Codebook construction

1. A method implemented in a base station used in a wireless communications system, the method comprising:

having 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission, each codebook including a plurality of precoding matrices;

precoding data with one of the plurality of precoding matrices; and

transmitting, from four transmit antennas of the base station to a user equipment, the precoded data,

wherein the 1-layer codebook comprises a first 1-layer codebook and a second 1-layer codebook each of which includes a plurality of 4×1 precoding matrices, and the 2-layer codebook comprises a first 2-layer codebook and a second 2-layer codebook each of which includes a plurality of 4×2 precoding matrices, and

wherein each precoding matrix in the first 1-layer and 2-layer codebooks comprises a first index and a second index.

2. The method as in claim 1 , wherein the first index is for a plurality of subbands and the second index is for each subband.

3. The method as in claim 1 , wherein each of the second 1-layer and 2-layer codebooks comprises a legacy codebook or a householder codebook.

4. The method as in claim 1 , wherein each of the 3-layer and 4-layer codebooks comprises a legacy codebook or a householder codebook.

5. The method as in claim 1 , wherein each precoding matrix W in the first 1-layer and 2-layer codebooks satisfies W=W (1) W (2) , where first matrix W (1) is chosen from inner codebook C (1) , and second matrix W (2) is chosen from an outer codebook.

6. A wireless communications system comprising:

a base station having 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission, each codebook including a plurality of precoding matrices and precoding data with one of the plurality of precoding matrices;

a user equipment receiving, from four transmit antennas of the base station, the precoded data,

wherein the 1-layer codebook comprises a first 1-layer codebook and a second 1-layer codebook each of which includes a plurality of 4×1 precoding matrices, and the 2-layer codebook comprises a first 2-layer codebook and a second 2-layer codebook each of which includes a plurality of 4×2 precoding matrices, and

wherein each precoding matrix in the first 1-layer and 2-layer codebooks comprises a first index and a second index.

7. A method implemented in a wireless communications system, the method comprising:

having 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission, each codebook including a plurality of precoding matrices;

precoding data with one of the plurality of precoding matrices; and

transmitting, from four transmit antennas of a base station to a user equipment, the precoded data,

wherein the 1-layer codebook comprises a first 1-layer codebook and a second 1-layer codebook each of which includes a plurality of 4×1 precoding matrices, and the 2-layer codebook comprises a first 2-layer codebook and a second 2-layer codebook each of which includes a plurality of 4×2 precoding matrices, and

wherein each precoding matrix in the first 1-layer and 2-layer codebooks comprises a first index and a second index.

8. The method as in claim 7 , wherein the first index is for a plurality of subbands and the second index is for each subband.

9. The method as in claim 7 , wherein each of the second 1-layer and 2-layer codebooks comprises a legacy codebook or a householder codebook.

10. The method as in claim 7 , wherein each of the 3-layer and 4-layer codebooks comprises a legacy codebook or a householder codebook.

11. The method as in claim 7 , wherein each precoding matrix W in the first 1-layer and 2-layer codebooks satisfies W=W (1) W (2) ,

where first matrix W (1) is chosen from inner codebook C (1) , and

second matrix W (2) is chosen from an outer codebook.