A method for transmitting and receiving uplink signals using an optimized rank 3 codebook is disclosed. The optimized rank 3 codebook includes 6 precoding matrix groups, each of which has 1 variable having an amplitude of 1. Preferably, the optimized 4Tx rank 3 codebook has 12 precoding matrix, two precoding matrixes are selected from each the above 6 precoding matrix groups considering chordal distance and the number of precoding matrix.