Method and apparatus to enable channel compression in advanced wireless communication systems

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 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.

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 =[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

∑

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.

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 i ,σ i ); 0≤i≤d−1} where u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H K,N H , u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H H K,N , and σ i is a squared-root of the (i+1)-th largest eigenvalue of H K,N H K,N H or H K,N H H K,N , and wherein the CSI matrix H K,N is represented based on an equation given by H K,N ≅{tilde over (H)} K,N =Σ i=0 d-1 σ i u i v i H .

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 {(w i ,σ i ); 0≤i≤d−1} where w i =vec(u i v i H ) is a column vector of a dimension KN×1, and σ i is a non-negative real number, and wherein a vector form of the CSI matrix H K,N , h=vec(H K,N ) is represented based on an equation given by h≅{tilde over (h)}=Σ i=0 d-1 σ 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.

5. The UE of claim 1 , wherein the d is a positive integer that is either a predetermined 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 1≤d<D where the D is determined as D=min(K,N).

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 d , or Σ d .

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, U d 1 , V d 1 , and Σ d 1 , based on a first CSI matrix H K,N (1) ; and

identify a second SCI indicator indicating a second triple of matrices, U d 2 , V d 2 , and Σ d 2 , based on a difference H K,N (2) −{tilde over (H)} K,N (1) between a second CSI matrix H K,N (2) and a representation {tilde over (H)} K,N (1) of the first CSI matrix H K,N (1) according to the first SCI indicator,

wherein the difference is determined in at least one of a time domain or a frequency domain and (d 1 ,d 2 ) satisfies d 1 ≥d 2 , wherein at least one of d 1 or d 2 is 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 U d 1 , V d 1 , and Σ d 1 over a first uplink channel; and

transmit, to the BS, a second CSI feedback including the second SCI indicator indicating U d 2 , V d 2 , and Σ d 2 over at least one of the first uplink channel or a second uplink channel.

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 K×1, a second set of d basis vectors comprising a dimension N×1, 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 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.

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 =[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

∑

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.

10. The BS of claim 9 , wherein the SCI indicator is identified based on a set of d triples {(u i ,v i ,σ i ); 0≤i≤d−1} where u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H K,N H , u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H H K,N , and σ i is a squared-root of the (i+1)-th largest eigenvalue of H K,N H K,N H or H K,N H H K,N , and wherein the CSI matrix H K,N is represented based on an equation given by H K,N ≅{tilde over (H)} K,N =Σ i=0 d-1 σ i u i v i H .

11. The BS of claim 9 , wherein the SCI indicator is identified based on a set of d pairs {(w i ,σ i ); 0≤i≤d−1} where w i =vec(u i ,v i H ) is a column vector of a dimension KN×1, and σ i is a non-negative real number, and wherein a vector form of the CSI matrix H K,N , h=vec(H K,N ), is represented based on an equation given by h≅{tilde over (h)}=Σ i=0 d-1 σ 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.

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 information or reported by the UE in the CSI feedback, and wherein the d is determined in a range given by 1≤d<D where the D is determined as D=min(K,N).

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 U d 1 , V d 1 , and Σ d 1 over a first uplink channel; and

receive, from the UE, a second CSI feedback including a second SCI indicator indicating U d 2 , V d 2 , and Σ 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 H K,N (1) using the first SCI indicator indicating U d 1 , V d 1 , and Σ d 1 ; and

represent a difference H K,N (2) −{tilde over (H)} K,N (1) between a second CSI matrix H K,N (2) and a representation {tilde over (H)} K,N (1) of the first CSI matrix H K,N (1) according to the first SCI indicator using the second SCI indicator indicating U d 2 , V d 2 , and Σ d 2 ,

wherein the difference is determined in at least one of a time domain or a frequency domain, and (d 1 ,d 2 ) satisfies d 1 ≥d 2 , wherein at least one of d 1 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.

14. A method of a user equipment (UE) for a channel state information (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 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;

identifying, 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; 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.

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 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

∑

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.

16. The method of claim 15 , further comprising identifying the SCI indicator based on a set of d triples {(u i ,v i ,σ i ); 0≤i≤d−1} where u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H K,N H , u i is an eigenvector associated with an (i+1)-th largest eigenvalue of a matrix H K,N H H K,N , and σ i is a squared-root of the (i+1)-th largest eigenvalue of H K,N H K,N H or H K,N H H K,N , wherein the CSI matrix H K,N is represented based on an equation given by H K,N ≅{tilde over (H)} K,N =Σ i=0 d-1 σ i u i v i H .

17. The method of claim 15 , further comprising identifying the SCI indicator based on a set of d pairs {(w i ,σ i ); 0≤i≤d−1} where w i =vec(u i ,v i H ) is a column vector of a dimension KN×1, and σ i is a non-negative real number, wherein a vector form of the CSI matrix H K,N , h=vec(H K,N ) is represented based on an equation given by h≅{tilde over (h)}=Σ i=0 d-1 σ 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.

18. The method of claim 14 , wherein the d is a positive integer that is either a predetermined 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 1≤d<D where the D is determined as D=min(K,N).

19. The method of claim 15 , further comprising identifying the SCI indicator based on a codebook for at least one of u d , V d , or Σ d .

20. The method of claim 15 , further comprising:

identifying a first SCI indicator indicating a first triple of matrices, U d 1 , V d 1 , and Σ d 1 based on a first CSI matrix H K,N (1) ;

identifying a second SCI indicator indicating a second triple of matrices, U d 2 , V d 2 , and Σ d 2 based on a difference H K,N (2) −{tilde over (H)} K,N (1) between a second CSI matrix H K,N (2) and a representation {tilde over (H)} K,N (1) of the first CSI matrix H K,N (1) according to the first SCI indicator,

wherein the difference is determined in at least one of a time domain or a frequency domain and (d 1 ,d 2 ) satisfies d 1 ≥d 2 , and wherein at least one of d 1 or d 2 is determined by either a predetermined value or the BS via CSI feedback configuration information, or the UE in the CSI feedback;

transmitting, to the BS, a first CSI feedback including the first SCI indicator indicating U d 1 , V d 1 , and Σ d 1 over a first uplink channel; and

transmitting, to the BS, a second CSI feedback including the second SCI indicator indicating u d 1 , V d 2 , and Σ d 2 over either the first uplink channel or a second uplink channel.