Precoding selection for retransmission in uplink MIMO hybrid ARQ

1. A method implemented in a user terminal, the method comprising:

obtaining known precoding matrix P of rank r and modulation and coding scheme assignments used in an original transmission, and a desired retransmission rank r′;

forming an approximate channel covariance matrix;

estimating a minimum mean square error receiver SINR for each layer to be retransmitted responsive to said forming; and

finding a retransmission precoding matrix from a preceding codebook that maximizes a sum-rate for enabling precoding selections for retransmissions in uplink multiple-input multiple-output MIMO hybrid automatic repeat request HARQ,

wherein said estimated minimum mean square error receiver SINR for each layer SINR′ i comprises

SIN

⁢

⁢

R

i

′

⁡

(

G

′

)

=

Ξ

i

,

i

1

-

Ξ

i

,

i

≈

α

i

1

-

α

i

 where G is a precoding matrix of rank r,

α

i

=

[

(

I

+

G

†

⁢

R

^

⁢

G

)

-

1

⁢

G

†

⁢

R

^

⁢

G

]

i

,

i

,

Ξ

≈

(

I

+

G

†

⁢

R

^

⁢

G

)

-

1

⁢

G

†

⁢

R

^

⁢

G

,

 and I is an identity matrix.

2. The method of claim 1 , wherein said retransmission precoding matrix G′ from a preceding codebook comprises

G

′

=

arg

⁢

⁢

∑

i

=

1

r

′

⁢

log

2

⁡

(

1

+

SIN

⁢

⁢

R

i

′

⁡

(

G

)

)

,

where

ℊ

n

T

×

r

is a complex matrix space of dimensions

n

T

×

r

,

SIN

⁢

⁢

R

i

′

⁡

(

G

′

)

is me signal-to-interference-plus-noise ratio (SINR) for the ith layer at a receiver, and G is a precoding matrix.

3. The method of claim 2 , wherein for a retransmission rank r′=1, said retransmission precoding matrix G′=g′ comprises

g

′

=

arg

⁢

⁢

g

†

⁢

H

†

⁢

Hg

,

where

ℊ

n

T

×

r

′

is a finite set, and G′ is obtained by searching from all elements in the set.

4. A method implemented in a user terminal, the method comprising:

obtaining known precoding matrix P of rank r in an uplink (UL) codebook in Long Term Evolution Advanced (LTE-A) standards and modulation and coding scheme assignments used in an original transmission, and a desired retransmission rank r′;

for precoding selection for transmit antennas n T =2 and desired retransmission rank r′=1, determining a receiver SINR for a given precoder; and

obtaining a precoding selection for transmit antennas n T =4 and a transmission rank r and desired retransmission rank r′ combination responsive to at least one of maximizing determination of

g

†

⁢

R

^

⁢

g

 and lookup information in the UL codebook in said LTE-A standards,

wherein for said transmit antennas n T =4 and a transmission rank r and desired retransmission rank r′ combination of r=3 and r′=1, said precoding selection for maximizing

g

†

⁢

R

^

⁢

g

=

g

†

⁢

R

^

⁢

g

=

λ

1

⁢



g

†

⁢

p

1



2

+

ζ

⁡

(

λ

2

-

λ

3

)

,

 where p 1 denotes the 1st column of known precoding matrix P, {circumflex over (R)} denotes an approximate channel covariance matrix, λ t denotes an indices of pairing.

5. The method of claim 4 , wherein for said transmit antennas n T =4 and a transmission rank r and desired retransmission rank r′ combination of r=2 and r′=1, said precoding selection for maximizing

g

†

⁢

R

^

⁢

g

=

g

†

⁢

R

^

⁢

g

=

λ

1

⁢



g

†

⁢

p

1



2

+

λ

2

⁢



g

†

⁢

p

2



2

,

where p 1 denotes the 1st column of known precoding matrix P, {circumflex over (R)} denotes an approximate channel covariance matrix, λ t denotes an indices of pairing.

6. The method of claim 4 , wherein when said precoding selection is not unique, said obtaining uses said precoding selection with the lowest index of the corresponding UL codebook in said LTE-A standards.