Joint Relay and Destination Design for Two-Way MIMO AF Multi-Relay Systems

In this paper, we propose a joint relay and destination optimization design for two-way half-duplex amplify-and-forward (AF) relay systems with multiple relays, each with multiple antennas. By using the sum mean-squared error (MSE) criterion and Wiener filtering principle, the joint relay and destination design is formulated as an optimization problem of the relay precoding matrix under the constraint of total relay transmit power. Then, constructing a virtual point to point MIMO channel and using the singular-value-decomposition (SVD), the optimization problem is simplified to a convex minimization of an upper bound of the sum MSE through a diagonalization process. Finally, a suboptimum scheme is proposed to solve the simplified convex optimization problem. Monte-Carlo simulation shows that the proposed suboptimal scheme gives a better MSE performance than the existing gradient descent algorithm does, and moreover, our method becomes more advantageous when the number of relays or the number of relay antennas increases.