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 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; 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 K × 1, a second set of d basis vectors comprising a dimension N × 1, 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, wherein the first set of d basis vectors comprises columns of a matrix U d = [ u 0 u 1 ··· u d -1]; the second set of d basis vectors comprises columns of a matrix V d = [ v 0 v 1 ··· v d -1]; and the set of d coefficients correspond to diagonal elements of a diagonal matrix Σ d = σ 0 0 ⋯ 0 0 σ 1 ⋯ 0 ⋮ ⋮ ⋱ 0 0 0 ⋯ σ d − 1 where σ 0, σ 1,..., σ d -1 are non-negative real numbers, and wherein u i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H K, N H, υ i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H H K, N, and σ i is a squared-root of the ( i +1)-th largest eigen value of H K, N H K, N H or H K, N H H K, N where 0 ≤ i ≤ d - 1. 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 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; 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 K × 1, a second set of d basis vectors comprising a dimension N × 1, 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, wherein the first set of d basis vectors comprises columns of a matrix U d = [ u 0 u 1 ··· u d -1]; the second set of d basis vectors comprises columns of a matrix V d = [ v 0 v 1 ··· v d -1]; and the set of d coefficients correspond to diagonal elements of a diagonal matrix Σ d = σ 0 0 ⋯ 0 0 σ 1 ⋯ 0 ⋮ ⋮ ⋱ 0 0 0 ⋯ σ d − 1 where σ 0, σ 1,..., σ d -1 are non-negative real numbers, and wherein u i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H K, N H, υ i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H H K, N, and σ i is a squared-root of the ( i +1)-th largest eigen value of H K, N H K, N H or H K, N H H K, N where 0 ≤ i ≤ d - 1. determine a CSI matrix H K,N comprising a dimension 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; 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 K × 1, a second set of d basis vectors comprising a dimension N × 1, 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, wherein the first set of d basis vectors comprises columns of a matrix U d = [ u 0 u 1 ··· u d -1]; the second set of d basis vectors comprises columns of a matrix V d = [ v 0 v 1 ··· v d -1]; and the set of d coefficients correspond to diagonal elements of a diagonal matrix Σ d = σ 0 0 ⋯ 0 0 σ 1 ⋯ 0 ⋮ ⋮ ⋱ 0 0 0 ⋯ σ d − 1 where σ 0, σ 1,..., σ d -1 are non-negative real numbers, and wherein u i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H K, N H, υ i is an eigenvector associated with an ( i +1)-th largest eigen value of a matrix H K, N H H K, N, and σ i is a squared-root of the ( i +1)-th largest eigen value of H K, N H K, N H or H K, N H H K, N where 0 ≤ i ≤ d - 1.