Reporting of channel state information

1. A non-transitory computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of:

determining K matrices for K frequency sub-bands, wherein K precoding matrix indicators (PMIs) of the K frequency sub-bands respectively represent the K matrices, a plurality of sub-carriers in a multi-carrier cellular communication system is divided into the K frequency sub-bands, and K is an integer greater than 1;

determining a first sub-index and K second sub-indices, wherein each of the K matrices is indexed by the first sub-index and one of the K second sub-indices, and wherein each of K PMIs comprises the first sub-index and one of the K second sub-indices; and

transmitting, to a base station, the first sub-index and at least one of the K second sub-indices, wherein the first sub-index is common for all of the K frequency sub-bands, and each of the K second sub-indices is specific for a matrix that corresponds to one frequency sub-band of the K frequency sub-bands.

2. The non-transitory computer-readable storage medium according to claim 1 , wherein

the first sub-index indicates a first sub-matrix from a first sub-codebook, and

a second sub-index in the K second sub-indices indicates a second sub-matrix from a second sub-codebook, wherein each one of the K matrices comprises the first sub-matrix and one of the K matrices comprises the second sub-matrix.

3. The non-transitory computer-readable storage medium according to claim 2 , wherein

each one of the K matrices is represented as W i , 0≤i≤K−1, and

W

i

=

[

M

k

1

M

k

1

⁢

M

k

2

i

]

,

where W i represents the i th matrix, k 1 represents a first sub-index identifying a first sub-matrix M k i , and k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

4. The non-transitory computer-readable storage medium according to claim 2 , wherein

each one of the K matrices is represented as W i , 0≤i≤K−1, and

W

i

=

[

M

k

1

M

k

2

i

⁢

M

k

1

]

,

where W i represents the i th matrix, k 1 represents a first sub-index identifying a first sub-matrix M k i , k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

5. The non-transitory computer-readable storage medium according to claim 2 , wherein

each one of the K matrices is represented as W i , 0≤i≤K−1, and

W i =M k 2 i M k 1 or W i =M k 1 M k 2 i ,

where W i represents the i th matrix, k 1 represents a first sub-index identifying a first sub-matrix M k 1 , k 2 represents a second sub-index identifying second sub-matrix M k 2 i .

6. The non-transitory computer-readable storage medium according to claim 2 , wherein

each one of the K matrices is represented as W i , 0≤i≤K−1, and

W

i

=

[

M

k

1

M

k

1

⁢

e

jd

k

2

]

,

where W i represents the i th matrix, k 1 represents a first sub-index identifying a first sub-matrix M k 1 , k 2 represents a second sub-index identifying d k 2 , and d k 2 represents a scalar.

7. The non-transitory computer-readable storage medium according to claim 1 , wherein the multi-carrier cellular communication system is a long term evolution (LTE) system or a long term evolution advanced (LTE-A) system.

8. An apparatus in a mobile station, comprising:

a memory storing executable instructions; and

a processor coupled to the memory, the processor executing the executable instructions to:

determine a matrix for K frequency sub-bands, wherein the mobile station communicates with a base station in a multi-carrier cellular communication system having a plurality of sub-carriers, wherein the plurality of sub-carriers is divided into the K frequency sub-bands, K is an integer greater than 1, and the matrix is represented by a precoding matrix indicator (PMI);

determine a first sub-index from a plurality of first sub-indices and a second sub-index for the matrix from a plurality of second sub-indices; and

transmit, to a base station, the first sub-index and the second sub-index on a periodic physical uplink control channel (PUCCH) for the K frequency sub-bands,

wherein the first sub-index and the second sub-index are common for the K frequency sub-bands, the PMI comprises the first sub-index and the second sub-index, the plurality of the first sub-indices are a subset of all possible first sub-indices, the plurality of second sub-indices are a subset of all possible second sub-indices, and a quantity of combinations of the plurality of first sub-indices and second sub-indices is smaller than a quantity of possible combinations of all possible first sub-indices and second sub-indices.

9. The apparatus according to claim 8 , wherein the matrix is one of a plurality of matrices, the first sub-index of the plurality of first sub-indices indicates a first sub-matrix from a first sub-codebook, and

the second sub-index of the plurality second sub-indices indicates a second sub-matrix from a second sub-codebook, wherein each one of the plurality of matrices comprises the first sub-matrix from the first sub-codebook and the second sub-matrix from the second sub-codebook.

10. The apparatus according to claim 9 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

1

⁢

M

k

2

i

]

,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , and k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

11. The apparatus according to claim 9 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

2

i

⁢

M

k

1

]

,

where W i represents the i th matrix, k 1 represents the first sub-index, identifying a first sub-matrix M k 1 , and k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

12. The apparatus according to claim 9 , wherein

each one of the plurality of matrices is represented as W i , and

W i =M k 2 i M k 1 or W i =M k 1 M k 2 i ,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , and k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

13. The apparatus according to claim 9 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

1

⁢

e

jd

k

2

]

,

where W i represents the i th matrix, k 1 represents a first sub-index identifying a first sub-matrix M k 1 , k 2 represents a second sub-index identifying d k 2 , and d k 2 represents a scalar.

14. The apparatus according to claim 8 , wherein the multi-carrier cellular communication system is a long term evolution (LTE) system or a long term evolution advanced (LTE-A) system.

15. A non-transitory computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of:

determining a matrix for K frequency sub-bands in a multi-carrier cellular communication system, wherein the multi-carrier cellular communication system has a plurality of sub-carriers, the plurality of sub-carriers is divided into the K frequency sub-bands, K is an integer greater than 1, and the matrix is represented by a precoding matrix indicator (PMI);

determining a first sub-index from a plurality of first sub-indices and a second sub-index for the matrix from a plurality of second sub-indices; and

transmitting, to a base station, the first sub-index and the second sub-index on a periodic physical uplink control channel (PUCCH) for the K frequency sub-bands,

wherein the first sub-index and the second sub-index are common for the plurality of frequency sub-bands, the PMI comprises the first sub-index and the second sub-index, the plurality of the first sub-indices are a subset of all possible first sub-indices, the plurality of second sub-indices are a subset of all possible second sub-indices, and a quantity of combinations of the plurality of first sub-indices and second sub-indices is smaller than a quantity of possible combinations of all possible first sub-indices and second sub-indices.

16. The non-transitory computer-readable storage medium according to claim 15 , wherein the matrix is one of a plurality of matrices, the first sub-index of the plurality of first sub-indices indicates a first sub-matrix from a first sub-codebook, and

the second sub-index of the plurality of first sub-indices indicates a second sub-matrix from a second sub-codebook, wherein each one of the plurality of matrices comprises the first sub-matrix from the first sub-codebook and the second sub-matrix from the second sub-codebook.

17. The non-transitory computer-readable storage medium according to claim 16 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

1

⁢

M

k

2

i

]

,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , and k 2 represents a second sub-index identifying a second sub-matrix M k 2 i .

18. The non-transitory computer-readable storage medium according to claim 17 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

2

i

⁢

M

k

1

]

,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , and k 2 represents a second sub-index identifying second sub-matrix M k 2 i .

19. The non-transitory computer-readable storage medium according to claim 17 , wherein

each one of the plurality of matrices is represented as W i , and

W i =M k 2 i M k 1 or W i =M k 1 M k 2 i ,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , k 2 represents a second sub-index identifying second sub-matrix M k 2 i .

20. The non-transitory computer-readable storage medium according to claim 16 , wherein

each one of the plurality of matrices is represented as W i , and

W

i

=

[

M

k

1

M

k

1

⁢

e

jd

k

2

]

,

where W i represents the i th matrix, k 1 represents the first sub-index identifying a first sub-matrix M k 1 , k 2 represents a second sub-index identifying d k 2 , and d k 2 represents a scalar.