Sum MSE Uplink-Downlink Duality of Multiuser Amplify-and-Forward MIMO Relay Systems

In this paper, we consider a two-hop multiuser amplify-and-forward MIMO relay system with multi-antenna nodes. By taking the antenna correlation and channel estimation error into account, the problems of minimum sum mean square error (MSE) transceiver optimization for the uplink and the dual downlink are formulated. When the direction of transmission is reversed and the total power constraints of the source and the relay are switched, an uplink-downlink duality in terms of average sum MSE region is established based on the Karush-Kuhn-Tucker (KKT) conditions of both problems. As a consequence of this duality, the downlink transceiver optimization satisfying the KKT conditions can be solved by focusing on an equivalent uplink problem, and vice versa. Simulation results are provided to demonstrate our analysis.