Impact of Limited Feedback on Multiple Relay Zero-Forcing Precoding Systems

In recent literature, it has been shown that in a relaying network utilizing multiple relay precoding, the signal-to- noise ratio (SNR) at each destination node will scale linearly with the number of relays K, which is referred to as the distributed array gain (DAG) K. Different from the prior studies which assume perfect channel state information (CSI) at each of the relay nodes, this work considers the impact of limited feedback on the performance of multiple relay precoding. We show that the conventional limited feedback scheme fails to obtain the DAG K, which is due to the phase ambiguity introduced by the channel quantization function. Based on the analysis, a novel feedback and precoding procedure is proposed. It is proved that the proposed procedure can obtain the DAG K with only one additional feedback bit for quantizing each relay-destination channel compared with the conventional scheme. Simulation results are also provided to verify our analysis.