Jointly optimal pre- and post-channel equalization and network beamforming in asynchronous two-way relay networks

We consider an asynchronous two-way relay network, consisting of two single-antenna transceivers and multiple single-antenna relays, where due to the fact that propagation delays of different transceiver-relay paths are different, inter-symbol-interference (ISI) exists at both transceivers. In this work, pre- and post-channel equalization blocks are used to combat ISI. The mean-squared error of the linearly estimated received signals at both transceivers is minimized under a total transmit power budget by optimally obtaining the transceivers´ transmit powers and the relay beamforming weight vectors as well as pre- and post-channel equalizers at the two transceivers. We prove that our proposed approach results in a certain relay selection scheme. We present the optimal values of design parameters in semi-closed-form solutions.