A method for channel state information (CSI) feedback by a user equipment (UE) is provided. The method comprises receiving, by the UE from a base station (BS), CSI feedback configuration information to report a covariance matrix indicator (CMI) indicating a N×N channel covariance matrix (K) associated with a downlink channel matrix, wherein N is a number of antenna ports at the BS; identifying, by the UE, the CMI that indicates a set of L basis vectors {ai}, i=0, 1, 2, . . . , L−1, each comprising a dimension N×1, and a set of L2 coefficients, {ci,j}, i,j=0, 1, 2, . . . , L−1, and that represent the covariance matrix (K) as a weighted linear sum {tilde over (K)}=Σi=0L-1Σj=0L-1ci,jaiajH, wherein L≤N and H denotes a Hermitian transpose, and transmitting, by the UE to the BS, the CSI feedback including the identified CMI over an uplink channel.