  In this paper, we investigate the minimum average transmit energy that can be
obtained in multiple antenna broadcast systems with channel inversion
technique. The achievable gain can be significantly higher than the
conventional gains that are mentioned in methods like perturbation technique of
Peel, et al. In order to obtain this gain, we introduce a Selective Mapping
(SLM) technique (based on random coding arguments). We propose to implement the
SLM method by using nested lattice codes in a trellis precoding framework.
