Asynchronous Two-Way MIMO Relaying: A Multi-Relay Scenario

We consider a single-carrier asynchronous relay network where two transceivers exchange information with the help of multiple multi-antenna relays. The network is assumed to be asynchronous, meaning that the signal transmitted by any of the two transceivers arrives at different relays with different delays and also signals transmitted by different relays arrive at any of the two transceivers with different delays. We further assume that each relay obtains the vector of the relay transmit signals via multiplying the vector of the relay received signals by a beamforming matrix. For such an asynchronous two-way network with multi-antenna relays, our goal is to obtain symmetric relay beamforming matrices and the transceivers' transmit powers such that the total power consumed in the entire network is minimized while guaranteeing given data rates at the two transceivers. To this end, we develop a model for the end-to-end channel and use this model to solve the total power minimization problem. Assuming symmetric relay beamforming matrices, we present a computationally efficient solution to this problem. Our simulation results suggest that for a given total number of antennas, there appears to be an optimal number of antennas per relays which results in the lowest power consumption in the network.