A relay selection approach to bidirectional collaborative communications with imperfect CSI

We herein study the problem of the design of a network beamformer for a two-way relay network, consisting of two transceivers and multiple relays, in the presence of uncertainty in the knowledge of channel coefficients. More specifically, we assume that one of the transceivers (the master transceiver) knows the (near) channel coefficients between itself and the relays but it has only statistical information about the (far) channels between the other transceiver and the relays. We aim to minimize the total transmit power, as perceived by the master transceiver, subject to two probabilistic constraints on the random received SNRs. These constraints ensure that the outage probabilities of the transceivers´ received SNRs are less than given thresholds. We prove rigourously that this approach leads to a relay selection scheme where the master transceiver should select the relay with the best near channel link.