A user equipment, UE, for a channel state information, CSI, feedback in an advanced communication system, the UE comprising: a transceiver configured to receive, from a base station, BS, CSI configuration information to report a wideband periodic CSI including a pre-coding matrix indicator, PMI, a rank indicator, RI, and a relative power indicator, RPI, based on a linear combination, LC, codebook which includes precoders determined based on a linear combination of a plurality of beams to which a plurality of weights are applied, wherein the PMI comprises a first PMI, i 1, indicating the plurality of beams and a second PMI, i 2, indicating the plurality of weights for linear combination of the plurality of beams, and the RPI indicates a power assigned to the plurality of beams; and at least one processor configured to determine, based on the CSI configuration information, the RI and the RPI, wherein the transceiver is further configured to transmit, to the BS over an uplink channel, a first CSI feedback comprising the RI and the RPI in a first periodic reporting instance out of a plurality of periodic reporting instances, wherein the plurality of beams comprises a first discrete Fourier transform, DFT vector and a second DFT vector for each layer of a precoding matrix corresponding to RI = 1 or 2 in a W1 codebook, and the RPI comprises a power assigned to the second DFT vector relative to a unit power assigned to the first DFT vector, and wherein in case that a number of the plurality of beams is 2, a value of the power assigned to the first DFT vector is 1, and a value of the power assigned to the second DFT vector is selected to be one of 0, 0.25, 0.5, 1 from a 2 bit power codebook. a transceiver configured to receive, from a base station, BS, CSI configuration information to report a wideband periodic CSI including a pre-coding matrix indicator, PMI, a rank indicator, RI, and a relative power indicator, RPI, based on a linear combination, LC, codebook which includes precoders determined based on a linear combination of a plurality of beams to which a plurality of weights are applied, wherein the PMI comprises a first PMI, i 1, indicating the plurality of beams and a second PMI, i 2, indicating the plurality of weights for linear combination of the plurality of beams, and the RPI indicates a power assigned to the plurality of beams; and at least one processor configured to determine, based on the CSI configuration information, the RI and the RPI, wherein the transceiver is further configured to transmit, to the BS over an uplink channel, a first CSI feedback comprising the RI and the RPI in a first periodic reporting instance out of a plurality of periodic reporting instances, wherein the plurality of beams comprises a first discrete Fourier transform, DFT vector and a second DFT vector for each layer of a precoding matrix corresponding to RI = 1 or 2 in a W1 codebook, and the RPI comprises a power assigned to the second DFT vector relative to a unit power assigned to the first DFT vector, and wherein in case that a number of the plurality of beams is 2, a value of the power assigned to the first DFT vector is 1, and a value of the power assigned to the second DFT vector is selected to be one of 0, 0.25, 0.5, 1 from a 2 bit power codebook.