A method for reporting, by a user equipment, UE, channel state information, CSI, in a two dimensional multi-antenna wireless communication system, the method comprising: receiving, from a base station, a channel state information reference signal, CSI-RS; and reporting, to the base station, the channel state information, wherein: the channel state information comprises a precoding matrix indicator, PMI, comprising a first PMI for selecting, from a codebook, a precoding vector set consisting of four precoding vectors and a second PMI for determining, from the precoding vector set, one precoding matrix applied to two layers, wherein the precoding matrix comprises a first precoding vector applied to a first layer and a second precoding vector applied to a second layer, each of the first precoding vector and the second precoding vector are generated as a Kronecker product of a first vector corresponding to a first dimension antenna port and a second vector corresponding to a second dimension antenna port, and by using a corresponding co-phasing factor for controlling a phase between the first and the second dimension antenna port in a cross-polarization antenna, the first vector corresponding to the first dimension antenna port is determined based on a first index, the second vector corresponding to the second dimension antenna port is determined based on a second index, a pair of the first index and the second index for each of the four precoding vectors of the precoding vector set selected by the first PMI consists of (x,y), (x+2,y), (x+1,y+1) and (x+3,y+1), and the x and y each have a specific value that is determined by the first PMI and is an integer other than a negative number. receiving, from a base station, a channel state information reference signal, CSI-RS; and reporting, to the base station, the channel state information, wherein: the channel state information comprises a precoding matrix indicator, PMI, comprising a first PMI for selecting, from a codebook, a precoding vector set consisting of four precoding vectors and a second PMI for determining, from the precoding vector set, one precoding matrix applied to two layers, wherein the precoding matrix comprises a first precoding vector applied to a first layer and a second precoding vector applied to a second layer, each of the first precoding vector and the second precoding vector are generated as a Kronecker product of a first vector corresponding to a first dimension antenna port and a second vector corresponding to a second dimension antenna port, and by using a corresponding co-phasing factor for controlling a phase between the first and the second dimension antenna port in a cross-polarization antenna, the first vector corresponding to the first dimension antenna port is determined based on a first index, the second vector corresponding to the second dimension antenna port is determined based on a second index, a pair of the first index and the second index for each of the four precoding vectors of the precoding vector set selected by the first PMI consists of (x,y), (x+2,y), (x+1,y+1) and (x+3,y+1), and the x and y each have a specific value that is determined by the first PMI and is an integer other than a negative number.