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; wherein the plurality of data streams comprises a first data stream, the candidate codebook vector selecting unit selects at least two first candidate codebook vectors associated with the first data stream from the codebook vectors, based on the quantization error corresponding to an angle between the codebook vectors and a space spanned by the channel vectors, and the selection codebook vector determining unit determines a first selection codebook vector corresponding to the first data stream from the first candidate codebook vectors, based on the SINR of the first data stream that is calculated according to the at least two first candidate codebook vectors.