Antenna array codebook with beamforming coefficients adapted to an arbitrary antenna response of the antenna array

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) to apply a set of beamforming weights to the antenna array (202, 304), the set of beamforming weights 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(A( l p, &thgr;),A ( h )(f,&thgr;),A( V )(<p,0)), the first antenna array response matrix(A( l p, 0), A( h )( l p,0),A ( v )(f, &thgr;)) defined by a second antenna array response matrix (D(f,&thgr;))and one or more characteristic matrices(G, G ( h ),G ( v )).The first antenna array response matrix (A(f,&thgr;),A ( h )(f, &thgr;),A ( v )(f, &thgr;))contains, for a plurality of directions, first array response vectors of the antenna array (202, 304), the second antenna array response matrix(D( l p,&THgr;)) 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(C, G( h)' G (V) )describing one or more characteristics of the antenna array (202, 304).