A method in a wireless device comprising: receiving a set of reference signals transmitted from a network entity in a wireless communication system ; selecting a subset of beams from a plurality of orthogonal beams based on the received set of reference signals; computing sets of amplitude and phase parameters for one or more channel compression matrices, wherein each channel compression matrix corresponds to one transmission layer of a multiple-layer transmission, wherein each channel compression matrix is composed of one or more column vectors; and sending indications of the sets of amplitude and phase parameters to a network entity in the wireless communication system; wherein each set of amplitude and phase parameters parameterizes one column of the channel compression matrix, and the sets of amplitude and phase parameters comprise: polarization-common amplitude coefficient parameters, polarization-specific phase coefficient parameters, and polarization amplitude offset coefficient parameters; and the method further comprising either: identifying a largest polarization-common amplitude coefficient parameter of the polarization-common amplitude coefficient parameters for each polarization, wherein the largest polarization-common amplitude coefficient parameter becomes a reference entry for that polarization; and quantizing, for each polarization, all other polarization-common amplitude coefficient parameters for that polarization relative to the reference entry for that polarization; or identifying a largest polarization amplitude offset coefficient parameter of the polarization amplitude offset coefficient parameters for each polarization, wherein the largest polarization amplitude offset coefficient parameter becomes a reference entry for that polarization; and quantizing, for each polarization, all other polarization amplitude offset coefficient parameters for that polarization relative to the reference entry for that polarization. receiving a set of reference signals transmitted from a network entity in a wireless communication system ; selecting a subset of beams from a plurality of orthogonal beams based on the received set of reference signals; computing sets of amplitude and phase parameters for one or more channel compression matrices, wherein each channel compression matrix corresponds to one transmission layer of a multiple-layer transmission, wherein each channel compression matrix is composed of one or more column vectors; and sending indications of the sets of amplitude and phase parameters to a network entity in the wireless communication system; polarization-common amplitude coefficient parameters, polarization-specific phase coefficient parameters, and polarization amplitude offset coefficient parameters; and identifying a largest polarization-common amplitude coefficient parameter of the polarization-common amplitude coefficient parameters for each polarization, wherein the largest polarization-common amplitude coefficient parameter becomes a reference entry for that polarization; and quantizing, for each polarization, all other polarization-common amplitude coefficient parameters for that polarization relative to the reference entry for that polarization; or identifying a largest polarization amplitude offset coefficient parameter of the polarization amplitude offset coefficient parameters for each polarization, wherein the largest polarization amplitude offset coefficient parameter becomes a reference entry for that polarization; and quantizing, for each polarization, all other polarization amplitude offset coefficient parameters for that polarization relative to the reference entry for that polarization. <EOS>