On Amplify-and-Forward Relay Networks with Multiple Source-Destination Pairs

The paper considers a scenario where there are multiple single antenna source-destination (S-D) pairs in the network that need to communicate simultaneously. An amplify and-forward relaying scheme is proposed, that employs single relay equipped with multiple antennas, and is implemented in two steps. In the first step the sources transmit simultaneously, while in the second step the relay retransmits the signals that it receives on its antennas after linearly processing them via a beamforming (BF) matrix. The BF matrix is obtained by maximizing the sumrate of all source-destination pairs subject to a total power constraint at the relay. Since the optimal BF design problem is non-convex and hard to solve, a suboptimal zero-forcing beamforming (ZFBF) design approach is proposed. It is shown that with high source power, or high relay power, such a relaying system achieves either the same sumrate as the cut- set bound with ZF receiver/precoder and timing parameter 1/2, or maintains a constant gap from it, which shows the optimality of the proposed scheme in terms of multiplexing gain.