Abstract — Regularized block diagonalization (RBD) is a new linear precoding technique for the multi-antenna broadcast channel and has a significantly improved sum rate and diversity order compared to all previously proposed linear precoding techniques. We consider a limited feedback system with RBD precoding, in which each receiver has perfect channel state information (CSI) and quantizes its channel. The transmitter receives the quantized CSI with a finite number of feedback bits from each receiver. In contrast to zeroforcing (ZF) or block diagonalization (BD) precoding, where the transmitter only requires the channel direction information which refers to the knowledge of subspaces spanned by the users’ channel matrices, for RBD precoding the transmitter additionally requires the channel magnitude information which defines the strength of the eigenmodes of the users’ channel matrices. The key contribution of our work is that we propose a new scheme for the channel quantizati...