Beamforming codebook adaption to antenna array imperfections

A transmitter includes an antenna array (202, 304) having a plurality of antennas for a wireless communication with one or more receivers, and a precoder (204) connected to the antenna array (202, 304). The precoder (204) applies a set of beamforming weights to the antenna array (202, 304). The set of beamforming weights is selected from a codebook (212) to form by the antenna array (202, 304) one or more transmit/receive beams or nulls pointing in selected directions. The codebook (212) includes a plurality of sets of beamforming weights for a plurality of directions. The beamforming weights in the codebook (212) are based on a first antenna array response matrix ( Ã ( Õ, & )) , the first antenna array response matrix ( Ã ( Õ, & )) defined by a second antenna array response matrix ( A ( Õ, & )) and one or more transformation matrices ( K,K q ). The first antenna array response matrix ( Ã ( Õ, & )) contains, for a plurality of directions, first array response vectors ( ã ( Õ m , & n )) of the antenna array (202, 304), the second antenna array response matrix ( A ( Õ , & )) contains, for one or more of the plurality of directions, second array response vectors of the antenna array (202, 304), the second array response vectors determined using a model of the antenna array (202, 304), and the one or more transformation matrices ( K, K q ) describing one or more characteristics of the antenna array (202, 304).