Generalized Beamforming Design for Cooperative MIMO Multirelay Networks with Infinite Constraints and Imperfect CSI

A generalized base station-relay-user equipment (BS-Relay-UE) beamforming design is investigated for a cooperative multiple-input multiple-output (MIMO) multirelay networks with imperfect channel state information (CSI). In order to minimize the worst-case mean square error (MSE) which is subject to a semi-infinite (SI) relay power constraints, a generalized optimal beamforming structure for the relay amplifying matrix is effectively proposed, and then the SI relay power constraints are converted into linear matrix inequalities (LMIs) version. In such conversion, the objective problem recasts as a decoupled biconvex semidefinite programming (SDP) one which can be efficiently solved by the proposed alternating algorithm. The system performance has been verified in terms of worst-case MSE using a set of qualitative analyses. The results show us that the proposed beamforming method outperforms the conventional schemes and can also effectively reduce the computational complexity when it is compared to the cutting-set schemes and also to the nonrobust ones.