Codebook construction
View Patent ↗A method implemented in a base station used in a wireless communications system is disclosed. The method comprises having a codebook including a plurality of precoding matrices, precoding data with one of the plurality of precoding matrices, and transmitting, to a user equipment, the precoded data, wherein each precoding matrix W satisfies W=W (1) W (2) , where first matrix W (1) is chosen from first codebook (1) , and second matrix W (2) is chosen from a second codebook. Other apparatuses, systems, and methods also are disclosed.
1. A method implemented in a base station used in a wireless communications system, the method comprising:
having a codebook including a plurality of precoding matrices;
precoding data with one of the plurality of precoding matrices; and
transmitting, to a user equipment, the precoded data,
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
;
k
=
0
,
…
,
L
-
1
;
q
1
=
1
,
…
,
Q
1
}
,
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . , L−1,
w n =[1 exp(j2πn/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(
L
-
1
)
K
≤
N
≤
LK
and
K
≤
L
N
is
the
number
of
transmit
antennas
,
A
(
q
1
)
=
[
1
0
0
exp
(
j
2
π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j
2
π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j
=
-
1
,
a
q
1
m
,
b
q
1
m
,
d
q
1
∈
[
0
,
1
]
,
and
(
a
q
1
m
)
2
+
(
b
q
1
m
)
2
=
1
/
2
∀
m
,
q
1.
2. The method as in claim 1 , wherein the second codebook for rank-1 transmission can be expressed as
𝒞
~
1
(
2
)
=
{
W
(
2
,
1
)
(
r
,
s
,
q
2
)
=
[
e
r
exp
(
j2γ
q
2
)
e
s
]
,
[
e
r
-
exp
(
j2π
γ
q
2
)
e
s
]
,
[
e
r
j
exp
(
j2πγ
q
2
)
e
s
]
,
[
e
r
-
jexp
(
j2πγ
q
2
)
e
s
]
}
,
where r,s={1, . . . , J}, q2ε{1 . . . , Q2}, γ q2 ε[0,1]∀q2, and
e i denotes the J×1 column selection vector selecting the i th column in the J×J identity matrix.
3. The method as in claim 2 , wherein part of feasible combinations (r, s, q2) are allowed.
4. The method as in claim 1 , wherein the second codebook for rank-2 transmission can be expressed as
𝒞
2
(
2
)
=
{
W
(
2
,
2
)
(
r
,
s
)
=
[
e
r
e
s
e
r
-
e
s
]
,
[
e
r
e
s
j
e
r
-
j
e
S
]
}
,
where r, s={1, . . . , J}, and
e i denotes the J×1 column selection vector selecting the i th column in the J×J identity matrix.
5. The method as in claim 4 , wherein part of feasible combinations (r, s) are allowed.
6. The method as in claim 4 , wherein r=s.
7. The method as in claim 1 , wherein the second codebook for rank-2 transmission can be expressed as
{
W
(
2
,
2
)
(
r
,
s
,
k
,
q
1
,
q
2
)
=
[
e
r
e
s
exp
(
j2πγ
q
2
)
-
exp
(
j2πγ
q
2
)
e
s
]
,
[
e
r
e
s
exp
(
j2πγ
q
2
)
e
s
-
exp
(
j2πγ
q
2
)
exp
(
jθ
(
r
,
s
,
k
,
q
1
,
q
2
)
)
e
r
]
[
e
r
e
s
jexp
(
j2πγ
q
2
)
e
r
-
jexp
(
2
πγ
q
2
)
e
s
]
,
[
e
r
e
s
jexp
(
j
2
πγ
q
2
)
e
s
-
jexp
(
j2πγ
q
2
)
exp
(
jθ
(
r
,
s
,
k
,
q
1
,
q
2
)
)
e
r
]
}
where r,sε{1, . . . , J},q2ε{1 . . . , Q2}, γ q2 ε[0,1]∀q2,
θ denotes a phase, and
e i denotes the J×1 column selection vector selecting the i th column in the J×J identity matrix.
8. The method as in claim 7 , wherein part of feasible combinations (r, s, q2) are allowed.
9. The method as in claim 1 , wherein A(q1)=B (q1).
10. The method as in claim 1 , wherein 2π(d q+1 −d q ) is small in comparison with 2π/N.
11. The method as in claim 1 , wherein the codebook consists of the plurality of precoding matrices.
12. The method as in claim 1 , wherein the first matrix is common across a plurality of subbands and the second matrix is for each subband.
13. The method as in claim 1 , wherein the codebook is for 4 transmit antenna (4TX) transmission.
14. The method as in claim 1 , wherein J=4.
15. A method implemented in a user equipment used in a wireless communications system, the method comprising:
receiving, from a base station, data precoded with one of a plurality of precoding matrices,
wherein a codebook includes the plurality of precoding matrices, and
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
;
k
=
0
,
…
,
L
-
1
;
q
1
=
1
,
…
,
Q
1
}
,
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . ,L−1,
w n =[1 exp(j2πm/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(L−1)K≦N≦LK and K≦J,
N is the number of transmit antennas,
A
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j=√{square root over (−1)},
a q1 m ,b q1 m ,d q1 ε[0,1], and
(a q1 m ) 2 +(b q1 m ) 2 =½∀m,q1.
16. A base station used in a wireless communications system, the base station comprising:
a transmitter to transmit, to a user equipment, data precoded with one of a plurality of precoding matrices,
wherein a codebook includes the plurality of precoding matrices, and
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
:
k=0, . . . ,L−1:q1=1, . . . , Q1},
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . ,L−1,
w n =[1 exp(j2πm/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(L−1)K≦N≦LK and K≦J,
N is the number of transmit antennas,
A
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j=√{square root over (−1)},
a q1 1 ,b q1 m ,d d1 ε[0,1], and
(a q1 m ) 2 +(b q1 m ) 2 =½∀m,q1.
17. A user equipment used in a wireless communications system, the user equipment comprising:
a receiver to receive, from a base station, data precoded with one of a plurality of precoding matrices,
wherein a codebook includes the plurality of precoding matrices, and
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
:
k=0, . . . ,L−1:q1=1, . . . , Q1},
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . ,L−1,
w n =[1 exp(j2πm/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(L−1)K≦N≦LK and K≦J,
N is the number of transmit antennas,
A
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j=√{square root over (−1)},
a q1 1 ,b q1 m ,d d1 ε[0,1], and
(a q1 m ) 2 +(b q1 m ) 2 =½∀m,q1.
18. A wireless communications system comprising:
a base station having a codebook including a plurality of precoding matrices and precoding data with one of the plurality of precoding matrices; and
a user equipment receiving, from the base station, the precoded data,
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
:
k=0, . . . ,L−1:q1=1, . . . , Q1},
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . ,L−1,
w n =[1 exp(j2πm/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(L−1)K≦N≦LK and K≦J,
N is the number of transmit antennas,
A
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j=√{square root over (−1)},
a q1 1 ,b q1 m ,d d1 ε[0,1], and
(a q1 m ) 2 +(b q1 m ) 2 =½∀m,q1.
19. A method implemented in a wireless communications system, the method comprising:
precoding data with one of the plurality of precoding matrices; and
transmitting, from a base station to a user equipment, the precoded data,
wherein a codebook includes the plurality of precoding matrices, and
wherein each precoding matrix W satisfies W=W (1) W (2) ,
where first matrix W (1) is chosen from first codebook (1) , and
second matrix W (2) is chosen from a second codebook, and
wherein
C
(
1
)
=
{
W
(
1
)
(
k
,
q
1
)
=
[
A
(
q
1
)
⊙
W
(
1
)
(
k
)
0
0
B
(
q
1
)
⊙
W
(
1
)
(
k
)
]
:
k=0, . . . ,L−1:q1=1, . . . , Q1},
where ⊙ denotes Hadamard product,
W (1) (k)=[w kK , . . . ,w kK+J−1 ],k=0, . . . ,L−1,
w n =[1 exp(j2πm/N)] T for n=0, . . . ,N−1,
J, K, and L are positive integers,
(L−1)K≦N≦LK and K≦J,
N is the number of transmit antennas,
A
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
a
q
1
1
a
q
1
2
…
a
q
1
J
b
q
1
1
b
q
1
2
…
b
q
1
J
]
,
B
(
q
1
)
=
[
1
0
0
exp
(
j2π
d
q
1
)
]
[
b
q
1
1
b
q
1
2
…
b
q
1
J
a
q
1
1
a
q
1
2
…
a
q
1
J
]
,
j=√{square root over (−1)},
a q1 1 ,b q1 m ,d d1 ε[0,1], and
(a q1 m ) 2 +(b q1 m ) 2 =½∀m,q1.