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. <EOS>