Precoder codebook for advanced wireless communication systems
A method for operating user equipment (UE) in an advanced wireless communication network. The method comprises receiving, from an eNodeB (eNB), downlink signals indicating precoder codebook parameters that include a first number of antenna ports (N 1 ) for a first dimension, a second number of antenna ports (N 2 ) for a second dimension, and a codebook configuration, swapping precoder matrix indicator (PMI) expressions based on the N 1 and N 2 , and the codebook configuration in order to derive a first PMI pair (i 1,1 , i 1,2 ), and a second PMI (i 2 ) using a single precoder codebook, and transmitting, to the eNB, channel state information (CSI) including the first PMI pair and the second PMI.
1. A user equipment (UE) in a wireless communication system, the UE comprising:
a transceiver configured to receive, from an eNodeB (eNB), downlink signals indicating precoder codebook parameters that include a first number of antenna ports (N 1 ) for a first dimension, a second number of antenna ports (N 2 ) for a second dimension, and a codebook configuration; and
at least one processor configured to swap precoder matrix indicator (PMI) expressions based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), and the codebook configuration in order to derive a first PMI pair (i 1,1 , i 1,2 ), and a second PMI (i 2 ) using a single precoder codebook, wherein the transceiver is further configured to transmit, to the eNB, channel state information (CSI) including the first PMI pair and the second PMI.
2. The UE of claim 1 , wherein the at least one processor is further configured to:
identify a pair of parameters (d 1 , d 2 ) based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ); and
parameterize a codebook table based on the identified pair of parameters (d 1 , d 2 ).
3. The UE of claim 2 , wherein the identified pair of parameters (d 1 , d 2 ) are defined as at least one of:
(d 1 , d 2 )=(1, 2) when the first number of antenna ports (N 1 ) is greater or equal to the N 2 ; or
(d 1 , d 2 )=(2, 1) when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ).
4. The UE of claim 3 , wherein the at least one processor is further configured to determine dummy variables including x and y based on a pair of parameters (d 1 , d 2 ) in accordance with the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), the dummy variables being determined as:
x=i 1,d1 and y=i 1,d2 .
5. The UE of claim 1 , wherein:
the swapped PMI expressions in a rank 1 codebook and a rank 2 codebook for a codebook configuration 3 and a codebook configuration 4 comprise an order of (m 1 , m 2 ) based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), and wherein m 1 is an index of a first discrete Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, and (m 1 , m 2 ) is an index pair of a two-dimensional DFT vector (w m 1 ,m 2 ) representing a beam,
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
a range of m 1 is
0
,
1
,
…
,
N
1
O
1
2
-
1
and a range of m 2 is
0
,
1
,
…
,
N
2
O
2
2
-
1
,
and
and O 1 is a first oversampling factor for the first dimension and O 2 is a second oversampling factor for the second dimension.
6. The UE of claim 5 , wherein the order of (m 1 , m 2 ) is defined as at least one of:
(m 1 , m 2 ) when the first number of antenna ports (N 1 ) is greater than or equal to the second number of antenna ports (N 2 ); or
(m 2 , m 1 ) when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ).
7. The UE of claim 6 , wherein,
when the first number of antenna ports (N 1 ) is greater than or equal to the second number of antenna ports (N 2 ), a rank 1 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
;
and a rank 2 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
;
and
when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 1 ), a rank 1 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
;
and a rank 2 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
ϕ
n
w
m
2
,
m
1
-
ϕ
n
w
m
2
′
,
m
1
′
]
,
where Q=2N 1 N 2 and ϕ n =e jπn/2 .
8. The UE of claim 4 , wherein a rank 1 codebook for a codebook configuration 3 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
2
3
W 2x,2y,0 (1)
W 2x,2y,1 (1)
W 2x,2y,2 (1)
W 2x,2y,3 (1)
i 2
4
5
6
7
W 2x+2,2y,0 (1)
W 2x+2,2y,1 (1)
W 2x+2,2y,2 (1)
W 2x+2,2y,3 (1)
i 2
8
9
10
11
W 2x+1,2y+1,0 (1)
W 2x+1,2y+1,1 (1)
W 2x+1,2y+1,2 (1)
W 2x+1,2y+1,3 (1)
i 2
12
13
14
15
W 2x+3,2y+1,0 (1)
W 2x+3,2y+1,1 (1)
W 2x+3,2y+1,2 (1)
W 2x+3,2y+1,3 (1)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
,
if
N
1
≥
N
2
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
,
if
N
1
<
N
2
;
and
the rank 1 codebook for a codebook configuration 4 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
2
3
W 2x,2y,0 (1)
W 2x,2y,1 (1)
W 2x,2y,2 (1)
W 2x,2y,3 (1)
i 2
4
5
6
7
W 2x+1,2y,0 (1)
W 2x+1,2y,1 (1)
W 2x+1,2y,2 (1)
W 2x+1,2y,3 (1)
i 2
8
9
10
11
W 2x+2,2y,0 (1)
W 2x+2,2y,1 (1)
W 2x+2,2y,2 (1)
W 2x+2,2y,3 (1)
i 2
12
13
14
15
W 2x+3,2y,0 (1)
W 2x+3,2y,1 (1)
W 2x+3,2y,2 (1)
W 2x+3,2y,3 (1)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
,
if
N
1
≥
N
2
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
,
if
N
1
<
N
2
;
wherein m 1 is an index of a first Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, n is an index of a co-phase ϕ n , and
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
where
φ
n
=
e
j
π
n
/
2
.
9. The UE of claim 4 , wherein a rank 2 codebook for a codebook configuration 3 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
W 2x,2x,2y,2y,0 (2)
W 2x,2x,2y,2y,1 (2)
2
3
W 2x+1,2x+1,2y+1,2y+1,0 (2)
W 2x+1,2x+1,2y+1,2y+1,1 (2)
i 2
4
5
W 2x+2,2x+2,2y,2y,0 (2)
W 2x+2,2x+2,2y,2y,1 (2)
6
7
W 2x+3,2x+3,2y+1,2y+1,0 (2)
W 2x+3,2x+3,2y+1,2y+1,1 (2)
i 2
8
9
W 2x,2x+1,2y,2y+1,0 (2)
W 2x,2x+1,2y,2y+1,1 (2)
10
11
W 2x+1,2x+2,2y+1,2y,0 (2)
W 2x+1,2x+2,2y+1,2y,1 (2)
i 2
12
13
W 2x,2x+3,2y,2y+1,0 (2)
W 2x,2x+3,2y,2y+1,1 (2)
14
15
W 2x+1,2x+3,2y+1,2y+1,0 (2)
W 2x+1,2x+3,2y+1,2y+1,1 (2)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
,
if
N
1
≥
N
2
and
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
φ
n
w
m
2
,
m
1
-
φ
n
w
m
2
′
,
m
1
′
]
,
if
N
1
<
N
2
and
the rank 2 codebook for a codebook configuration 4 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
W 2x,2x,2y,2y,0 (2)
W 2x,2x,2y,2y,1 (2)
2
3
W 2x+1,2x+1,2y,2y,0 (2)
W 2x+1,2x+1,2y,2y,1 (2)
i 2
4
5
W 2x+2,2x+2,2y,2y,0 (2)
W 2x+2,2x+2,2y,2y,1 (2)
6
7
W 2x+3,2x+3,2y,2y,0 (2)
W 2x+3,2x+3,2y,2y,1 (2)
i 2
8
9
W 2x,2x+1,2y,2y,0 (2)
W 2x,2x+1,2y,2y,1 (2)
10
11
W 2x+1,2x+2,2y,2y,0 (2)
W 2x+1,2x+2,2y,2y,1 (2)
i 2
12
13
W 2x,2x+3,2y,2y,0 (2)
W 2x,2x+3,2y,2y,1 (2)
14
15
W 2x+1,2x+3,2y,2y,0 (2)
W 2x+1,2x+3,2y,2y,1 (2)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
,
if
N
1
≥
N
2
and
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
φ
n
w
m
2
,
m
1
-
φ
n
w
m
2
′
,
m
1
′
]
,
if
N
1
<
N
2
wherein m 1 is an index of a first Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, n is an index of the co-phase ϕ n , and
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
where
φ
n
=
e
j
π
n
/
2
.
10. An eNodeB (eNB) in a wireless communication system, the eNB comprising:
a transceiver configured to:
transmit downlink signals, to a user equipment (UE), indicating precoder codebook parameters that include a first number of antenna ports (N 1 ) for a first dimension, a second number of antenna ports (N 2 ) for a second dimension, and a codebook configuration; and
receive, from the UE, channel state information (CSI) including a first PMI pair (i 1,1 , i 1,2 ) and a second PMI (i 2 ); and
at least one processor configured to swap precoder matrix indicator (PMI) expressions based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), and the codebook configuration in order to reconstruct a PMI precoder using a single precoder codebook based on the received first PMI pair and second PMI.
11. The eNB of claim 10 , wherein the at least one processor is further configured to:
identify a pair of parameters (d 1 , d 2 ) based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ); and
parameterize a codebook table based on the identified pair of parameters (d 1 , d 2 ), wherein the identified pair of parameters (d 1 , d 2 ) is defined as at least one of:
(d 1 , d 2 )=(1, 2) when the first number of antenna ports (N 1 ) is greater or equal to the second number of antenna ports (N 2 ); or
(d 1 , d 2 )=(2, 1) when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ); and
determine dummy variables including x and y based on the identified pair of parameters (d 1 , d 2 ) in accordance with the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), the dummy variables being determined as:
x=i 1,d1 and y=i 1,d2 .
12. A method for operating user equipment (UE) in a wireless communication system, the method comprising:
receiving, from an eNodeB (eNB), downlink signals indicating precoder codebook parameters that include a first number of antenna ports (N 1 ) for a first dimension, a second number of antenna ports (N 2 ) for a second dimension, and a codebook configuration;
swapping precoder matrix indicator (PMI) expressions based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ), and the codebook configuration in order to derive a first PMI pair (i 1,1 , i 1,2 ), and a second PMI (i 2 ) using a single precoder codebook; and
transmitting, to the eNB, channel state information (CSI) including the first PMI pair and the second PMI.
13. The method of claim 12 , further comprising:
identifying a pair of parameters (d 1 , d 2 ) based on the first number of antenna ports (N 1 ) and the second number of antenna ports (N 2 ); and
parameterizing a codebook table based on the identified pair of parameters (d 1 , d 2 ).
14. The method of claim 13 , wherein the identified pair of parameters (d 1 , d 2 ) are defined as at least one of:
(d 1 , d 2 )=(1, 2) when the first number of antenna ports (N 1 ) is greater or equal to the second number of antenna ports (N 2 ); or
(d 1 , d 2 )=(2, 1) when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ).
15. The method of claim 14 , further comprising determining dummy variables including x and y based on a pair of parameters (d 1 , d 2 ) in accordance with the first number of antenna ports (N 1 ) and second number of antenna ports (N 2 ), the dummy variables being determined as:
x=i 1,d1 and y=i 1,d2 .
16. The method of claim 12 , wherein:
the swapped PMI expressions in a rank 1 codebook and a rank 2 codebook for a codebook configuration 3 and a codebook configuration 4 comprise an order of (m 1 , m 2 ) based on the first number of antenna ports (N 1 ) and second number of antenna ports (N 2 ), and wherein m 1 is an index of a first discrete Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, and (m 1 , m 2 ) is an index pair of a two-dimensional DFT vector (w m 1 ,m 2 ) representing a beam,
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
a range of m 1 is
0
,
1
,
…
,
N
1
O
1
2
-
1
and a range of m 2 is
0
,
1
,
…
,
N
2
O
2
2
-
1
,
and
O 1 is a first oversampling factor for the first dimension and O 2 is a second oversampling factor for the second dimension.
17. The method of claim 16 , wherein the order of (m 1 , m 2 ) is defined as at least one of:
(m 1 , m 2 ) when the first number of antenna ports (N 1 ) is greater than or equal to the second number of antenna ports (N 2 ); or
(m 2 , m 1 ) when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ).
18. The method of claim 17 , wherein:
when the first number of antenna ports (N 1 ) is greater than or equal to the second number of antenna ports (N 2 ), a rank 1 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
;
and a rank 2 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
;
and
when the first number of antenna ports (N 1 ) is less than the second number of antenna ports (N 2 ), the rank 1 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
;
and a rank 2 precoder based on the swapped PMI expressions is determined as:
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
ϕ
n
w
m
2
,
m
1
-
ϕ
n
w
m
2
′
,
m
1
′
]
,
where Q=2N 1 N 2 and ϕ n =e jπn/2 .
19. The method of claim 15 , wherein a rank 1 codebook for a codebook configuration 3 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
2
3
W 2x,2y,0 (1)
W 2x,2y,1 (1)
W 2x,2y,2 (1)
W 2x,2y,3 (1)
i 2
4
5
6
7
W 2x+2,2y,0 (1)
W 2x+2,2y,1 (1)
W 2x+2,2y,2 (1)
W 2x+2,2y,3 (1)
i 2
8
9
10
11
W 2x+1,2y+1,0 (1)
W 2x+1,2y+1,1 (1)
W 2x+1,2y+1,2 (1)
W 2x+1,2y+1,3 (1)
i 2
12
13
14
15
W 2x+3,2y+1,0 (1)
W 2x+3,2y+1,1 (1)
W 2x+3,2y+1,2 (1)
W 2x+3,2y+1,3 (1)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
,
if
N
1
≥
N
2
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
,
if
N
1
<
N
2
;
and
the rank 1 codebook for a codebook configuration 4 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
2
3
W 2x,2y,0 (1)
W 2x,2y,1 (1)
W 2x,2y,2 (1)
W 2x,2y,3 (1)
i 2
4
5
6
7
W 2x+1,2y,0 (1)
W 2x+1,2y,1 (1)
W 2x+1,2y,2 (1)
W 2x+1,2y,3 (1)
i 2
8
9
10
11
W 2x+2,2y,0 (1)
W 2x+2,2y,1 (1)
W 2x+2,2y,2 (1)
W 2x+2,2y,3 (1)
i 2
12
13
14
15
W 2x+3,2y,0 (1)
W 2x+3,2y,1 (1)
W 2x+3,2y,2 (1)
W 2x+3,2y,3 (1)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
1
,
m
2
φ
n
w
m
1
,
m
2
]
,
if
N
1
≥
N
2
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
n
(
1
)
=
1
Q
[
w
m
2
,
m
1
φ
n
w
m
2
,
m
1
]
,
if
N
1
<
N
2
;
wherein m 1 is an index of a first discrete Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, n is an index of the co-phase ϕ n , and
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
where
φ
n
=
e
j
π
n
/
2
.
20. The method of claim 15 , wherein a rank 2 codebook for a codebook configuration 3 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
W 2x,2x,2y,2y,0 (2)
W 2x,2x,2y,2y,1 (2)
2
3
W 2x+1,2x+1,2y+1,2y+1,0 (2)
W 2x+1,2x+1,2y+1,2y+1,1 (2)
i 2
4
5
W 2x+2,2x+2,2y,2y,0 (2)
W 2x+2,2x+2,2y,2y,1 (2)
6
7
W 2x+3,2x+3,2y+1,2y+1,0 (2)
W 2x+3,2x+3,2y+1,2y+1,1 (2)
i 2
8
9
W 2x,2x+1,2y,2y+1,0 (2)
W 2x,2x+1,2y,2y+1,1 (2)
10
11
W 2x+1,2x+2,2y+1,2y,0 (2)
W 2x+1,2x+2,2y+1,2y,1 (2)
i 2
12
13
W 2x,2x+3,2y,2y+1,0 (2)
W 2x,2x+3,2y,2y+1,1 (2)
14
15
W 2x+1,2x+3,2y+1,2y+1,0 (2)
W 2x+1,2x+3,2y+1,2y+1,1 (2)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
,
if
N
1
≥
N
2
and
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
φ
n
w
m
2
,
m
1
-
φ
n
w
m
2
′
,
m
1
′
]
,
if
N
1
<
N
2
and
the rank 2 codebook for a codebook configuration 4 is determined based on the dummy variables including the x and y according to a following codebook table:
i 2
0
1
W 2x,2x,2y,2y,0 (2)
W 2x,2x,2y,2y,1 (2)
2
3
W 2x+1,2x+1,2y,2y,0 (2)
W 2x+1,2x+1,2y,2y,1 (2)
i 2
4
5
W 2x+2,2x+2,2y,2y,0 (2)
W 2x+2,2x+2,2y,2y,1 (2)
6
7
W 2x+3,2x+3,2y,2y,0 (2)
W 2x+3,2x+3,2y,2y,1 (2)
i 2
8
9
W 2x,2x+1,2y,2y,0 (2)
W 2x,2x+1,2y,2y,1 (2)
10
11
W 2x+1,2x+2,2y,2y,0 (2)
W 2x+1,2x+2,2y,2y,1 (2)
i 2
12
13
W 2x,2x+3,2y,2y,0 (2)
W 2x,2x+3,2y,2y,1 (2)
14
15
W 2x+1,2x+3,2y,2y,0 (2)
W 2x+1,2x+3,2y,2y,1 (2)
where
x
=
i
1
,
1
,
y
=
i
1
,
2
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
1
,
m
2
w
m
1
′
,
m
2
′
φ
n
w
m
1
,
m
2
-
φ
n
w
m
1
′
,
m
2
′
]
,
if
N
1
≥
N
2
and
x
=
i
1
,
2
,
y
=
i
1
,
1
,
W
m
1
,
m
2
,
m
1
′
,
m
2
′
,
n
(
2
)
=
1
2
Q
[
w
m
2
,
m
1
w
m
2
′
,
m
1
′
φ
n
w
m
2
,
m
1
-
φ
n
w
m
2
′
,
m
1
′
]
,
if
N
1
<
N
2
wherein m 1 is an index of a first discrete Fourier transform (DFT) vector representing a beam for the first dimension, m 2 is an index of a second DFT vector representing a beam for the second dimension, n is an index of the co-phase ϕ n , and
w
m
1
,
m
2
=
[
u
m
2
e
j
2
π
m
1
O
1
N
1
u
m
2
…
e
j
2
π
m
1
(
N
1
-
1
)
O
1
N
1
u
m
2
]
T
where
u
m
2
=
[
1
e
j
2
π
m
2
O
2
N
2
…
e
j
2
π
m
2
(
N
2
-
1
)
O
2
N
2
]
,
where
φ
n
=
e
j
π
n
/
2
.