A receiver, comprising: an antenna (202, 304) for a wireless communication with a transmitter; and a signal processor (302, 306, 306) to receive and process a radio signal received at the antenna via a radio channel; wherein the receiver is configured to construct a codebook including a plurality of sets of beamforming weights for a plurality of directions, the beamforming weights in the codebook being based on a first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) of a transmitter antenna array (202, 304), and the transmitter selecting a set of beamforming weights from the codebook to form by the transmitter antenna array (202, 304) a transmit/receive beam pointing in a selected direction, wherein the receiver is configured to calculate one or more characteristic matrices ( G, G ( h), G ( v)) based on a model of the transmitter antenna array (202, 304) using (a) received position data of antenna elements of the transmitter antenna array and a preferred polarization of each antenna element, and/or (b) structural and/or geometrical data of the transmitter antenna array; wherein the receiver is configured to construct the codebook using a second antenna array response matrix ( D ( φ, θ)) and the one or more calculated characteristic matrices ( G, G ( h), G ( v)), and wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) contains, for a plurality of directions, the first array response vectors of the transmitter 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 transmitter antenna array (202, 304), and the one or more characteristic matrices ( G, G ( h), G ( v)) describing one or more characteristics of the transmitter antenna array (202, 304), and 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). an antenna (202, 304) for a wireless communication with a transmitter; and a signal processor (302, 306, 306) to receive and process a radio signal received at the antenna via a radio channel; wherein the receiver is configured to construct a codebook including a plurality of sets of beamforming weights for a plurality of directions, the beamforming weights in the codebook being based on a first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) of a transmitter antenna array (202, 304), and the transmitter selecting a set of beamforming weights from the codebook to form by the transmitter antenna array (202, 304) a transmit/receive beam pointing in a selected direction, wherein the receiver is configured to calculate one or more characteristic matrices ( G, G ( h), G ( v)) based on a model of the transmitter antenna array (202, 304) using (a) received position data of antenna elements of the transmitter antenna array and a preferred polarization of each antenna element, and/or (b) structural and/or geometrical data of the transmitter antenna array; (a) received position data of antenna elements of the transmitter antenna array and a preferred polarization of each antenna element, and/or (b) structural and/or geometrical data of the transmitter antenna array; wherein the receiver is configured to construct the codebook using a second antenna array response matrix ( D ( φ, θ)) and the one or more calculated characteristic matrices ( G, G ( h), G ( v)), and wherein the first antenna array response matrix ( A ( φ, θ), A ( h) ( φ, θ), A ( v) ( φ, θ)) contains, for a plurality of directions, the first array response vectors of the transmitter 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 transmitter antenna array (202, 304), and the one or more characteristic matrices ( G, G ( h), G ( v)) describing one or more characteristics of the transmitter antenna array (202, 304), and 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).