Probabilistic Behavior of Average Transmit Energy in Broadcast Systems with Precoding

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Abstract— In this paper, we introduce a shaping concept to reduce average transmit energy for channel inversion techniques in multiple antenna broadcast systems. Based on the probabilistic view point for the input constellations, the optimal probability distribution for the data vectors in the channel inversion techniques is found. We have also introduced a theoretical Selective Mapping (SLM) technique (based on random coding arguments) in channel inversion techniques to reduce the transmit average energy. The asymptotic gain that the SLM technique can provide is derived. The proposed technique results in a significant saving in energy as the corresponding shaping gain can be much higher than the upper bound of 1.53, known for the conventional shaping. The exact gain depends on the orthogonality defect of the channel.