Multi-Carrier Asynchronous Bi-Directional Relay Networks: Joint Subcarrier Power Allocation and Network Beamforming

We consider an asynchronous bi-directional relay network, consisting of two single-antenna transceivers and multiple single-antenna relays, where the transceiver-relay paths are subject to different relaying and/or propagation delays. Such a network can be viewed as a multipath channel which can cause inter-symbol-interference (ISI) in the signals received by the two transceivers. Hence, we model such a communication scheme as a frequency selective multipath channel which produces ISI at the two transceivers, when the data rates are high. To tackle ISI, the transceivers can employ an orthogonal frequency division multiplexing (OFDM) scheme to diagonalize the end-to-end channel. The relays use simple amplify-and-forward relaying, thereby materializing a distributed beamformer. For such a scheme, we propose two different algorithms, based on the max-min fair design approach, to calculate the subcarrier power loading at the transceivers as well as the relay beamforming weights. We develop computationally efficient solutions to these two approaches. Simulation results are presented to show that our proposed schemes outperform equal or maximum power allocation schemes.