Robust far-end channel estimation design for MIMO relay systems

In this paper, we propose a robust far-end channel estimation for a multiple-input multiple-output (MIMO) relay system, where channel estimation is accomplished in two phases. In the first phase, the relay-to-destination channel is estimated. In the second phase, the destination estimate the far-end channel, i.e., the source-to-relay link, based on the source pilots, relay precoder, and the estimated channel in the first phase. This work aims to conduct a robust design by deriving the optimum source pilots and relay precoder according to the minimum mean-squared error (MMSE) criterion. Although the optimization problem can be formulated mathematically; however, the problem is not convex and difficult to be solved. Thus, we replace the objective function with its lower bound, and simplify the matrix optimization problem as a scalar-convex optimization. We show that the optimum solution of the optimization with the lower bound equals to that of the original problem when the channel correlation matrices satisfy certain structures. Simulations show that our proposed method outperforms existing non-robust methods.