Real vs. complex BPSK precoding for MIMO broadcast channels

Recently Muller et al. (IEEE J. Select. Areas Commun. 2008) used asymptotic methods from statistical physics to analyze non-linear vector precoding for MIMO broadcast channels. They proposed to extend BPSK input alphabets onto both real and complex supersets of the original constellation points. They showed that, as the optimization space is greater, lower energies are achieved when the extended alphabets are complex. In this work we use similar asymptotic methods and propose an alternative channel inversion technique which makes purely real alphabets perform as well as their complex extensions, which results in reduced complexity in the optimization process.