Methods for codebook sub-sampling

A method in a wireless terminal, the method comprising:

• receiving a reference signal;
• determining, by the wireless terminal, based on the reference signal, a first precoding index i2 corresponding to a first precoding matrix for a first subband, wherein i2 is an index of a first codebook;
• determining, by the wireless terminal, based on the reference signal, a second precoding index i2′ corresponding to a second precoding matrix for a second subband that is different from the first subband, wherein i2′ is an index of the first codebook, and wherein i2′ belongs to the set Si2, which is a subset of the first codebook and includes the first precoding index i2;
• transmitting, by the wireless terminal, a representation of i2 and a representation of i2′ to a base station;
• and
• determining a third precoding index i1 based on the reference signal, wherein the third precoding index i1 points to a third precoding matrix of a second codebook, and wherein the third precoding matrix corresponding to the third precoding index commonly applies to the first subband and the second subband.