System and method for wireless communications with codebook quantization

1. A method for communications device operations, the method comprising:

estimating, by the communications device, a channel between a controller and a mobile device;

generating channel state information from the channel estimate;

quantizing the channel state information by selecting a codeword from a rank n codebook in accordance with a codeword selection mechanism, where n is a non-negative integer value;

transmitting an index corresponding to the selected codeword; and

receiving a transmission from the controller, wherein the transmission is precoded in accordance with the index,

wherein the rank n codebook comprises 2 K codewords with each codeword comprising n columns of a transformed base matrix of dimension N t ×N t , where K is a positive integer number representing a number of bits in the rank n codebook, and N t is a number of transmit antennas at the controller, and

wherein an i-th codeword of the rank n codebook is expressible as C i =diag(u i )×DFT N t , where DFT N t is the base matrix, u i (n)=e jπ sin(k sin(θ i ))n ,

iε[0, . . . , 2 K −1], nε[0, . . . , N t −1], k is a constant, θ i ε[0,2π], and diag( ) is a function that returns diagonal elements of u i .

2. The method of claim 1 , wherein the channel is estimated in accordance with a measurement of a pilot transmitted on the channel.

3. The method of claim 1 , wherein n is equal to one, and wherein

k

=

2

⁢

3

⁢

π

9

.

4. The method of claim 3 , wherein

θ

i

=

-

π

3

+

2

⁢

i

⁢

⁢

π

45

.

5. The method of claim 1 , wherein n is equal to one, and wherein the rank 1 codebook is generated using generator

codeword

index

codeword

u i

i

C K,N t i (1, :)

i ε [0, . . . , (2 K − 1)].

6. The method of claim 1 , wherein n is equal to one, and wherein the i-th codeword of the rank 1 codebook is a first column of the transformed base matrix.

7. The method of claim 1 , wherein n is equal to two, and wherein an i-th codeword of the rank 2 codebook is expressible as

W K,N t 1 ( i )= C K,N t (1 :j ,:)/√{square root over (2)},

where iε[1, . . . , 2 K ] and jε[2, . . . , N t ].

8. The method of claim 7 , wherein N t =8, K=6, and the rank 2 codebook is generated using generator

codeword

index

codeword

u i

4i

C K,N t i (1:2, :)/{square root over (2)}

i ε [0, . . . , 15]

4i + 1

C K,N t i (1:4, :)/{square root over (2)}

4i + 2

C K,N t i (1:6, :)/{square root over (2)}

4i + 3

C K,N t i (1:8, :)/{square root over (2)}.

9. The method of claim 1 , wherein n is equal to two, and wherein the i-th codeword of the rank 2 codebook comprises two columns of the transformed base matrix.

10. The method of claim 1 , wherein an element in row p and column q of the DFT N t base matrix is expressible as

D

⁢

⁢

F

⁢

⁢

T

N

t

⁡

(

p

,

q

)

=

1

N

t

⁢

ⅇ

2

⁢

π

⁢

⁢

pq

N

t

⁢

j

,

where p and q are positive integer values less than or equal to N t .

11. The method of claim 1 , wherein the codeword selection mechanism is expressible as

F CS ( W )=max(| HW i |,iε[ 0, . . . , 2 K −1]),

where H is a channel estimate, W i is an i-th codeword in the rank n codebook, and K is the number of bits of the rank n codebook.

12. A method for controller operation, the method comprising:

receiving, by the controller, an index from a communications device, the index corresponding to a codeword in a rank n codebook, and the codeword representing a quantized channel estimate, where n is a non-negative integer value representing a number of transmit antennas at a controller;

computing a precoding matrix from the codeword;

precoding data to be transmitted to the communications device in accordance with the precoding matrix; and

transmitting the precoded data to the communications device,

wherein the rank n codebook comprises 2 K codewords with each codeword comprising n columns of a transformed base matrix of dimension N t ×N t , where K is a positive integer number representing a number of bits in the rank n codebook, and N t is a number of transmit antennas at the controller, and

wherein an i-th codeword of the rank n codebook is expressible as C i =diag(u i )×DFT N t , where DFT N t is the base matrix, u i (n)=e jπ sin(k sin(θ t ))n , iε[0, . . . , 2 K −1], nε[0, . . . , N t −1], k is a constant, and θ i ε[0,2π], and diag( ) is a function that returns diagonal elements of u i .

13. The method of claim 12 , further comprising transmitting a pilot.

14. The method of claim 12 , wherein n is equal to one, and wherein

k

=

2

⁢

3

⁢

π

9

,

⁢

θ

i

=

-

π

3

+

2

⁢

i

⁢

⁢

π

45

,

⁢

i

∈

[

0

,

…

⁢

,

2

K

-

1

]

,

⁢

and

⁢

⁢

n

∈

[

0

,

…

⁢

,

N

t

-

1

]

.

15. The method of claim 12 , wherein n is equal to two and N t =8, K=6, and the rank 2 codebook is generated using generator

codeword

index

codeword

u i

4i

C K,N t i (1:2, :)/{square root over (2)}

i ε [0, . . . , 15]

4i + 1

C K,N t i (1:4, :)/{square root over (2)}

4i + 2

C K,N t i (1:6, :)/{square root over (2)}

4i + 3

C K,N t i (1:8, :)/{square root over (2)}.

16. A communications device comprising:

a channel estimate unit coupled to a signal input, the channel estimate unit configured to estimate a channel between the communications device and a controller serving the communications device;

a quantization unit coupled to the channel estimate unit, the quantization unit configured to quantize the channel estimate in accordance with a rank n codebook and to output an index to a codeword from the rank n codebook in accordance with a codeword selection mechanism;

a codebook store coupled to the quantization unit, the codebook store configured to store the rank n codebook; and

a transmitter coupled to the quantization unit, the transmitter configured to transmit the index to the controller,

wherein the rank n codebook comprises 2 K codewords with each codeword comprising n columns of a transformed base matrix of dimension N t ×N t , where K is a positive integer number representing a number of bits in the rank n codebook, and N t is a number of transmit antennas at the controller, and

wherein an i-th codeword of the rank n codebook is expressible as C i =diag(u i )×DFT N t , where DFT N t is the base matrix, u i (n)=e jπ sin(θ t ))n , iε[0, . . . , 2 K −1],nε[0, . . . , N t −1], k is a constant, θ i ε[0,2π], and diag( ) is a function that returns diagonal elements of u i .

17. The communications device of claim 16 , wherein the channel estimate unit is configured to estimate the channel in accordance with a measurement of a pilot transmitted on the channel.

18. The communications device of claim 16 , wherein n is equal to one, and wherein the i-th codeword of the rank 1 codebook is a first column of the transformed base matrix.

19. The communications device of claim 16 , wherein n is equal to two, and wherein the i-th codeword of the rank 2 codebook comprises two columns of the transformed base matrix.

20. A controller comprising:

a feedback decoder coupled to a signal input, the feedback decoder configured to decode feedback information from a communications device to produce an index, where the index corresponds to a codeword in a rank n codebook, the codeword corresponding to a quantized version of channel state information for a communications channel between the controller and the communications device;

a beamforming vector compute unit coupled to the feedback decoder, the beamforming vector compute unit configured to compute a beamforming vector from the codeword;

a transmit beamforming unit coupled to the beamforming vector compute unit and to a data input, the transmit beamforming unit configured to apply the beamforming vector to data provided by the data input; and

a transmitter coupled to the transmit beamforming unit and to an antenna, the transmitter configured to transmit beamformed data provided by the transmit beamforming unit to a source of the feedback information using the antennas,

wherein the rank n codebook comprises 2 K codewords with each codeword comprising n columns of a transformed base matrix of dimension N t ×N t , where K is a positive integer number representing a number of bits in the rank n codebook, and N t is a number of transmit antennas at the controller, and

wherein an i-th codeword of the rank n codebook is expressible as C i =diag(u i )×DFT N t , where DFT N t is the base matrix, u i (n)=e jπ sin(k sin(θ t ))n , iε[0, . . . , 2 K −1], nε[0, . . . , N t −1], k is a constant, θ i ε[0,2π], and diag( ) is a function that returns diagonal elements of u i .

21. The controller of claim 20 , wherein the transmitter is further configured to transmit a pilot.

22. The controller of claim 20 , wherein n is equal to one, and wherein

k

=

2

⁢

3

⁢

π

9

,

θ

i

=

-

π

3

+

2

⁢

i

⁢

⁢

π

45

,

i

∈

[

0

,

…

⁢

,

2

K

-

1

]

,

and

⁢

⁢

n

⁢

∈

[

0

,

…

⁢

,

N

t

-

1

]

.

23. The controller of claim 20 , wherein n is equal to two and N t =8, K=6, and the rank 2 codebook is generated using generator

codeword

index

codeword

u i

4i

C K,N, i (1:2,:)/{square root over (2)}

iε[0, . . . , 15]

4i + 1

C K,N, i (1:4,:)/{square root over (2)}

4i + 2

C K,N, i (1:6,:)/{square root over (2)}

4i + 3

 C K,N, i (1:8,:)/{square root over (2)}.