User Ordering and Subchannel Selection for Power Minimization in MIMO Broadcast Channels using BD-GMD

This paper studies the power minimization problem for the MIMO broadcast channel. The optimal solution involves interference-balancing (IB) and iterative convex optimization procedures. In this paper, the zero-forcing (ZF) problem is considered, with dirty paper coding (DPC), resulting in a simple non-iterative implementation using the block diagonal geometric mean decomposition (BD-GMD). Subchannel selection is applied in order to approach the performance of the optimal IB solution. Optimal and near-optimal solutions are provided to find the encoding order and subchannel selection for each user. The advantages of the methods proposed are their non-iterative nature and much reduced computational complexity. Simulations run on both uncorrelated and correlated channels show that a transmit power close to the optimal IB solution can be reached.