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 approximate channel covariance matrix {circumflex over (R)} comprises R H † H≈PDP † {circumflex over (R)}, where D=diag{λ 1 , . . . , λ r }, complex matrix H is an uplink (UL) channel, and (•)† denotes the matrix conjugate transpose.

2. The method of claim 1 , 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 † {circumflex over (R)}G) −1 G † {circumflex over (R)}G] i,i , Θ≈(I+G † {circumflex over (R)}G) −1 G † {circumflex over (R)}G, and I is an identity matrix.

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

G

′

=

arg

⁢

⁢

max

G

∈

g

n

T

×

r

′

⁢

∑

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 , SINR i 1 (G′) is the signal-to-interference-plus-noise ratio (SINR) for the ith layer at a receiver, and G is a precoding matrix.

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

g

′

=

arg

⁢

⁢

max

g

∈

𝒢

n

⁢

T

×

1

⁢

g

†

⁢

H

†

⁢

Hg

,

where g n T × r ′ is a finite set, and G′ is obtained by searching from all elements in the set.

5. 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 † {circumflex over (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=4 and r′=2, said precoding selection for maximizing

g

†

⁢

R

^

⁢

g

=

∑

t

=

1

r

⁢

⁢

λ

t

⁢



g

†

⁢

p

t



2

,

where

g

∈

G

n

T

×

1

,

G

n

T

×

1

is a complex matrix space of dimensions n T ×1 , p t denotes the tth column of known precoding matrix P, {circumflex over (R)} denotes an approximate channel covariance matrix, λ t denotes an indices of pairing, and (•)† denotes the matrix conjugate transpose.

6. The method of claim 5 , 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

=

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.

7. The method of claim 5 , 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 554 {circumflex over (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.

8. The method of claim 5 , 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.