Network beamforming for asynchronous MIMO two-way relay networks

We consider a single-carrier asynchronous relay network, where two transceivers wish to communicate with the help of multiple multi-antenna relays. In an asynchronous network, the signal transmitted by any of the two transceivers arrives at different relays with significantly different delays. Similarly, the signals forwarded by different relays arrive at the receiver frontend of any of the two transceivers with different delays. In such a network, aiming to minimize the total transmit power consumed in the entire network, we obtain the relay beamforming matrices and the transceivers' transmit powers such that two given date rates at the two transceivers are to be satisfied. We develop a model for the end-to-end channel and use this model to address the network beamforming problem. Assuming symmetric relay beamforming matrices, we present a computationally efficient solution to this problem. The numerical results show that for a given total number of antennas, there is an optimal number of antennas per relays which results in the lowest total power consumption in the entire network.