Convex Precoding for Vector Channels in High Dimensions

We analyze a non-linear vector preceding technique for MIMO channels in high dimensions. Channel inversion is carried out at the transmitter with the aim of minimizing signal processing at the receiver. In order to contain the transmission power, symbol constellations are extended onto the complex plane using convex alphabets. We compare the case where full channel inversion is possible at the transmitter (more transmitting elements than receiving elements), and the converse case where only partial channel inversion is possible and matched filter detection is required at the receiver. We show that, in some cases, it might be advantageous to turn off some receiving elements in order to contain the transmitted energy per bit. We also propose the use of two novel 8PSK modulation schemes.