Codebook with nested structure
View Patent ↗A multi-rank beamforming (MRBF) scheme in which the downlink channel is estimated and an optimal precoding matrix to be used by the MRBF transmitter is determined accordingly. The optimal precoding matrix is selected from a codebook of matrices having a recursive structure which allows for efficient computation of the optimal precoding matrix and corresponding Signal to Interference and Noise Ratio (SINR). The codebook also enjoys a small storage footprint. Due to the computational efficiency and modest memory requirements, the optimal precoding determination can be made at user equipment (UE) and communicated to a transmitting base station over a limited uplink channel for implementation over the downlink channel.
1. A transmitter used in a wireless communications system, the transmitter comprising:
a precoding unit to precode a symbol with a precoding matrix selected from a codebook comprising a plurality of matrices; and
a transmission unit to transmit to a receiver the precoded symbol using at least two transmit antennas,
wherein the plurality of matrices have a nested structure and are in accordance with the following expression:
A
(
v
i
1
1
,
v
i
2
2
,
v
i
3
3
,
…
)
=
[
v
i
1
1
,
H
(
v
i
1
1
e
1
M
)
[
0
v
i
2
2
]
,
H
(
v
i
1
1
e
1
M
)
[
0
HH
(
v
i
2
2
-
e
1
M
-
1
)
[
0
v
i
3
3
]
]
,
…
]
,
wherein e 1 N =[1,0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space, and
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
and {v i j j εC M−j+1 } is a vector codebook, and
wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.
2. The transmitter as in claim 1 , wherein the transmitter comprises a base station and the receiver comprises a user equipment (UE).
3. The transmitter as in claim 1 , wherein the transmission is downlink transmission.
4. The transmitter as in claim 1 , wherein v i a is selected from a set V a where V 1 ={v i 1 εC M } i=1 N 1 , V 2 ={e 1 M−1 }, V 3 ={e 1 M−1 }, . . . .
5. The transmitter as in claim 1 , further comprising:
a deriving unit to derive the precoding matrix by picking k columns of one of the plurality of matrices for rank-k transmission.
6. The transmitter as in claim 1 , wherein the number of transmit antennas is 2 or 4.
7. The transmitter as in claim 5 , wherein the number of selected columns to form the precoding matrix is less than the number of transmit antennas.
8. The transmitter as in claim 5 , wherein all the columns are selected to form the precoding matrix.
9. A receiver used in a wireless communications system, the receiver comprising:
a receiving unit to receive from a transmitter a symbol precoded with a precoding matrix and transmitted using at least two transmit antennas,
wherein the precoded matrix is selected from a codebook comprising a plurality of matrices which have a nested structure and are in accordance with the following expression:
A
(
v
i
1
1
,
v
i
2
2
,
v
i
3
3
,
…
)
=
[
v
i
1
1
,
H
(
v
i
1
1
e
1
M
)
[
0
v
i
2
2
]
,
H
(
v
i
1
1
e
1
M
)
[
0
HH
(
v
i
2
2
-
e
1
M
-
1
)
[
0
v
i
3
3
]
]
,
…
]
,
wherein e 1 N =[1,0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space, and
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
and {v i j j εC M−j+1 } is a vector codebook, and
wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.
10. The receiver as in claim 9 , wherein the transmitter comprises a base station and the receiver comprises a user equipment (UE).
11. The receiver as in claim 9 , wherein the reception is downlink reception.
12. The receiver as in claim 9 , wherein v i a is selected from a set V a where V 1 ={v i 1 εC M } i=1 N 1 , V 2 ={e 1 M−1 }, V 3 ={e 1 M−1 }, . . . .
13. The receiver as in claim 9 , wherein the precoding matrix is derived by picking k columns of one of the plurality of matrices for rank-k transmission.
14. The receiver as in claim 9 , wherein the number of transmit antennas is 2 or 4.
15. The receiver as in claim 13 , wherein the number of selected columns to form the precoding matrix is less than the number of transmit antennas.
16. The receiver as in claim 13 , wherein all the columns are selected to form the precoding matrix.
17. A receiver used in a wireless communications system, the receiver comprising:
a generation unit to generate feedback information by selecting a precoding matrix from a codebook comprising a plurality of matrices; and
a providing unit to provide to a transmitter the feedback information,
wherein the transmitter uses at least two transmit antennas for transmission,
wherein the plurality of matrices have a nested structure and are in accordance with the following expression:
A
(
v
i
1
1
,
v
i
2
2
,
v
i
3
3
,
…
)
=
[
v
i
1
1
,
H
(
v
i
1
1
e
1
M
)
[
0
v
i
2
2
]
,
H
(
v
i
1
1
e
1
M
)
[
0
HH
(
v
i
2
2
-
e
1
M
-
1
)
[
0
v
i
3
3
]
]
,
…
]
,
wherein e 1 N =[1,0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space, and
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
and {v i j j εC M−j+1 } is a vector codebook, and
wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.
18. The receiver as in claim 17 , wherein the transmitter comprises a base station and the receiver comprises a user equipment (UE).
19. The receiver as in claim 17 , wherein the transmission is downlink transmission.
20. The receiver as in claim 17 , wherein v i a is selected from a set V a where V 1 ={v i 1 εC M } i=1 N 1 , V 2 ={e 1 M−1 }, V 3 ={e 1 M−1 }, . . . .
21. The receiver as in claim 17 , further comprising:
a deriving unit to derive the precoding matrix by picking k columns of one of the plurality of matrices for rank-k transmission.
22. The receiver as in claim 17 , wherein the number of transmit antennas is 2 or 4.
23. The receiver as in claim 21 , wherein the number of selected columns to form the precoding matrix is less than the number of transmit antennas.
24. The receiver as in claim 21 , wherein all the columns are selected to form the precoding matrix.
25. A wireless communications system comprising:
a transmitter to transmit a symbol precoded with a precoding matrix selected from a codebook comprising a plurality of matrices; and
a receiver to receive from the transmitter the precoded symbol using at least two transmit antennas,
wherein the plurality of matrices have a nested structure and are in accordance with the following expression:
A
(
v
i
1
1
,
v
i
2
2
,
v
i
3
3
,
…
)
=
[
v
i
1
1
,
H
(
v
i
1
1
e
1
M
)
[
0
v
i
2
2
]
,
H
(
v
i
1
1
e
1
M
)
[
0
HH
(
v
i
2
2
-
e
1
M
-
1
)
[
0
v
i
3
3
]
]
,
…
]
,
wherein e 1 N =[1,0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space, and
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
and
{v i j j εC M−j+1 } is a vector codebook, and
wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.
26. The wireless communications system as in claim 25 , wherein the transmitter comprises a base station and the receiver comprises a user equipment (UE).
27. The wireless communications system as in claim 25 , wherein the transmission is downlink transmission.
28. A wireless communications system comprising:
a receiver to provide feedback information generated by selecting a precoding matrix from a codebook comprising a plurality of matrices; and
a transmitter to receive the feedback information,
wherein the transmitter uses at least two transmit antennas for transmission,
wherein the plurality of matrices have a nested structure and are in accordance with the following expression:
A
(
v
i
1
1
,
v
i
2
2
,
v
i
3
3
,
…
)
=
[
v
i
1
1
,
H
(
v
i
1
1
e
1
M
)
[
0
v
i
2
2
]
,
H
(
v
i
1
1
e
1
M
)
[
0
HH
(
v
i
2
2
-
e
1
M
-
1
)
[
0
v
i
3
3
]
]
,
…
]
,
wherein e 1 N =[1,0, . . . , 0] T εC N , M is the number of transmit antennas, C N is an N-dimensional complex space, and
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
and {v i j j εC M−j+1 } is a vector codebook, and
wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.
29. The wireless communications system as in claim 28 , wherein the transmitter comprises a base station and the receiver comprises a user equipment (UE).
30. The wireless communications system as in claim 28 , wherein the transmission is downlink transmission.