Rate Optimization for Relay Precoding Design with Imperfect CSI in Two-hop MIMO Relay Networks

This paper presents a relay precoding scheme under the imperfect channel state information (CSI) assumption for two-hop amplify-and-forward based MIMO relay networks with one source, one destination and multiple relays. The forward channel mean and covariance available at the relays is assumed to be for the robust design of the linear relay precoder. By using the average mutual information criterion along with a total relay transmitting power constraint, an optimization problem is formulated by assuming the imperfect CSIT (CSI at the transmitter) at the relays. We first derive the approximation of the average mutual information rate, and then simplify the constrained optimization problem into the equivalent problem involving scalar optimization variables. Through an in-depth study of the problem formulation, it is revealed that the objective function is convex only when each optimization variable is larger than a certain threshold, which can be determined mainly by the system configurations and the channel condition. The effectiveness of the proposed relay precoder is validated by Monte-Carlo simulations with comparison to that under perfect CSI assumption.