A method for transmitting and receiving uplink signals using an optimized rank 3 codebook is disclosed. The optimized rank 3 codebook includes 12 precoding matrix groups, which are consisted of 6 Tx antenna power balanced precoding matrix groups and 6 layer power balanced precoding matrix groups. Preferably, the optimized 4Tx rank 3 codebook has 20 precoding matrix, two precoding matrixes are selected from each the 6 Tx antenna power balanced precoding matrix groups, considering chordal distance and the number of precoding matrix. And then 8 precoding matrices are selected from the layer balanced precoding matrix groups.