In Equation 9, the codebook configurations are designed to reflect channel correlation properties generated when cross polarized antennas are used and when a space between antennas is dense, for example, when a distance between adjacent antennas is less than a half of signal wavelength. The cross polarized antennas may be categorized into a horizontal antenna group and a vertical antenna group. Each antenna group has the characteristic of a Uniform Linear Array (ULA) antenna and the two groups are co-located.
Accordingly, a correlation between antennas of each group has characteristics of the same linear phase increment and a correlation between antenna groups has characteristics of phase rotation. Consequently, since a codebook is a value obtained by quantizing a channel, it is necessary to design a codebook such that characteristics of a channel are reflected. For convenience of description, a rank-1 codeword generated by the aforementioned configurations is shown as follows: