Robust General Rank Precoding Design for Amplify-and-Forward Relay Network

In this paper, we consider the problem of precoding design for amplify-and-forward (AF) relay network with imperfect channel state information (CSI). We find a general rank precoding matrix at the relay such that the relay transmit power is minimized subject to quality of service (QoS) constraint as the worst case signal-to-noise ratio (SNR) at the destination. Since the direct optimization is nonconvex, we apply conservative methods to reformulate it as a semi-definite programming (SDP) problem which provides the upperbound of the original objective. Specifically, we suggest two SDP formulations that can be solved efficiently via convex optimization tools. We numerically compare the proposed suboptimal methods with the existing method, i.e., collaborative robust relay beamforming (CRBF), and show that the proposed schemes achieve a significant performance gain for a majority of feasible uncertainty sizes.