Power-Optimal Distributed Beamforming for Multi-Carrier Asynchronous Bidirectional Relay Networks

We consider the problem of joint power allocation and distributed beamforming design for asynchronous two-way multi-relay networks, where two transceivers rely on an orthogonal frequency division multiplexing (OFDM) scheme to exchange information through multiple amplify-and-forward relay nodes. The network is assumed to be asynchronous in the sense that different relaying paths are subject to different propagation delays. This assumption renders the end-to-end channel between the two transceivers frequency-selective. The impulse response of such a channel can be modeled as a finite impulse response (FIR) system with multiple taps. We present a simple semi-closed-form solution for the problem of minimization of the total transmission power consumed in such networks subject to two quality of service constraints on the transceivers rates. We show that at the optimum, the end-to-end channel must be frequency-flat, which means only one tap of the end-to-end channel impulse response is non-zero. As a result, our semi-closed-form solution leads to a relay selection scheme, in which only those relays associated with the non-zero tap of the end-to-end channel impulse response are switched on, and the rest of the relays are kept off. The simulation results demonstrate that using the proposed semi-closed-form algorithm significantly outperforms the traditional best relay selection method.