A transmitter includes an antenna array having a plurality of antennas for a wireless communication with one or more receivers, and a precoder connected to the antenna array. The precoder applies a set of beamforming weights to the antenna array. The set of beamforming weights is selected from a codebook to transmit/receive beams or nulls pointing in selected directions. The codebook includes sets of beamforming weights for a plurality of directions. The beamforming weights are based on a first antenna array response matrix defined by a second antenna array response matrix and one or more transformation matrices. The first antenna array response matrix contains first array response vectors of the antenna array, the second antenna array response matrix contains second array response vectors determined using a model of the antenna array. The transformation matrices describe one or more characteristics of the antenna array.