WHAT IS CLAIMED IS:

[Claim 1 ]

A user equipment (UE) for a 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 the CSI feedback including a spatial channel information (SCI) indicator for each subband (SB), wherein the SCI indicator indicates a SCI associated with a downlink (DL) channel matrix;

at least one processor configured to:

determine a CSI matrix ^{H}K,N comprising a dimension κ x N based on the CSI feedback configuration information, where K indicates a number of SBs and N indicates a number of components of the SCI; and

identify, based on the CSI matrix ^{H}K,N , the SCI indicator that indicates a first set of d basis vectors comprising a dimension κ * I, a second set of d basis vectors comprising a dimension Af x i , and a set of d coefficients,

wherein the transceiver is further configured to transmit, to the BS, the CSI feedback including the identified SCI indicator indicating the first set of d basis vectors, the second set of d basis vectors, and the set of d coefficients over an uplink channel.

[Claim 2 ]

The UE of Claim 1 , wherein the SCI associated with the DL channel matrix comprises at least one of the DL channel matrix itself, a covariance matrix of the DL channel matrix, or at least one eigenvector of the covariance matrix of the DL channel matrix, and wherein:

the first set of d basis vectors comprises columns of a matrix U_{d} = [«o "i ·" "d-i];

the second set of d basis vectors comprises columns of a matrix

V_{d} = [v_{0} v, · · · v_{d}_, ] _{; anc}l

the set of d coefficients correspond to diagonal elements of a diagonal

matrix

where ^{σ}ο· ^{σ}ι ^{σ}<ι-ι are non-negative real numbers.

[Claim 3 ]

The UE of Claim 2, wherein the at least one processor is further configured to identify the SCI indicator based on a set of d triples {(u_{i}, v_{l}, a_{i}): 0≤i≤d - i} where "i is an eigenvector associated with an (i+l )-th largest eigen value of a matrix ^{H}K,N H",N , "I is an eigenvector associated with an
(i+ l )-th largest eigen value of a matrix ^{Η}κ,Ν ^{Η}χ^ - ^{ΆηΑ σ}< is a squared-root of the (i+l )-th largest eigen value of »^{r} and wherein the CSI matrix is represented based on an equation given by ^{W}KA ∑Jo w .

[Claim 4]

The UE of Claim 2, wherein the at least one processor is further configured to identify the SCI indicator based on a set of d pairs {(νν,, σ,): o < ί < d - 1} where w, =

j_{s a co}l_{U}mn vector of a dimension KN x l, and σ, i_{s} a non-negative real number, and wherein a vector fonn of the CSI matrix ^{Η}κ^ ^ h = vec(H_{K N}) j_{s} represented based on an equation given by ^{h} - ^{h a}i^{w}i where a notation vec(x) denotes a column vector that is constructed by concatenating columns of a matrix x into a single column.

[Claim 5 ]

The UE of Claim 1 , wherein the d is a positive integer that is either a predetemiined value or configured by the BS via CSI feedback configuration information or reported by the UE in the CSI feedback, and wherein the d is determined in a range given by i < d < D where the D is determined as

D = min(A:, N).

[Claim 6]

The UE of Claim 2, whether the at least one processor is further configured to identify the SCI indicator based on a codebook for at least one of u_{d}, v_{a}, or ∑_{d}_

[Claim 7 ]

The UE of Claim 2 wherein the at least one processor is further configured to:

identify a first SCI indicator indicating a first triple of matrices, Ud v_{dl}, and -phased on a first CSI matrix and

identify a second SCI indicator indicating a second triple of matrices, t/ri_{2}. v_{d2} , and b_{ase(}j _{on a} difference between a second CSI matrix and a representation of the first CSI matrix according to the first SCI indicator,

wherein the difference is determined in at least one of a time domain or a frequency domain and (. _{x}, d_{2} ) satisfies ^{d}i≥ wherein at least one of or d_{2} i_{s} determined by either a predetermined value or the BS via CSI feedback configuration information, or the UE in the CSI feedback, and wherein

the transceiver is further configured to:

transmit, to the BS, a first CSI feedback including the first SCI indicator indicating ^{υ}α, , v_{dl}, and∑_{dl over a} f_{irs}t uplink channel; and

transmit, to the BS, a second CSI feedback including the second SCI indicator indicating ^d_{2}. ^{and} over at least one of the first uplink channel or a second uplink channel.

[Claim 8 ]

A base station (BS) for a 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 the CSI feedback including a spatial channel information (SCI) indicator for each subband (SB), wherein the SCI indicator indicates a SCI associated with a downlink (DL) channel matrix; and

receive, from the UE, the CSI feedback including the identified SCI indicator indicating a first set of d basis vectors comprising a dimension κ * i, a second set of d basis vectors comprising a dimension N χ l, and a set of d coefficients over an uplink channel,

at least one processor configured to:

represent a CSI matrix ^{H}K,N using the first set of d basis vectors, the second set of d basis vectors, and the set of d coefficients, indicated by the SCI indicator, wherein the CSI matrix ^{H}K,N comprises a dimension κ x N based on the CSI feedback configuration information, where K indicates a number of SBs and N indicates a number of components of the SCI.

[Claim 9]

The BS of Claim 8, wherein the SCI associated with the DL channel matrix comprises at least one of the DL channel matrix itself, a covariance matrix of the DL channel matrix, or at least one an eigenvector of the covariance matrix of the DL channel matrix, and wherein:

the first set of d basis vectors comprises columns of a matrix u_{d} = [«o

the second set of d basis vectors comprises columns of a matrix

V_{d} = [v_{0} v, · ·· v_{d}_, ] _{; anc}l

the set ofd coefficients correspond to diagonal elements of a diagonal

matrix

<½ - i are non-negative real numbers.

[Claim 10]

The BS of Claim 9, wherein the SCI indicator is identified based on a set of d triples { ("i . Vj , ^ ): o < i ; < d - i} where «■ is an eigenvector associated with an
(i+ l)-th largest eigen value of a matrix ¾/v^{w}" /v. "i is an eigenvector associated with an (i+ l )-th largest eigen value of a matrix ^{H}K,N^{H}Kji < ^{d}' ^{nd} °i is a squared-root of the (i+ l)-th largest eigen value of H^ _{N}H_{K N} ^ _{anc}j wherein the CSI matrix is represented based on an equation given by ^{Η}κ =∑f=i ^{a}i^{u}i ^{v}i .

[Claim 1 1 ]

The BS of Claim 9, wherein the SCI indicator is identified based on a set of d pairs {(^.^ o < i < d - i} where wj = veciu^) j_{s a} column vector of a dimension KN X I, and σ_{( 1S} a non-negative real number, and wherein a vector form of the CSI matrix ^{w h} - ^{vec}(^{w}*,/v) is represented based on an equation given by ^{h} - k

^{a}i ^{w}i , where a notation vec(x) denotes a column vector that is constructed by concatenating columns of a matrix x into a single column.

[Claim 12 ]

The BS of Claim 8, wherein the d is a positive integer that is either a predetermined value or configured by the BS via CSI feedback configuration infonnation or reported by the UE in the CSI feedback, and wherein the d is determined in a range given by i < d < D where the D is determined as

D = mm{K, N).

[Claim 13 ]

The BS of Claim 9,

wherein the transceiver is further configured to:

receive, from the UE, a first CSI feedback including the first SCI indicator indicating v_{dl}, and∑_{di over a} f_{irs}t uplink channel; and

receive, from the UE, a second CSI feedback including a second SCI indicator indicating ^{ϋ}<«_{2}. ^_{2}. ^{and ∑}d_{2} over at least one of the first uplink channel or a second uplink channel, and

wherein the at least one processor is further configured to:

represent a first CSI matrix

using the first SCI indicator indicating ^{u}^ " and x_{dl}. _{an(}j

represent a difference between a second CSI matrix and a representation

of the first CSI matrix ^{w} according to the first SCI indicator using the second SCI indicator indicating * ^{and ∑}<*_{2} ,

wherein the difference is determined in at least one of a time domain or a frequency domain, and (di. d_{2}) satisfies ^{d}i ^{≥ d}2 , wherein at least one of ^{d}\ ^{or d}2 is configured by either a predetermined value or the BS via CSI feedback configuration information, or the UE in the CSI feedback.

[Claim 14]

A method of a user equipment (UE) for a channel state infonnation (CSI)

feedback in a wireless communication system, the method comprising:

receiving, from a base station (BS), CSI feedback configuration information for the CSI feedback including a spatial channel information (SCI) indicator for each subband (SB), wherein the SCI indicator indicates a SCI associated with a downlink (DL) channel matrix;

determining a CSI matrix ^{Η}κ^ comprising a dimension ^{H}K,N based on the CSI feedback configuration information, where K indicates a number of SBs and N indicates a number of components of the SCI;

identifying, based on the CSI matrix ^{H}K,N , the SCI indicator that indicates a first set of d basis vectors comprising a dimension « * l, a second set of d basis vectors comprising a dimension N ^{χ} l, and a set of d coefficients; and

transmitting, to the BS, the CSI feedback including the identified SCI indicator indicating the first set of d basis vectors, the second set of d basis vectors, and the set of d coefficients over an uplink channel.

[Claim 15]

The method of Claim 14, wherein the SCI associated with the DL channel matrix comprises at least one of the DL channel matrix itself, a covariance matrix of the DL channel matrix, or at least one eigenvector of the covariance matrix of the DL channel matrix, and wherein:

the first set of d basis vectors comprises columns of a matrix

the second set of d basis vectors comprises columns of a matrix

V_{d} = [v_{0} v, · ·· _{an(}j

the set of d coefficients correspond to diagonal elements of a diagonal cr_{0} 0 ... 0

0 σ, - 0

• : ··· 0

matrix where ^{σ} · ^{σ}ι ^{σ}α-ι are non-negative real numbers.