Channel Estimation and Optimal Training Design for Amplify and Forward MIMO Relay Channel under Spatial Fading Correlation

In this paper, we study the channel estimation problem for time division multiplex amplify-and-forward (AF) relay channels. Both the source and the destination and also the in-between relay node comprise multiple antennas, and there are spatial fading correlations in each hop. We first derive a linear minimum mean square error (LMMSE) channel estimator from a simple scenario where there are no correlations among the relay antennas to a more general scenario where the multiple relay antennas are also spatially correlated. And then we design the optimal training sequences by minimizing the mean square error (MSE). Also the impacts of spatial correlations, relay power gain and the number of relay antennas on the MSE are studied to some extent. It is proved that the channel estimation and optimal training sequences have nothing to do with the spatial correlation at the destination and the derived estimator and designed sequences can be directly extended to multi-hop relay channels. Simulations are conducted to corroborate the proposed studies.