Joint Optimization of Transceiver Matrices for MIMO-Aided Multiuser AF Relay Networks: Improving the QoS in the Presence of CSI Errors

This paper addresses the problem of amplify-and-forward (AF) relaying for multiple-input-multiple-output (MIMO) multiuser relay networks, where each source transmits multiple data streams to its corresponding destination with the assistance of multiple relays. Assuming realistic imperfect channel state information (CSI) of all the source-relay and relay-destination links, we propose a robust optimization framework for the joint design of the source transmit precoders (TPCs), relay AF matrices and receive filters. Specifically, two well-known CSI error models are considered, namely, the statistical and the norm-bounded error models. We commence by considering the problem of minimizing the maximum per-stream mean square error (MSE) subject to the source and relay power constraints (min-max problem). Then, the statistically robust and worst-case robust versions of this problem, which take into account the statistical and norm-bounded CSI errors, respectively, are formulated. Both of the resultant optimization problems are nonconvex (semi-infinite in the worst-case robust design). Therefore, algorithmic solutions having proven convergence and tractable complexity are proposed by resorting to the iterative block coordinate update approach along with matrix transformation and convex conic optimization techniques. We then consider the problem of minimizing the maximum per-relay power subject to the quality-of-service (QoS) constraints for each stream and the source power constraints (QoS problem). Specifically, an efficient initial feasibility search algorithm is proposed based on the relationship between the feasibility check and the min-max problems. Our simulation results show that the proposed joint transceiver design is capable of achieving improved robustness against different types of CSI errors when compared with nonrobust approaches.