Joint Power Allocation and Distributed Beamforming Design for Multi-Carrier Asynchronous Two-Way Relay Networks

A novel semi-closed-form solution is proposed to the joint problem of distributed beamforming and power allocation design for multi-carrier asynchronous two-way networks. The network is composed of two multi-carrier transceivers and multiple single-antenna amplify-and-forward relay nodes which enable the transmissions between the transceivers. We assume an asynchronous transmission scheme in which relay-transceiver paths are subject to different propagation delays. The immediate impact of such asynchronous transmission scheme at high data-rates is that the otherwise flat-fading end-to-end channel turns into a frequency-selective channel, which causes inter-symbol-interference at the two transceivers. The two transceivers are equipped with an orthogonal division multiplexing technology to eliminate the resultant inter-symbol-interference. We formulate a total transmit power minimization subject to two quality of service constraints measured by the sum-rates at the transceivers. We show that at the optimum, the end-to-end channel becomes frequency-flat, and thus, we can obtain a semi-closed-form solution for our problem by solving the problem for each tap of the end-to-end channel impulse response. Our solution leads to a relay selection scheme in which only those relays contributing to the optimum tap of the end-to-end channel impulse response are kept active while the rest of the relays must be switched off. The simulation results show that the proposed semi-closed form algorithm significantly outperforms the traditional relay selection method which chooses a relay that leads to a minimal power consumption in the network.