MIMO Precoder Selections in Decode-Forward Relay Networks with Finite Feedback

We consider a system with precoding in the half duplex Decode-Forward (DF) relay networks, where multiple antennas are adopted at the source, the destination and the relay. Based on the channel state information (CSI), a few feedback bits are fed back from the destination to the source and the relay to select the source and the relay precoders. A suboptimal precoder selection criterion for the symbol vector error minimization and an optimal precoder selection criterion for the capacity maximization are proposed for the practical situation where relays are placed between the source and the destination. We analyze the diversity performance of the criteria and show that the full diversity is achieved when the rank one precoder sets span the vector channel space formed by the transmit antennas of the source and the those of the relay.