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), 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, wherein:
each of the plurality of coefficients comprises at least an amplitude coefficient and a phase coefficient;
the PMI comprises a first PMI (i 1 ) and a second PMI (i 2 ) indicating wideband (WB) and subband (SB) components of the LC pre-coding matrix, respectively;
the first PMI (i i ) includes first and second sets of indicators indicating common WB components for all layers of a plurality of layers and independent WB components for each layer of the plurality of layers, respectively;
the second PMI (i 2 ) includes a set of indicators indicating independent SB components for each layer of the plurality of layers; and
the plurality of layers is determined based on a value v associated with a rank indicator (RI); and
at least one processor configured to determine the first PMI (i 1 ) and the 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 i ) includes a first set of indicators s 1 =[i 1,1 i 1,2 ] indicating the plurality of L beams that comprise common WB components for all layers of the plurality of layers.
3. The UE of claim 1 , wherein the first PMI (i i ) 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the plurality of 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.
4. The UE of claim 1 , wherein 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, and wherein 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.
5. The UE of claim 1 , wherein the second PMI (i 2 ) includes 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, and wherein 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 (1/8)}
5
{square root over (1/4)}
6
{square root over (1/2)}
7
1.
7. The UE of claim 1 , wherein an LC codebook for ν=1 and ν=2 is given by:
Layers
υ = 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
υ = 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,
ν 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, . . . , ν 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, . . . , ν 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, . . . , ν, 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, N PSK indicates an order of phase shift keying (PSK), and ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers.
8. The UE of claim 7 , wherein CSI feedback configuration information 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 CSI feedback configuration information 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 i ) 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
an LC codebook for both ν=1 and ν=2 is given by:
Layers
υ = 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
υ = 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
,
ν i 1,1 d+i , is i-th of the plurality of L selected antenna ports indicated by i 1,1 , where ν 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, . . . , ν 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, . . . , ν 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, . . . , ν, 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 ν=1 corresponds to a first layer and ν=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), 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, wherein:
each of the plurality of coefficients comprises at least an amplitude coefficient and a phase coefficient;
the PMI comprises a first PMI (i 1 ) and a second PMI (i 2 ) indicating wideband (WB) and subband (SB) components of the LC pre-coding matrix, respectively;
the first PMI (i i ) includes first and second sets of indicators indicating common WB components for all layers of a plurality of layers and independent WB components for each layer of the plurality of layers, respectively;
the second PMI (i 2 ) includes a set of indicators indicating independent SB components for each layer of the plurality of layers, and
the plurality of layers is determined based on a value ν associated with a rank indicator (RI);
determining the first PMI (i i ) and the second PMI (i 2 ); and
transmitting, to the BS, the CSI feedback including the first PMI (i i ) and the second PMI (i 2 ) over an uplink channel.
11. The method of claim 10 , wherein the first PMI (i i ) includes a first set of indicators s 1 =[i 1,1 i 1,2 ] indicating the plurality of L beams that comprise common WB components for all layers of the plurality of layers.
12. 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the plurality of 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.
13. The method of claim 10 , wherein 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, and wherein 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.
14. The method of claim 10 , wherein the second PMI (i 2 ) includes 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 ν=1 or ν=2 layers, and wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, and wherein 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 (1/8)}
5
{square root over (1/4)}
6
{square root over (1/2)}
7
1.
16. The method of claim 10 , wherein an LC codebook for ν=1 and ν=2 is given by:
Layers
υ = 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
υ = 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,
ν 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, . . . , ν 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, . . . , ν 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, . . . , ν, 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, N PSK indicates an order of phase shift keying (PSK), and ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers.
17. The method of claim 16 , wherein the CSI feedback configuration information 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 CSI feedback configuration information 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 i ) 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
an LC codebook for both ν=1 and ν=2 is given by:
Layers
υ = 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
υ = 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 ν 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, . . . , ν 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, . . . , ν 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, . . . , ν, 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 ν=1 corresponds to a first layer and ν=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), 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, wherein:
each of the plurality of coefficients comprises at least an amplitude coefficient and a phase coefficient;
the PMI comprises a first PMI (i 1 ) and a second PMI (i 2 ) indicating wideband (WB) and subband (SB) components of the LC pre-coding matrix, respectively;
the first PMI (i i ) includes first and second sets of indicators indicating common WB components for all layers of a plurality of layers and independent WB components for each layer of the plurality of layers, respectively;
the second PMI (i 2 ) includes a set of indicators indicating independent SB components for each layer of the plurality of layers; and
the plurality of layers is determined based on a value v associated with a rank indicator (RI); and
at least one processor configured to reconstruct the LC pre-coding matrix indicated by the first PMI (i i ) and the second PMI (i 2 ), wherein the transceiver is further configured to receive, from the UE, the CSI feedback including the first PMI (i i ) and the second PMI (i 2 ) over an uplink channel.
20. The BS of claim 19 , wherein:
the first PMI (i i ) 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 ν=1 or ν=2 layers, wherein ν=1 corresponds to a first layer and ν=2 corresponds to first and second layers, and wherein i 1,3,1 and i 1,3,2 indicate a strongest coefficient among the plurality of 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 ν=1 or ν=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 ν=1 or ν=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 the second layer, respectively.