Robust linear beamforming for MIMO relay with imperfect Channel State Information

In this paper the linear beamforming design of a point to point relay system having multiple antennas at the transmitter, the relay and the receive side is addressed. The Channel State Information (CSI) is assumed to be perfectly known for the link from the source to the relay station. However, it is assumed that CSI from the relay station to the destination is imperfectly known. This uncertainty is described using stochastic and deterministic models known as Stochastic Error (SE) and Norm Bounded Error (NBE) models. The problem formulation is based on the Mean Square Error (MSE) of the signal at both ends of the transmission channel. This problem is constrained to satisfy the transmit power limitation of the relay station. It is shown that both the MSE of the system and the transmit power have a Second Order Cone (SOC) structure. The design problem for the SE model, is recast as a Second Order Cone Program (SOCP) while for the NBE model, the same design problem is a Semidefinite Program (SDP). Using the SE model, the average performance and using the NBE model, the worst-case related performance measure is guaranteed. Both problems are solved numerically and simulation results are provided.