Configurations and feedback schemes for compressed channel state information (CSI) feedback are provided. A User Equipment (UE) determines a constraint on a total number of transfer domain coefficients to be reported for compressed Channel State Information (CSI) feedback by the UE for a plurality of beams identified for the feedback, wherein each transfer domain coefficient is associated with amplitude information and phase information. The UE selects from a transfer domain coefficient compression matrix, based on the constraint, a set of one or more transfer domain coefficients to report for each of the beams. The UE reports information indicating a number of selected transfer domain coefficients in the set of transfer domain coefficients for each beam and a location of each transfer domain coefficient within the transfer domain coefficient compression matrix and reports at least the amplitude and phase information for the selected coefficients.