Selective Mapping for channel inversion precoding in multiple-antenna broadcast systems

In this paper, a new Selective Mapping (SLM) technique is introduced for a Multiple-Input Multiple-Output (MIMO) broadcast (or MIMO point-to-point) system with channel inversion. We present a unified framework which links the problem of minimizing the average transmit energy from the constellation point of view, to the sum-rate maximization problem from the capacity viewpoint. First, we consider the point-to-point setup and derive the average transmit energy that can asymptotically be achieved by the proposed SLM technique. It is established that SLM achieves the minimum theoretical average transmit energy achievable by constellation shaping. Then, using the same idea, the average transmit energy in a broadcast system is derived and the relation between this value and the transmission rate is established. Finally, it is shown that the proposed SLM method can achieve the sum-capacity of the MIMO broadcast (or capacity of a MIMO point-to-point) channel at high SNR values.