On the sumrate of amplify-and-forward relay networks with multiple source-destination pairs

The paper considers a network scenario in which multiple source-destination node pairs need to communicate simultaneously. Each source and destination is equipped with one antenna and the communication is assisted by a multi-antenna relay operating in Amplify-and-Forward fashion. The communication occurs in two slots; in the first slot, the sources transmit simultaneously, and in the second slot, the relay retransmits the signals which were received by its antennas during the first slot, after linearly processing them via a Zeroforcing Beamforming (ZFBF) matrix. Two different designs for the ZFBF matrix are proposed. The first design allocates the relay power so that all data streams have the same useful power. The second design adjusts the relay weights for all S-D pairs in a way that maximizes the sumrate. It is shown analytically that, when the source or relay power is high, the proposed sumrate maximization method has the same ergodic sumrate as the cut-set bound with two identical slots and a ZF precoder in the broadcast hop or a ZF equalizer in the multiple access hop, or maintains a constant gap from the cut-set bound with a ZF precoder in the broadcast hop. Although initially perfect channel state information (CSI) is assumed available at the relay, an upper bound of the ergodic sumrate loss caused by relay CSI errors is also derived.