1. A receiver for feeding back channel information, comprising: a channel vector measuring unit to measure channel vectors corresponding to a plurality of receiving antennas, respectively, that receive a plurality of data streams; a candidate codebook vector selecting unit to select at least two candidate codebook vectors from codebook vectors included in a codebook, by considering a quantization error based on the channel vectors with respect to each of the data streams; and a selection codebook vector determining unit to determine selection codebook vectors corresponding to the plurality of data streams respectively from the at least two candidate codebook vectors, based on a signal-to-interference and noise ratio (SINR) of each of the data streams that is calculated according to each of the candidate codebook vectors.