Decentralized beamforming for multi-carrier asynchronous bi-directional relaying networks

We consider an asynchronous two-way relay network, where multiple asynchronous relays cooperate to establish a connection between two transceivers. In such an asynchronous relay network, a certain signal path (originating from one transceiver and going through a certain relay) introduces a propagation and/or relaying delay to the corresponding relayed signal. We assume that such delays are different for different signal paths which correspond to different relays. Based on this model, the end-to-end communication link can be viewed as a multi-path channel, and thus, it can cause inter-symbol-interference (ISI) at the two transceivers when the data rate is sufficiently high. To tackle such an ISI, the two transceivers are herein assumed to employ orthogonal frequency division multiplexing (OFDM) technology. The relays however use amplify-and-forward relaying to materialize a distributed beamforming scheme. For such a communication scheme, we use a max-min fair design approach to optimally obtain the relay beamforming weights and the transceivers´ subcarrier powers such that the smallest subcarrier signal-to-noise ratio (SNR) is maximized under a total power budget. Furthermore, we prove that this approach (which has been shown to equivalent to a SNR balancing scheme) leads to certain relay selection solution. We then present a semi-closed-form solution to obtain the relay beamforming weights and the associated maximum balanced SNR. Simulation results show that the performance of this solution is superior to an equal power allocation approach, where all relays and two transceivers consume the same level of power.