Method and apparatus to enable multi-resolution CSI reporting in advanced wireless communication systems
A method of user equipment (UE) for channel state information (CSI) feedback in a wireless communication system. The method comprises receiving, from a base station (BS), CSI feedback configuration information for a pre-coding matrix indicator (PMI) feedback indicating a linear combination (LC) pre-coding matrix that corresponds to a linear combination of a plurality of L beams and a plurality of coefficients, determining the first PMI (i 1 ) and the second PMI (i 2 ), and transmitting, to the BS, the CSI feedback including the first PMI (i 1 ) and the second PMI (i 2 ) over an uplink channel.
1. A user equipment (UE) for channel state information (CSI) feedback in a wireless communication system, the UE comprising:
a transceiver configured to receive, from a base station (BS), configuration information for the CSI feedback, the CSI feedback including pre-coding matrix indicator (PMI) information indicating a pre-coding matrix that corresponds to a sum of L quantities, wherein:
each of the L quantities is a product of a beam and a coefficient,
the coefficients comprise at least an amplitude coefficient and a phase coefficient,
the PMI information includes common components for all layers of a plurality of layers and independent components for each of the plurality of layers, and
the plurality of layers is determined based on a value υ associated with a rank indicator (RI); and
at least one processor configured to determine the PMI information including a first PMI (i 1 ) and a second PMI (i 2 ),
wherein the transceiver is further configured to transmit, to the BS, the CSI feedback including the first PMI (i 1 ) and the second PMI (i 2 ) over an uplink channel.
2. The UE of claim 1 , wherein:
the first PMI (i 1 ) and the second PMI (i 2 ) indicate wideband (WB) and subband (SB) components of the pre-coding matrix, respectively,
the first PMI (i 1 ) includes first and second sets of indicators indicating common WB components for all layers of the plurality of layers and independent WB components for each layer of the plurality of layers, respectively, and
the second PMI (i 2 ) includes a set of indicators indicating independent SB components for each layer of the plurality of layers.
3. The UE of claim 1 , wherein the first PMI (i 1 ) includes a first set of indicators S 1 =[i 1,1 i 1,2 ]indicating beams that comprise common WB components for all layers of the plurality of layers.
4. The UE of claim 1 , wherein the first PMI (i 1 ) includes a second set of indicators
S
2
=
{
[
i
1
,
3
,
1
i
1
,
4
,
1
]
if
υ
=
1
[
i
1
,
3
,
1
i
1
,
4
,
1
i
1
,
3
,
2
i
1
,
4
,
2
]
if
υ
=
2
to indicate independent WB components for each layer of the plurality of υ=1 or υ=2 layers, where:
υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers,
i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the coefficients for each of the first layer and the second layer, respectively, and
i 1,4,1 and i 1,4,2 indicate a plurality of WB amplitude coefficients for each of the first layer and the second layer, respectively.
5. The UE of claim 1 , wherein the second PMI (i 2 ) includes:
a set of indicators
i
2
,
1
=
{
[
i
2
,
1
,
1
]
if
υ
=
1
[
i
2
,
1
,
1
i
2
,
1
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers; and
a set of indicators
i
2
,
2
=
{
[
i
2
,
2
,
1
]
if
υ
=
1
[
i
2
,
2
,
1
i
2
,
2
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers, where:
υ=1 corresponds to a first layer,
υ=2 corresponds to first and second layers,
i 2,1,1 and i 2,1,2 indicate a plurality of SB phase coefficients for each of the first layer and the second layer, respectively, and
i 2,2,1 and i 2,2,2 indicate a plurality of SB amplitude coefficients for each of the first layer and the second layer, respectively.
6. The UE of claim 1 , wherein the amplitude coefficient is determined as given in table:
Indicator
Amplitude coefficient
0
0
1
{square root over ( 1/64)}
2
{square root over ( 1/32)}
3
{square root over ( 1/16)}
4
{square root over (⅛)}
5
{square root over (¼)}
6
{square root over (½)}
7
1.
7. The UE of claim 1 , wherein a codebook for υ=1 and υ=2 is given by:
Layers
v = 1
W q 1 ,q 2 ,n 1 ,n 2 ,p 1 (1) ,p 1 (2) ,i 2,1,1 (1) = W q 1 ,q 2 ,n 1 ,n 2 ,p 1 (1) ,p 1 (2) ,i 2,1,1 1
v = 2
W
q
1
,
q
2
,
n
1
,
n
2
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
(
2
)
=
1
2
[
W
q
1
,
q
2
,
n
1
,
n
2
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
1
W
q
1
,
q
2
,
n
1
,
n
2
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
2
]
where:
W
q
1
,
q
2
,
n
1
,
n
2
,
p
l
(
1
)
,
p
l
(
2
)
,
c
l
l
=
1
N
1
N
2
∑
i
=
0
2
L
-
1
(
p
l
,
i
(
1
)
p
l
,
i
(
2
)
)
2
[
∑
i
=
0
L
-
1
v
m
1
(
i
)
,
m
2
(
i
)
p
l
,
i
(
1
)
p
l
,
i
(
2
)
φ
l
,
i
∑
i
=
0
L
-
1
v
m
1
(
i
)
,
m
2
(
i
)
p
l
,
i
+
L
(
1
)
p
l
,
i
+
L
(
2
)
φ
l
,
i
+
L
]
,
l
=
1
,
2
,
(N 1 , N 2 ) is dual polarized CSI reference signal (CSI-RS) port layout values that determine a number of CSI-RS ports P CSI-RS =2N 1 N 2 at the BS,
V m 1 (i) ,m 2 (i) is i-th of a plurality of L discrete Fourier transform (DFT) beams indicated by i 1,1 and i 1,2 ,
u
m
=
{
[
1
e
j
2
π
m
O
2
N
2
…
e
j
2
π
m
(
N
2
-
1
)
O
2
N
2
]
N
2
>
1
1
N
2
=
1
v
l
,
m
=
[
u
m
e
j
2
π
l
O
1
N
1
u
m
…
e
j
2
π
l
(
N
1
-
1
)
O
1
N
1
u
m
]
T
,
[p l,0 (1) , p l,1 (1) , . . . , p l,2L−1 (1) ] are WB amplitude coefficients for layer l=1, . . . , υ indicated by i 1,3,1 , i 1,3,2 , i 1,4,1 and i 1,4,2 ,
[p l,0 (2) , p l,1 (2) , . . . , p l,2L−1 (2) ] are SB amplitude coefficients for layer l=1, . . . , υ indicated by i 2,2,1 and i 2,2,2 ,
[c l,0 , c l,1 , . . . , c l,2L−1 ] are SB phase coefficient indicator for layer l=1, . . . , υ, indicated by i 2,1,1 and i 2,1,2 , a phase value is given by φ l,i =e j2πc l,i /N PSK , O 1 and O 2 are oversampling factors, NPSK indicates an order of phase shift keying (PSK), and υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers.
8. The UE of claim 7 , wherein the configuration information for the CSI feedback includes a value of the plurality of L DFT beams, a value of a phase alphabet size N PSK , and a value of (N 1 ,N 2 ), and wherein the L is determined as L∈{2,3,4} , the N PSK is determined as N PSK ∈{4,8} , and values for (N 1 , N 2 ) and (O 1 ,O 2 ) are determined as:
Number of CSI-RS ports, P CSI-RS
(N 1 , N 2 )
(O 1 , O 2 )
4
(2, 1)
(4, 1)
8
(2, 2)
(4, 4)
(4, 1)
(4, 1)
12
(3, 2)
(4, 4)
(6, 1)
(4, 1)
16
(4, 2)
(4, 4)
(8, 1)
(4, 1)
24
(4, 3)
(4, 4)
(6, 2)
(4, 4)
(12, 1)
(4, 1)
32
(4, 4)
(4, 4)
(8, 2)
(4, 4)
(16, 1)
(4, 1).
9. The UE of claim 1 , wherein:
the configuration information for the CSI feedback includes a value of L∈ {2,3,4} , a value of N PSK ∈ {4,8}, a value of a number of CSI-RS ports P CSI-RS ∈ {4,8,12,16,24,32} at the BS, and a value of d∈ {1,2,3,4} where
d
≤
min
(
P
CSI
-
RS
2
,
L
)
;
the first PMI (i 1 ) comprises a first set of indicators s 1 =[i 1,1 ] indicating the plurality of L beams out of P CSI-RS /2 antenna port selection where this selection is common for all layers of the plurality of layers; and
a codebook for both υ=1 and υ=2 is given by:
Layers
v = 1
W i 1,1 ,p 1 (1) ,p 1 (2) ,i 2,1,1 (1) = W i 1,1 ,p 1 (1) ,p 1 (2) ,i 2,1,1 1
v = 2
W
i
1
,
1
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
(
2
)
=
1
2
[
W
i
1
,
1
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
1
W
i
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
2
]
where:
W
i
1
,
1
,
p
l
(
1
)
,
p
l
(
2
)
,
i
2
,
1
,
l
l
=
1
∑
i
=
0
2
L
-
1
(
p
l
,
i
(
1
)
p
l
,
i
(
2
)
)
2
[
∑
i
=
0
L
-
1
v
i
1
,
1
d
+
i
p
l
,
i
(
1
)
p
l
.
i
(
2
)
φ
l
,
i
∑
i
=
0
L
-
1
v
i
1
,
1
d
+
i
p
l
,
i
+
L
(
1
)
p
l
,
i
+
L
(
2
)
φ
l
,
i
]
,
l
=
1
,
2
,
v i 1,1 d+i is i-th of the plurality of L selected antenna ports indicated by i 1,1 where v m is a P CSI-RS /2-element column vector containing a value of 1 in element (m mod P CSI-RS /2) and zeros elsewhere where a first element is element 0;
[p l,0 (1) , p l,1 (1) , . . . , p l,2L−1 (1) ] are WB amplitude coefficients for layer l=1, . . . , υ indicated by i 1,3,1 , i 1,3,2 , i 1,4,1 and i 1,4,2 ;
[p l,0 (2) , p l,1 (2) , . . . , p l,2L−1 (2) ] are SB amplitude coefficients for layer l=1, . . . , υ indicated by i 2,2,1 and i 2,2,2 ;
[c l,0 , c l,1 , . . . , c l,2L−1 ] are SB phase coefficient indicator for layer l=1, . . . , υ, indicated by i 2,1,1 and i 2,1,2 ; a phase value is given by φ l,i =e j2πc l,i /N PSK ; and υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers.
10. A method of user equipment (UE) for channel state information (CSI) feedback in a wireless communication system, the method comprising:
receiving, from a base station (BS), configuration information for the CSI feedback, the CSI feedback including pre-coding matrix indicator (PMI) information indicating a pre-coding matrix that corresponds to a sum of L quantities, wherein:
each of the L quantities is a product of a beam and a coefficient,
the coefficients comprises at least an amplitude coefficient and a phase coefficient,
the PMI information includes common components for all layers of a plurality of layers and independent components for each of the plurality of layers, and
the plurality of layers is determined based on a value υ associated with a rank indicator (RI);
determining the PMI information including a first PMI (i 1 ) and a second PMI (i 2 ); and
transmit, to the BS, the CSI feedback including the first PMI (i 1 ) and the second PMI (i 2 ) over an uplink channel.
11. The method of claim 10 , wherein:
the first PMI (i 1 ) and the second PMI (i 2 ) indicate wideband (WB) and subband (SB) components of the pre-coding matrix, respectively,
the first PMI (i 1 ) includes first and second sets of indicators indicating common WB components for all layers of the plurality of layers and independent WB components for each layer of the plurality of layers, respectively, and
the second PMI (i 2 ) includes a set of indicators indicating independent SB components for each layer of the plurality of layers.
12. The method of claim 10 , wherein the first PMI (i 1 ) includes a first set of indicators s 1 =[i 1,1 i 1,2 ] indicating beams that comprise common WB components for all layers of the plurality of layers.
13. The method of claim 10 , wherein the first PMI (i 1 ) includes a second set of indicators
S
2
=
{
[
i
1
,
3
,
1
i
1
,
4
,
1
]
if
υ
=
1
[
i
1
,
3
,
1
i
1
,
4
,
1
i
1
,
3
,
2
i
1
,
4
,
2
]
if
υ
=
2
to indicate independent WB components for each layer of the plurality of υ=1 or υ=2 layers, where:
υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers,
i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the coefficients for each of the first layer and the second layer, respectively, and
i 1,4,1 and i 1,4,2 indicate a plurality of WB amplitude coefficients for each of the first layer and the second layer, respectively.
14. The method of claim 10 , wherein the second PMI (i 2 ) includes:
a set of indicators
i
2
,
1
=
{
[
i
2
,
1
,
1
]
if
υ
=
1
[
i
2
,
1
,
1
i
2
,
1
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers; and
a set of indicators
i
2
,
2
=
{
[
i
2
,
2
,
1
]
if
υ
=
1
[
i
2
,
2
,
1
i
2
,
2
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers, where:
υ=1 corresponds to a first layer,
υ=2 corresponds to first and second layers,
i 2,1,1 and i 2,1,2 indicate a plurality of SB phase coefficients for each of the firs layer and the second layer, respectively, and
i 2,2,1 and i 2,2,2 indicate a plurality of SB amplitude coefficients for each of the first layer and the second layer, respectively.
15. The method of claim 10 , wherein the amplitude coefficient is determined as given in table:
Indicator
Amplitude coefficient
0
0
1
{square root over ( 1/64)}
2
{square root over ( 1/32)}
3
{square root over ( 1/16)}
4
{square root over (⅛)}
5
{square root over (¼)}
6
{square root over (½)}
7
1.
16. The method of claim 10 , wherein a codebook for υ=1 and υ=2 is given by:
Layers
v = 1
W q 1 ,q 2 ,n 1 ,n 2 ,p 1 (1) ,p 1 (2) ,i 2,1,1 (1) = W q 1 ,q 2 ,n 1 ,n 2 ,p 1 (1) ,p 1 (2) ,i 2,1,1 1
v = 2
W
q
1
,
q
2
,
n
1
,
n
2
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
(
2
)
=
1
2
[
W
q
1
,
q
2
,
n
1
,
n
2
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
1
W
q
1
,
q
2
,
n
1
,
n
2
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
2
]
where:
W
q
1
,
q
2
,
n
1
,
n
2
,
p
l
(
1
)
,
p
l
(
2
)
,
c
l
l
=
1
N
1
N
2
∑
i
=
0
2
L
-
1
(
p
l
,
i
(
1
)
p
l
,
i
(
2
)
)
2
[
∑
i
=
0
L
-
1
v
m
1
(
i
)
,
m
2
(
i
)
p
l
,
i
(
1
)
p
l
,
i
(
2
)
φ
l
,
i
∑
i
=
0
L
-
1
v
m
1
(
i
)
,
m
2
(
i
)
p
l
,
i
+
L
(
1
)
p
l
,
i
+
L
(
2
)
φ
l
,
i
+
L
]
,
l
=
1
,
2
,
(N 1 , N 2 ) is dual polarized CSI reference signal (CSI-RS) port layout values that determine a number of CSI-RS ports P CSI-RS =2N 1 N 2 at the BS,
V m 1 (i) ,m 2 (i) is i-th of a plurality of L discrete Fourier transform (DFT)beams indicated by i l,1 and i 1,2 ,
u
m
=
{
[
1
e
j
2
π
m
O
2
N
2
…
e
j
2
π
m
(
N
2
-
1
)
O
2
N
2
]
N
2
>
1
1
N
2
=
1
v
l
,
m
=
[
u
m
e
j
2
π
l
O
1
N
1
u
m
…
e
j
2
π
l
(
N
1
-
1
)
O
1
N
1
u
m
]
T
,
[p l,0 (1) , p l,1 (1) , . . . , p l,2L−1 (1) ] are WB amplitude coefficients for layer l=1, . . . , υ indicated by i 1,3,1 , i 1,3,2 , i 1,4,1 and i 1,4,2 ,
[p l,0 (2) , p l,1 (2) , . . . , p l,2L−1 (2) ] are SB amplitude coefficients for layer l=1, . . . , υ indicated by i 2,2,1 and i 2,2,2 ,
[c l,0 , c l,1 , . . . , c l,2L−1 ] are SB phase coefficient indicator for layer l=1, . . . , υ, indicated by i 2,1,1 and i 2,1,2 , a phase value is given by φ l,i =e j2πc l,i /N PSK , O 1 and O 2 are oversampling factors, NPSK indicates an order of phase shift keying (PSK), and υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers.
17. The method of claim 16 , wherein the configuration information for the CSI feedback includes a value of the plurality of L DFT beams, a value of a phase alphabet size N PSK , and a value of (N 1 , N 2 ) , and wherein the L is determined as L∈ {2, 3, 4} , the N PSK is determined as N PSK ∈ {4,8} , and values for (N 1 , N 2 ) and (O 1 , O 2 ) are determined as:
Number of CSI-RS ports, P CSI-RS
(N 1 , N 2 )
(O 1 , O 2 )
4
(2, 1)
(4, 1)
8
(2, 2)
(4, 4)
(4, 1)
(4, 1)
12
(3, 2)
(4, 4)
(6, 1)
(4, 1)
16
(4, 2)
(4, 4)
(8, 1)
(4, 1)
24
(4, 3)
(4, 4)
(6, 2)
(4, 4)
(12, 1)
(4, 1)
32
(4, 4)
(4, 4)
(8, 2)
(4, 4)
(16, 1)
(4, 1).
18. The method of claim 10 , wherein:
the configuration information for the CSI feedback includes a value of L∈ {2,3,4}, a value of N PSK ∈ {4,8}, a value of a number of CSI-RS ports P CSI-RS ∈ {4,8,12,16,24,32} at the BS, and a value of d∈ {1,2,3,4} where
d
≤
min
(
P
CSI
-
RS
2
,
L
)
;
the first PMI (i 1 ) comprises a first set of indicators s 1 =[i 1,1 ] indicating the plurality of L beams out of P CSI-RS /2 antenna port selection where this selection is common for all layers of the plurality of layers; and
a codebook for both υ=1 and υ=2 is given by:
Layers
v = 1
W i 1,1 ,p 1 (1) ,p 1 (2) ,i 2,1,1 (1) = W i 1,1 ,p 1 (1) ,p 1 (2) ,i 2,1,1 1
v = 2
W
i
1
,
1
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
(
2
)
=
1
2
[
W
i
1
,
1
,
p
1
(
1
)
,
p
1
(
2
)
,
i
2
,
1
,
1
1
W
i
1
,
1
,
p
2
(
1
)
,
p
2
(
2
)
,
i
2
,
1
,
2
2
]
where:
W
i
1
,
1
,
p
l
(
1
)
,
p
l
(
2
)
,
i
2
,
1
,
l
l
=
1
∑
i
=
0
2
L
-
1
(
p
l
,
i
(
1
)
p
l
,
i
(
2
)
)
2
[
∑
i
=
0
L
-
1
v
i
1
,
1
d
+
i
p
l
,
i
(
1
)
p
l
.
i
(
2
)
φ
l
,
i
∑
i
=
0
L
-
1
v
i
1
,
1
d
+
i
p
l
,
i
+
L
(
1
)
p
l
,
i
+
L
(
2
)
φ
l
,
i
]
,
l
=
1
,
2
,
v i 1,1 d+i is i-th of the plurality of L selected antenna ports indicated by i 1,1 , where v m is a P CSI-RS/ 2-element column vector containing a value of 1 in element (m mod P CSI-RS/ 2) and zeros elsewhere where a first element is element 0;
[p l,0 (1) , p l,1 (1) , . . . , p l,2L−1 (1) ] are WB amplitude coefficients for layer l=1, . . . , υ indicated by i 1,3,1 , i 1,3,2 , i 1,4,1 and i 1,4,2 ;
[p l,0 (2) , p l,1 (2) , . . . , p l,2L−1 (2) ] are SB amplitude coefficients for layer l=1, . . . , υ indicated by i 2,2,1 and i 2,2,2 ;
[c l,0 , c l,1 , . . . , c l,2L−1 ] are SB phase coefficient indicator for layer l=1, . . . , υ, indicated by i 2,1,1 and i 2,1,2 ; a phase value is given by φ l,i =e j2πc l,i /N PSK ; and υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers.
19. A base station (BS) for channel state information (CSI) feedback in a wireless communication system, the BS comprising:
a transceiver configured to:
transmit, to a user equipment (UE), configuration information for the CSI feedback, the CSI feedback including pre-coding matrix indicator (PMI) information indicating a pre-coding matrix that corresponds to a sum of L quantities, wherein:
each of the L quantities is a product of a beam and a coefficient,
the coefficients comprises at least an amplitude coefficient and a phase coefficient,
the PMI information includes common components for all layers of a plurality of layers and independent components for each of the plurality of layers, and
the plurality of layers is determined based on a value υ associated with a rank indicator (RI); and
receive, from the UE, the CSI information including a first PMI (i 1 ) and a second PMI (i 2 ) over an uplink channel; and
at least one processor configured to reconstruct the pre-coding matrix indicated by the first PMI (i 1 ) and the second PMI (i 2 ).
20. The BS of claim 19 , wherein:
the first PMI (i 1 ) includes:
a first set of indicators s 1 =[i 1,1 i 1,2 ] indicating the plurality of L beams comprises common WB components for all layers of the plurality of layers; and
a second set of indicators
S
2
=
{
[
i
1
,
3
,
1
i
1
,
4
,
1
]
if
υ
=
1
[
i
1
,
3
,
1
i
1
,
4
,
1
i
1
,
3
,
2
i
1
,
4
,
2
]
if
υ
=
2
to indicate independent WB components for each layer of the plurality of υ=1 or υ=2 layers, wherein υ=1 corresponds to a first layer and υ=2 corresponds to first and second layers, and wherein i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the coefficients for each of the first layer and the second layer, respectively, and i 1,4,1 and i 1,4,2 indicate a plurality of WB amplitude coefficients for each of the first layer and the second layer, respectively; and
the second PMI (i 2 ) includes:
the set of indicators
i
2
,
1
=
{
[
i
2
,
1
,
1
]
if
υ
=
1
[
i
2
,
1
,
1
i
2
,
1
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers where i 2,1,1 and i 2,1,2 indicate a plurality of SB phase coefficients for each of the first layer and the second layer, respectively; and
the set of indicators
i
2
,
2
=
{
[
i
2
,
2
,
1
]
if
υ
=
1
[
i
2
,
2
,
1
i
2
,
2
,
2
]
if
υ
=
2
to indicate independent SB components for each layer of the plurality of υ=1 or υ=2 layers where i 2,2,1 and i 2,2,2 indicate a plurality of SB amplitude coefficients for each of the first layer and second layer, respectively.