Joint Design of Linear Relay and Destination Processing for Two-Hop MIMO Multi-Relay Networks

This paper presents a joint linear processing scheme for two-hop and half-duplex distributed amplify-and-forward (AF) relaying networks with one source, one destination and multiple relays, each having multiple antennas. Under the perfect CSI (channel state information) assumption, a joint relay and destination design is proposed to minimize the mean-square error (MSE) of the output signal at the destination. By the Wiener filter principle, it is formulated as an optimization problem with respect to the relay precoding matrix under the constraint of a total relay transmit power. And then, the constrained optimization with an objective to design the relaying block-diagonal matrix is simplified to an equivalent problem with scalar optimization variables. Moreover, it is revealed that the scalar-version optimization is convex when the total relay power or the second-hop SNR (signal to noise ratio) is above a certain threshold. The underlying optimization problem, which is non-convex in general, is solved by the complementary geometric programming (CGP). Simulation results show that the proposed scheme outperforms the existing relaying method in the case of relatively large second-hop SNR.