The precoding is based on knowledge of all the channels between the AP and each of the intended receivers. Denote the channel between the AP and user i as Hi. If there are Nu users, we have: Hi,i=1, . . . ,Nu??(1) where Hi is an NRX,i×NTX matrix, assuming that the receiver i has NRX,i receive antennas and the AP has NTX transmit antennas. For each of the users, the AP determines a precoding matrix Qj, j=1, . . . , Nu, such that: HiQj=0,i≠j??(2) if the number of streams sent to user j is NSTS,j, Qj is an NTX×NSTS,j matrix.
If we build a composite channel matrix consisting of all individual channel matrices Hi and a full precoding matrix that has the various Qj as columns, we find that: