1

Y

2

Y

2

-

Y

1

]

,

}

⁢

(

Y

1

,

Y

2

)

∈

{

(

e

1

,

e

3

)

,

(

e

2

,

e

4

)

,

(

e

3

,

e

1

)

,

(

e

4

,

e

2

)

}

wherein e i represents a column vector with a dimension of 4×1, an i th element in e i is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein B is a constant.

19. The base station according to claim 18 , wherein the rank received by the receiver is 2, and mutual relationships between the second PMI, the first codebook index, and the second codebook index are determined according to Table F1 or F2:

TABLE F1

I PMI2

i 1

i 2

0-3

0-7 

2 × I PMI2

8-15

2 × I PMI2 + 1

TABLE F2

I PMI2

i 1

i 2

0-3

0-7

2 × I PMI2

8-15

2 × I PMI2 + 8

wherein I PMI2 represents the second PMI, i 1 represents the first codebook index, and i 2 represents the second codebook index.

20. The base station according to claim 16 , wherein the rank received by the receiver is 3 or 4, the precoding matrices comprised in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G

Codebook

RI

Index

u n

1

2

3

4

0

u 0 = [1 −1 −1 −1] T

W 0 {1}

W 0 {14} /{square root over (2)}

W 0 {124} /{square root over (3)}

W 0 {1234} /2

1

u 1 = [1 −j 1 j] T

W 1 {1}

W 1 {12} /{square root over (2)}

W 1 {123} /{square root over (3)}

W 1 {1234} /2

2

u 2 = [1 1 −1 1] T

W 2 {1}

W 2 {12} /{square root over (2)}

W 2 {123} /{square root over (3)}

W 2 { 3214} /2

3

u 3 = [1 j 1 −j] T

W 3 {1}

W 3 {12} /{square root over (2)}

W 3 {123} /{square root over (3)}

W 3 { 3214} /2

4

u 4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}] T

W 4 {1}

W 4 {14} /{square root over (2)}

W 4 {124} /{square root over (3)}

W 4 {1234} /2

5

u 5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}] T

W 5 {1}

W 5 {14} /{square root over (2)}

W 5 {124} /{square root over (3)}

W 5 {1234} /2

6

u 6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}] T

W 6 {1}

W 6 {13} /{square root over (2)}

W 6 {134} /{square root over (3)}

W 6 {1324} /2

7

u 7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}] T

W 7 {1}

W 7 {13} /{square root over (2)}

W 7 {134} /{square root over (3)}

W 7 {1324} /2

8

u 8 = [1 −1 1 1] T

W 8 {1}

W 8 {12} /{square root over (2)}

W 8 {124} /{square root over (3)}

W 8 {1234} /2

9

u 9 = [1 −j −1 −j] T

W 9 {1}

W 9 {14} /{square root over (2)}

W 9 {134} /{square root over (3)}

W 9 {1234} /2

10

u 10 = [1 1 1 −1] T

W 10 {1}

W 10 {13} /{square root over (2)}

W 10 {123} /{square root over (3)}

W 10 {1324} /2

11

u 11 = [1 j −1 j] T

W 11 {1}

W 11 {13} /{square root over (2)}

W 11 {134} /{square root over (3)}

W 11 {1324} /2

12

u 12 = [1 −1 −1 1] T

W 12 {1}

W 12 {12} /{square root over (2)}

W 12 {123} /{square root over (3)}

W 12 {1234} /2

13

u 13 = [1 −1 1 −1] T

W 13 {1}

W 13 {13} /{square root over (2)}

W 13 {123} /{square root over (3)}

W 13 {1324} /2

14

u 14 = [1 1 −1 −1] T

W 14 {1}

W 14 {13} /{square root over (2)}

W 14 {123} /{square root over (3)}

W 14 { 3214} /2

15

u 15 = [1 1 1 1] T

W 15 {1}

W 15 {12} /{square root over (2)}

W 15 {123} /{square root over (3)}

W 15 {1234} /2

wherein W n {s} represents a matrix formed by a column set {s} of a matrix W n =I−2u n u n H /u n H u n , and I is a 4×4 identity matrix.