Training Designs for Amplify-and-Forward Relaying With Spatially Correlated Antennas

This paper proposes an optimal training design for an amplify-and-forward (AF) relay system, in which the source, relay, and destination are all equipped with multiple antennas. Examined is the scenario when spatial correlation exists among the multiple antennas employed at each node. By properly exploiting the correlation information, the training design problem is formulated as a convex optimization problem, which can be efficiently solved with the iterative bisection procedure. A simpler suboptimal design based on minimizing an upper bound on the channel estimation error is also suggested. Simulation results demonstrate the performance advantage of the proposed training designs for the linear minimum mean-squared-error (LMMSE) channel vector estimation over the training design for the LMMSE channel matrix estimation.