Efficient Power Minimization for MIMO Broadcast Channels with BD-GMD

The problem of downlink power minimization given user rate requirements has been solved optimally in J. Lee and N. Jindal (Jul. 2006), M. Mohseni, et al. (Aug. 2006). However, due to the non-linear nature of the problem, convex optimization techniques have to be used, resulting in a high computational complexity. In this paper, the power minimization problem using dirty paper coding (DPC) is investigated. The SNR is distributed equally among the subchannels of each user to reduce each user's transceiver complexity, through the use of equal-rate modulation. The zero-forcing (ZF)-DPC problem is considered, therefore facilitating a closed form solution and resulting in a simple implementation. The optimum encoding order can be found with limited computations. To further reduce the complexity, a simple suboptimal method for finding the encoding order is given. This method is shown to have a sum power very close to the ZF-optimal power. The advantages of the methods proposed are their non-iterative nature and much reduced computational complexity.