Iterative LMMSE Individual Channel Estimation over Relay Networks with Multiple Transmit and Receive Antennas

In this paper, we investigate the individual channel estimation over the three-node one-way relay network (OWRN), where all nodes are equipped with multiple antennas. We first examine the scenario where the relay node is equipped with single antenna. An iterative linear minimum mean-square-error (LMMSE) method, which has fast convergence speed, is proposed to estimate the individual channels. The closed-form least square (LS) channel estimator is also derived through matrix unitary diagonalization to provide one good initialization point for the iterative LMMSE estimator. To evaluate the performance of the proposed algorithm, we present two performance lower bounds: Bayesian Cramér lower bound (BCRB) and linear estimation lower bound (LELB). Then, the training block and the relay amplification factor are optimized through minimizing the LELB. After that, our studies are extended to the general case where all the nodes are equipped with multiple nodes. Finally, numerical results are provided to corroborate our proposed studies.