Maximum Eigenmode Relaying with statistical Channel State Information at the Relay

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Optimal precoding in the relay is investigated to maximize ergodic capacity of a multiple antenna relay channel. The source and the relay nodes are equipped with multiple antennas and the destination with a single antenna. It is assumed that the channel covariance matrices of the relay's receive and transmit channels are available to the relay, and optimal precoding at the relay is investigated. It is shown that the optimal transmission from the relay should be conducted in the direction of the eigenvectors of the transmit-channel covariance matrix. Then, we derive the necessary and sufficient conditions under which the relay transmission only from the strongest eigenvector achieves capacity; this method is called Maximum Eigenmode Relaying (MER).