Codebook method for a multiple input multiple output wireless system

1. A method implemented in a wireless communication system, comprising the steps of:

encoding wireless multiple input and multiple output signals in accordance with a codebook comprising:

a discrete codebook restricting elements of codebook entries to be within a predetermined finite set of complex numbers; and

a constant amplitude codebook including each entry in its codebook having both equal column norm and equal row norm; and

transmitting the precoded signals to a mobile terminal,

wherein the codebook entries are matrices that are determined in accordance with the following expression:

A

(

v

i

1

1

,

v

i

2

2

,

v

i

3

3

,

…

⁢

)

=

[

v

i

1

1

,

HH

⁡

(

v

i

1

1

-

ⅇ

1

M

)

⁡

[

0

v

i

2

2

]

,

HH

⁡

(

v

i

1

1

-

ⅇ

1

M

)

⁡

[

0

HH

⁡

(

v

i

2

2

-

ⅇ

1

M

-

1

)

⁡

[

0

v

i

3

3

]

]

,

…

⁢

]

,

where e 1 N =[1, 0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space,

HH

⁡

(

w

)

=

{

I

-

2

⁢

ww

H



w



2

if

w

≠

0

I

if

w

=

0

and {v i l j εC M−j+1 } is a vector codebook and v i l j denotes a column vector.

2. The method of claim 1 , wherein, for the discrete codebook, restricting elements of codebook entries to be within a predetermined finite set of complex numbers comprises one of {1, −1, j, −j}, and {1, −1, j, −j, 1+j, 1−j, −1+j, −1−j}, and {±1, ±2, ±j, ±2j, ±1±j, ±1±2j, ±2, ±j, ±2±2j}, and {e 2πjα 1 , e 2πjα 2 , e 2πjα 3 , e 2πjα 4 }, {1, −1, j, −j, a(1+j), a(1−j), a(−1+j), a(−1−j)} where

a

=

1

2

and α 1 , α 2 , α 3 , and α 4 are complex numbers.

3. The method of claim 1 , wherein the discrete codebook comprises restricting elements of a finite set in the discrete codebook to be in the form of 2 a +j2 b , where a and b are positive integers.

4. The method of claim 1 , wherein the discrete codebook comprises restricting elements of a finite set in the discrete codebook to be in the form of k a +jk b for a base-k computer, where a and b are positive integers.

5. The method of claim 1 , wherein constant amplitude codebook further comprises being obtained through a series of successive householder transformations.

6. The method of claim 5 , wherein for a communication involving 4 transmit antennas, the constant amplitude householder codebook comprises considering a set of 4 by 1 vectors where each elements of the vector is taken from a set of complex number in the form {1, e 2πjα 1 , e 2πjα 2 . . . , e 2πjα g } which has g+1 elements, and the first element of each vector is 1, where α 1 , . . . , α g are complex numbers.

7. The method of claim 1 , wherein the codebook is configured as a constrained codebook in which the codebook is configured for multiple scenarios.

8. The method of claim 7 , wherein the multiple scenarios comprises different set of channel statistics.

9. The method of claim 7 ,

wherein the constrained codebook comprises a union set configuration, and

wherein a union of the set of all channel realizations is taken for all scenarios and the codebook is configured for such union set.

10. The method of claim 7 , wherein the constrained codebook comprises a successive approach wherein the codebook is configured of a smaller size for one scenario.

11. The method of claim 7 , wherein the constrained codebook comprises a successive approach wherein the codebook is configured with fixing the designed entries and expanding the codebook by adding more entries to the codebook, then configuring new entries responsive to a new scenario and considering a constraint on fixed entries, then again fixing all configured entries and adding more entries and configuring the more entries responsive to a next scenario until all scenarios are accounted for.

12. The method of claim 11 , wherein the constrained codebook comprises optimization of the number of codebook entries that are added in each step, also depends on the order in which the scenarios are treated, picking at each step the scenario which requires a smaller codebook for a given performance with respect to other remaining scenarios.