Block triangularization: A new linear precoding strategy for Gaussian MIMO BC

Finding an optimal linear precoding transmission strategy still remains an open problem, since it cannot be transformed to a convex problem. In this paper, we introduce some condition under which a duality of the rate regions of MMO broadcast channel (BC) and MIMO multiple-access channel (MAC) with linear precoding is established. In particular, we convert the non-convex and untractable sum rate optimization problem at hand to a well-structured dual problem like the dirty-paper coding (DPC) strategy. We provide sum-rate analysis of the proposed linear precoding strategy, referred to as block triangularization (BT), and address its optimality at high SNR. Specifically, we show that not only BT, but also the more familiar block diagonalization (BD) strategy is asymptotically optimal at high SNR. However, BT is shown to be always at least as good as BD over the entire SNR range. A sum-rate optimal solution at any SNR for the proposed BT strategy is also found.