Joint LMMSE and MAP channel estimation using BCRLB training signals for correlated two-way MIMO relay systems

In this paper, we propose a two-stage channel estimation scheme for two-way MIMO relay systems with a single relay antenna. We assume the training process is performed under correlated Rayleigh fading channels. At the first stage, the backward channel is estimated by using linear minimum mean square estimator (LMMSE). Based on the backward channel estimator, we propose a novel forward channel estimation scheme by using asymptotic maximum a posterior (MAP) method. Since Bayesian Cramér-rao Lower Bound (BCRLB) is more amenable to handle and has been widely used in practice, we seek BCRLB based on asymptotic likelihood function as the criterion for training signal design. Finally, the numerical results show that the proposed training signal can improve the MSE performance.