On the Precoder Design for Block Diagonalized MIMO Broadcast Channels

Block diagonalization (BD) is a linear precoding technique for MIMO broadcast channels such that it completely eliminates the multiuser interference. Consequently, the precoder of a user must lie in the null space of a matrix composing of other users´ channel matrices. In this way, the problem of the precoder design is closely related to finding a basis of the null space of the matrix, which can be computed by, e.g., the singular value decomposition (SVD). Recently, a generalized channel inversion (GCI) method was introduced as a low-complexity design for BD. The GCI-based precoder design is also shown to be optimal for BD. However, since the GCI-based design relies on the pseudo-inverse of a matrix, there are many settings, to which this method is not applicable. In this letter, we first provide a connection between the SVD- and GCI-based designs using the results from linear algebra. Then, from this connection, we propose a precoder design that is devised for the cases where the GCI-based method cannot handle.