is selected according to a first description and a second description which are unique to the precoding matrix and wherein the second description provides a finer description of the codebook than the first description other methods systems and apparatuses also are disclosed application_number US 201314037601 A description an exemplary multiple antenna communication system 100 with quantized feedback is schematically shown in fig1 a transmitter 110 transmits from t transmitting antennas 111 1 111 t over a fading channel 130 to r receiving antennas 121 1 121 r coupled to a receiver 120 a channel estimator 125 provides an estimate of the channel 130 to the receiver 120 the channel estimate is also quantized and provided to the transmitter 110 via a quantized rate control feedback channel 135 for purposes of analysis a flat fading channel model is assumed in which the channel remains constant for each block of transmission furthermore the feedback channel 135 is assumed to be an error free zero delay feedback channel from the receiver to the transmitter carrying b bits of information about the channel realization every frame for a multiple antenna system with r receive and t transmit antennas the baseband channel model can be expressed as follows where y is the r u00d7 1 received column vector h is the r u00d7 t channel matrix x is the t u00d7 1 transmit column vector and w is the r u00d7 1 noise column vector the input is subject to an average power constraint p i e tr q u2266 p where q xx h 2 denotes the expected value and tr represents the trace of a.