A method and apparatus for transmitting and receiving signals is provided for use in a codebook-based closed-loop multiple antenna system. A method for receiving signals in a codebook-based multiple antenna system according to the present disclosure includes estimating a desired signal and an interference channel, determining a codebook index using the desired channel, a Hermitian of the desired channel, and the interference channel, and feeding back the codebook index to a transmitter. The multi-antenna system of the present disclosure is advantageous in suppressing the interference from other cells and maximizing the gain of the desired signal especially when the number of receive antennas is greater than the reception streams and in designing a codebook with high performance as compared to the Grassmanian codebook and low complexity.