A transmitter, comprising: an antenna array (202, 304) having a plurality of antennas for a wireless communication with one or more receivers; and a precoder connected to the antenna array (202, 304), the precoder to apply a set of beamforming weights to the antenna array (202, 304), the set of beamforming weights selected from a codebook to form by the antenna array (202, 304) one or more transmit/receive beams or nulls pointing in selected directions; wherein the codebook includes a plurality of sets of beamforming weights for a plurality of directions, wherein the beamforming weights in the codebook are based on a first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)), the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) defined by a second antenna array response matrix ( D ( φ, θ)) and one or more characteristic matrices ( G, G ( h), G ( v)), wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) contains, for a plurality of directions, first array response vectors of the antenna array (202, 304), the second antenna array response matrix ( D ( φ, θ)) contains, for one or more of the plurality of directions, second array response vectors of another antenna array, the other antenna array being different from the antenna array (202, 304), and the one or more characteristic matrices ( G, G ( h), G ( v)) describing one or more characteristics of the antenna array (202, 304), wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) is modeled using the second antenna array response matrix ( D ( φ, θ)) and the one or more characteristic matrices ( G, G ( h), G ( v)), each of the first array response vectors ( a ( φ m, θ n), a ( h) ( φ m, θ n), a ( v) ( φ m, θ n)) being a product of a characteristic matrix ( G, G ( h), G ( v)) and a corresponding second array response vectors d ( φ m, θ n), and the transmitter is configured to transmit the one or more characteristic matrices ( G, G ( h), G ( v)) to the one or more receivers as part of control information for the receiver. an antenna array (202, 304) having a plurality of antennas for a wireless communication with one or more receivers; and a precoder connected to the antenna array (202, 304), the precoder to apply a set of beamforming weights to the antenna array (202, 304), the set of beamforming weights selected from a codebook to form by the antenna array (202, 304) one or more transmit/receive beams or nulls pointing in selected directions; wherein the codebook includes a plurality of sets of beamforming weights for a plurality of directions, wherein the beamforming weights in the codebook are based on a first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)), the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) defined by a second antenna array response matrix ( D ( φ, θ)) and one or more characteristic matrices ( G, G ( h), G ( v)), wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) contains, for a plurality of directions, first array response vectors of the antenna array (202, 304), the second antenna array response matrix ( D ( φ, θ)) contains, for one or more of the plurality of directions, second array response vectors of another antenna array, the other antenna array being different from the antenna array (202, 304), and the one or more characteristic matrices ( G, G ( h), G ( v)) describing one or more characteristics of the antenna array (202, 304), wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) is modeled using the second antenna array response matrix ( D ( φ, θ)) and the one or more characteristic matrices ( G, G ( h), G ( v)), each of the first array response vectors ( a ( φ m, θ n), a ( h) ( φ m, θ n), a ( v) ( φ m, θ n)) being a product of a characteristic matrix ( G, G ( h), G ( v)) and a corresponding second array response vectors d ( φ m, θ n), and the transmitter is configured to transmit the one or more characteristic matrices ( G, G ( h), G ( v)) to the one or more receivers as part of control information for the receiver.