Single-carrier equalization and distributed beamforming for asynchronous two-way relay networks

In this paper, we consider a single-carrier communication scheme, where two transceivers exchange information with the help of multiple relays. The propagation delay in each relaying path is assumed to be different from those of the other paths. As such, the end-to-end channel is frequency selective, and hence, it produces inter-symbol-interference (ISI) at the two transceivers. The simple amplify-and-forward scheme is used at the relays and channel equalization is employed at both transceivers to combat ISI. We minimize the mean square error (MSE) of the total estimated received signals at the both transceivers, subject to a total power budget constraint, by optimizing the channel equalizers, the relay beamforming weights, and the transceivers' powers. We show that our proposed approach leads to a relay selection method which transforms the end-to-end channel into a frequency flat channel. We also present a semi-closed-form solution for the optimal relay beamforming weight.