Optimum beamforming in the broadcasting phase of bidirectional cooperative communication with multiple decode-and-forward relays

This letter focuses on the broadcasting phase of bidirectional cooperative networks with multiple decode-and-forward relays. In this phase, the relays first combine the information-bearing symbols transmitted by the sources, and then broadcast them back to the sources in order to achieve bidirectional communications. Two different combining methods at the relays are considered. The first one is that the relays transmit linear combinations of the information-bearing symbols to the sources by beamforming. We develop an algorithm that can compute the optimum beamforming vector in closed form and this beamforming vector minimizes the outage probability of the bidirectional cooperative network. The second method is that the relays combine the information-bearing symbols by exclusive-or and then transmit them to the sources by beamforming. For this case, we show that the instantaneous signal-to-noise ratios at the sources depend on the values of the information-bearing symbols. Based on, the optimum beamforming vector is computed and it minimizes an upper bound of the outage probability of the bidirectional cooperative network.